diff --git a/SNA/presentation/sna.Rmd b/SNA/presentation/sna.Rmd
new file mode 100644
index 0000000..a2b10d2
--- /dev/null
+++ b/SNA/presentation/sna.Rmd
@@ -0,0 +1,66 @@
+---
+title: "Social Network Analysis"
+author:
+ name: Sebnem Er
+ affiliation: University of Cape Town | Statistical Sciences Department
+ # email: sebnem.er@uct.ac.za
+date: Lecture 1 #"`r format(Sys.time(), '%d %B %Y')`"
+output:
+ html_document:
+ theme: flatly
+ highlight: haddock
+ # code_folding: show
+ toc: yes
+ toc_depth: 4
+ toc_float: yes
+ keep_md: true
+---
+
+title: "R Notebook"
+output: html_notebook
+
+```{r setup, include=FALSE}
+knitr::opts_chunk$set(echo = TRUE, cache = TRUE, dpi=300)
+```
+
+This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code.
+
+Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Ctrl+Shift+Enter*.
+
+```{r}
+plot(cars)
+```
+
+Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Ctrl+Alt+I*.
+
+When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the *Preview* button or press *Ctrl+Shift+K* to preview the HTML file).
+
+The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike *Knit*, *Preview* does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.
+
+## Requirements
+
+### External libraries (requirements vary by OS)
+
+We're going to be doing all our spatial analysis and plotting today in R. Behind the scenes, R provides bindings to powerful open-source GIS libraries. These include the [Geospatial Data Abstraction Library (GDAL)](http://www.gdal.org/) and [Interface to Geometry Engine Open Source (GEOS)](https://trac.osgeo.org/geos/) API suite, as well as access to projection and transformation operations from the [PROJ.4 library](https://proj4.org/about.html). You needn't worry about all this, but for the fact that you *may* need to install some of these external libraries first. The requirements vary by OS:
+
+- **Linux:** Requirements vary by distribution. See [here](https://github.com/r-spatial/sf#linux).
+- **Mac:** You should be fine to proceed directly to the R packages installation below. An unlikely exception is if you've configured R to install packages from source; in which case see [here](https://github.com/r-spatial/sf#macos).
+- **Windows:** Same as Mac, you should be good to go unless you're installing from source. In which case, see [here](https://github.com/r-spatial/sf#windows).
+
+### R packages
+
+- **New:** `sf`, `lwgeom`, `maps`, `mapdata`, `spData`, `tigris`, `tidycensus`, `leaflet`, `tmap`, `tmaptools`
+- **Already used:** `tidyverse`, `hrbrthemes`
+
+Note that you'll need `ggplot2` version 3.0.0 or above for the required [plotting support](https://www.tidyverse.org/articles/2018/07/ggplot2-3-0-0/) of `sf` objects. That's almost certainly the case, but now is a good time to upgrade you existing packages if you haven't done that for a while.
+
+Okay, let's install (if necessary) and load everything. As per usual, I'll also set my preferred plotting theme, but this is unnecessary.
+
+```{r, cache=F, message=F}
+if (!require("pacman")) install.packages("pacman")
+pacman::p_load(sf, tidyverse, hrbrthemes, lwgeom, rnaturalearth, maps, mapdata, spData, tigris, tidycensus, leaflet, tmap, tmaptools)
+theme_set(hrbrthemes::theme_ipsum())
+```
+
+
+### Census API key
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diff --git a/SNA/snapresentation.Rpres b/SNA/snapresentation.Rpres
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+
+
+Social Network Analysis
+========================================================
+author: Sebnem Er
+date:
+autosize: true
+
+
+Structure of the Workshop
+========================================================
+
+
What is social network analysis?
+
+
foundational concepts of social networks: graph theory
+
+
Types of social network analysis.
+
+
visualization of social networks,
+
descriptive analysis of social networks,
+
statistical network models.
+
+
Network data: collection and applications in South Africa.
+
Packages.
+
+
+-
+
+Simple example - Edge list with no information
+========================================================
+
+```{r}
+library(igraph)
+# example in data frame
+a=c("A","A","A","A","A","E","F")
+b=c("B","C","D","E","F","F","G")
+df = cbind(a,b)
+df = as.data.frame(df)
+df
+```
+
+Slide With Plot
+========================================================
+
+```{r, echo=FALSE}
+g = graph.edgelist(as.matrix(df),directed = FALSE)
+get.adjacency(g)
+```
+
+Slide With Plot
+========================================================
+
+```{r, echo=FALSE}
+plot(g)
+```
diff --git a/SNA/snapresentation.html b/SNA/snapresentation.html
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+++ b/SNA/snapresentation.html
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+
+
+
+
+
+ snapresentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
A genetic algorithm approach to determine stratum boundaries and sample sizes of each stratum in stratified sampling
+
+
Description
+
+
This is a package for Genetic Algorithm approach for the determination of the stratum boundaries and sample sizes in each stratum in stratified sampling.
Since the package is not in CRAN package repository yet, these steps should be followed in order to use the package:
+
The file can be saved as a zip document.
+Then after extracting the zip file into your R library where R is downloaded, the R package is ready to use in Windows.
+The R library is something like this in my computer:
+
By just typing the name of the data, and defining the following arguments,
+you can obtain the boundaries and sample sizes to be drawn from each stratum with Genetic Algorithm developed by Keskinturk and Er (2007) given a sampling allocation scheme.
+The sampling allocation scheme could be either "Equal", "Proportional", "Neyman" or "GA" sampling allocation scheme.
+
+
Arguments
+
+
+
dataName
+
+Any type of numeric data containing the values of a univariate stratification variable.
+
numberOfStrata
+
+An integer: The number of strata.
+
sampleSize
+
+An integer: The number total sample size.
+
iteration
+
+An integer: The number of iterations in Genetic Algorithm process.
+
GAgenerationSize
+
+An integer: The number of generations in Genetic Algorithm process.
+
mutationRate
+
+A numeric: The mutation rate in Genetic Algorithm process. Mutation rate must be in between 0 and 1, inclusive. Small levels of mutation rate is preferable in Genetic Algorithms.
+
sampleAllocation
+
+A string: sampleAllocation defines the type sample allocation method, which are "Equal", "Proportional", "Neyman" and "GA".
+
+
+
+
Note
+
+
+This study is part of a project supported by the Scientific and Technological Research Council of Turkey (TUBITAK).
+
+
+
References
+Timur Keskinturk, Sebnem Er, "A Genetic Algorithm Approach To Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling"
+Computational Statistics and Data Analysis, Vol. 52, Issue 1, 15 September 2007, s.53-67.
+
+Timur Keskintürk, Şebnem Er, “A Genetic Algorithm Approach To Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling”,
+Computational Statistics and Data Analysis, Vol. 52, Issue 1, 15 September 2007, s.53-67.
+
+
Examples
+
+
+data(beta10_3)
+
+
+
[]
+
diff --git a/english/GA4Stratification/dataHTML/chi1.html b/english/GA4Stratification/dataHTML/chi1.html
new file mode 100644
index 0000000..e60f585
--- /dev/null
+++ b/english/GA4Stratification/dataHTML/chi1.html
@@ -0,0 +1,52 @@
+
+
+
+R: A randomly generated data
+
+
+
+
+
chi1 {}
R Documentation
+
+
A randomly generated data
+
+
+
Description
+
+
Chi1 is a randomly generated data from Chisquare
+distribution with 1 degrees of freedom.
+
+
+
Usage
+
+
data(chi1)
+
+
+
Format
+
+
+A data frame with 1000 observations on the following variable.
+
+
+Timur Keskintürk, Şebnem Er, “A Genetic Algorithm Approach To Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling”,
+Computational Statistics and Data Analysis, Vol. 52, Issue 1, 15 September 2007, s.53-67.
+
+
Examples
+
+
+data(chi1)
+
+
+
[]
+
diff --git a/english/GA4Stratification/dataHTML/chi10.html b/english/GA4Stratification/dataHTML/chi10.html
new file mode 100644
index 0000000..97f47ec
--- /dev/null
+++ b/english/GA4Stratification/dataHTML/chi10.html
@@ -0,0 +1,52 @@
+
+
+
+R: A randomly generated data
+
+
+
+
+
chi10 {}
R Documentation
+
+
A randomly generated data
+
+
+
Description
+
+
Chi10 is a randomly generated data from Chisquare
+distribution with 10 degrees of freedom.
+
+
+
Usage
+
+
data(chi10)
+
+
+
Format
+
+
+A data frame with 1000 observations on the following variable.
+
+
+Timur Keskintürk, Şebnem Er, “A Genetic Algorithm Approach To Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling”,
+Computational Statistics and Data Analysis, Vol. 52, Issue 1, 15 September 2007, s.53-67.
+
+
Examples
+
+
+data(chi10)
+
+
+
[]
+
diff --git a/english/GA4Stratification/dataHTML/chi15.html b/english/GA4Stratification/dataHTML/chi15.html
new file mode 100644
index 0000000..35664ea
--- /dev/null
+++ b/english/GA4Stratification/dataHTML/chi15.html
@@ -0,0 +1,52 @@
+
+
+
+R: A randomly generated data
+
+
+
+
+
chi15 {}
R Documentation
+
+
A randomly generated data
+
+
+
Description
+
+
Chi15 is a randomly generated data from Chisquare
+distribution with 15 degrees of freedom.
+
+
+
Usage
+
+
data(chi15)
+
+
+
Format
+
+
+A data frame with 1000 observations on the following variable.
+
+
+Timur Keskintürk, Şebnem Er, “A Genetic Algorithm Approach To Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling”,
+Computational Statistics and Data Analysis, Vol. 52, Issue 1, 15 September 2007, s.53-67.
+
+
Examples
+
+
+data(chi15)
+
+
+
[]
+
diff --git a/english/GA4Stratification/dataHTML/chi5.html b/english/GA4Stratification/dataHTML/chi5.html
new file mode 100644
index 0000000..a32e227
--- /dev/null
+++ b/english/GA4Stratification/dataHTML/chi5.html
@@ -0,0 +1,52 @@
+
+
+
+R: A randomly generated data
+
+
+
+
+
chi5 {}
R Documentation
+
+
A randomly generated data
+
+
+
Description
+
+
Chi5 is a randomly generated data from Chisquare
+distribution with 5 degrees of freedom.
+
+
+
Usage
+
+
data(chi5)
+
+
+
Format
+
+
+A data frame with 1000 observations on the following variable.
+
+
+Timur Keskintürk, Şebnem Er, “A Genetic Algorithm Approach To Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling”,
+Computational Statistics and Data Analysis, Vol. 52, Issue 1, 15 September 2007, s.53-67.
+
+
Examples
+
+
+data(chi5)
+
+
+
[]
+
diff --git a/english/GA4Stratification/dataHTML/g b/english/GA4Stratification/dataHTML/g
new file mode 100644
index 0000000..8b13789
--- /dev/null
+++ b/english/GA4Stratification/dataHTML/g
@@ -0,0 +1 @@
+
diff --git a/english/GA4Stratification/dataHTML/iso2004.html b/english/GA4Stratification/dataHTML/iso2004.html
new file mode 100644
index 0000000..5d81a16
--- /dev/null
+++ b/english/GA4Stratification/dataHTML/iso2004.html
@@ -0,0 +1,56 @@
+
+
+
+R: Net sales data of 487 Turkish manufacturing firms
+
+
+
+
+
iso2004 {}
R Documentation
+
+
Net sales data of 487 Turkish manufacturing firms
+
+
+
Description
+
+
Net sales data of 487 Turkish manufacturing firms from the first 500 largest corporations belonging to the Istanbul Chamber of Industry
+ICI in year 2004
+
+
+
Usage
+
+
data(iso2004)
+
+
+
Format
+
+
+A data frame with 487 observations on the following variable.
+
+
+Timur Keskintürk, Şebnem Er, “A Genetic Algorithm Approach To Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling”,
+Computational Statistics and Data Analysis, Vol. 52, Issue 1, 15 September 2007, s.53-67.
+
+
Examples
+
+
+data(iso2004)
+
+
+
[]
+
diff --git a/english/GA4Stratification/dataHTML/normal100_10.html b/english/GA4Stratification/dataHTML/normal100_10.html
new file mode 100644
index 0000000..185eb39
--- /dev/null
+++ b/english/GA4Stratification/dataHTML/normal100_10.html
@@ -0,0 +1,52 @@
+
+
+
+R: A randomly generated data
+
+
+
+
+
normal100_10 {}
R Documentation
+
+
A randomly generated data
+
+
+
Description
+
+
normal100_10is a randomly generated data from normal
+distribution with mean 100 and standart deviation 10.
+
+
+
Usage
+
+
data(normal100_10)
+
+
+
Format
+
+
+A data frame with 1000 observations on the following variable.
+
+
+Timur Keskinturk, Şebnem Er, “A Genetic Algorithm Approach To Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling”,
+Computational Statistics and Data Analysis, Vol. 52, Issue 1, 15 September 2007, s.53-67.
+
+
Examples
+
+
+data(normal100_10)
+
+
+
[]
+
diff --git a/english/GA4Stratification/functions/randomnumGenerator.html b/english/GA4Stratification/functions/randomnumGenerator.html
new file mode 100644
index 0000000..4c1d748
--- /dev/null
+++ b/english/GA4Stratification/functions/randomnumGenerator.html
@@ -0,0 +1,97 @@
+
+
+
+
+R: Random number generator
+
+
+
+
+
randomnumGenerator {}
R Documentation
+
+
Random number generator
+
+
+
Description
+
+
This function generates random variables that don't repeat in a given range
Honours Applied Spatial Data Analysis 2020 - Spatial Point and Lattice Data Analysis"ASDA", University of Cape Town.
+
+
+
+
+
+
+
+
diff --git a/english/courses/20100929Lab1.txt b/english/courses/20100929Lab1.txt
new file mode 100644
index 0000000..3400285
--- /dev/null
+++ b/english/courses/20100929Lab1.txt
@@ -0,0 +1,270 @@
+# Title: Probability and Statistics
+# Module Code: CA266
+# Jane M Horgan
+
+
+# R IS CASE SENSITIVE: Help or HELP or even help are all different.
+
+# R is also a calculator
+
+6+7*3/2
+
+x = 1:4
+x
+
+x2 = x**2
+x2
+
+x = 10
+prod1 = x*x
+prod1
+
+# Objects: The entities that R creates and manipulates, # e.g. variables,arrays,strings, functions.
+# Workspace: All objects created in R are stored in workspace
+
+setwd("C:\\Documents and Settings\\SamsungXP\\Belgelerim")
+
+# or equivalently
+
+setwd("C:/Documents and Settings/SamsungXP/Belgelerim")
+
+# in order to see which directory is assigned:
+
+getwd()
+
+
+# Getting Help
+# click the Help button on the toolbar.
+
+help()
+help.start()
+
+help(mean)
+
+# is the same with
+
+?mean
+
+demo()
+?read.table
+help.search ("data.entry")
+apropos (boxplot}
+
+"boxplot", "boxplot.default", "boxplot.stat
+
+# Data Entry and Summary
+# Entering data from the screen to a vector
+
+downtime =c(0, 1, 2, 12, 12, 14, 18, 21, 21, 23,
+24,25,28,29,30,30,30,33,36,44,45,47,51)
+
+# you may need to write an array
+
+sebnem=array(c(1,2,3,4,5,6),dim=c(3,2))
+
+mean(downtime)
+median(downtime)
+range(downtime)
+sd(downtime)
+
+# Data Entry
+# Entering data from a file to a data frame
+
+
+results =read.table ("G:/data/results.txt" , header = T)
+
+# if you don't want to write the directory each time
+# you can specify a folder in a specific directory
+# and assign this directory as your work place
+
+setwd("C:/Documents and Settings/SamsungXP/Belgelerim")
+
+
+# in order to see which directory is assigned:
+
+getwd()
+
+results=read.table(results.txt, header=T)
+
+# You would get an error because the file name must be always written in quotes:
+
+results=read.table("results.txt", header=T)
+results
+
+results$arch1[5]
+
+# Alternatively
+
+attach(results)
+names(results)
+
+#allows you to access without prefix results.
+
+arch1[5]
+
+# Missing Values
+
+mean(arch1)
+
+# No result because some marks are missing.
+
+# na.rm = T (not available, remove)
+
+or
+
+# na.rm = TRUE
+
+mean(arch1, na.rm = T)
+mean(prog1, na.rm = T)
+mean(arch2, na.rm = T)
+mean(prog2, na.rm = T)
+
+mean(results, na.rm = T)
+
+# Obviously there is no point in getting the mean of "gender", therefore you can specify the columns of the variables that you can actually get the mean for.
+
+mean(results[,2:5], na.rm = T)
+
+median(arch1, na.rm=T)
+median(prog1, na.rm=T)
+median(arch2, na.rm=T)
+median(prog2, na.rm=T)
+
+
+rangeComp = max(arch1, na.rm=T)-min(arch1, na.rm=T)
+rangeEcon= max(prog1, na.rm=T)-min(prog1, na.rm=T)
+rangeAnal =max(arch2, na.rm=T)-min(arch2, na.rm=T)
+rangeLinA=max(prog2, na.rm=T)-min(prog2, na.rm=T)
+
+rangeComp
+rangeEcon
+rangeAnal
+rangeLinA
+
+# or equivalently
+
+
+range(arch1,na.rm=T)
+range(prog1,na.rm=T)
+range(arch2,na.rm=T)
+range(prog2,na.rm=T)
+
+sd(results, na.rm=T)
+
+quantile(arch1, na.rm=T)
+quantile(prog1, na.rm=T)
+quantile(arch2, na.rm=T)
+quantile(prog2, na.rm=T)
+
+# Deciles
+
+deciles <-seq(0,1,0.1)
+deciles
+quantile(arch1, deciles,na.rm=T)
+
+# Percentiles
+
+percentiles <-seq(0,1,0.01)
+percentiles
+quantile(arch1, percentiles,na.rm=T)
+
+summary(results,na.rm=T)
+
+summary(arch1,na.rm=T)
+summary(prog1,na.rm=T)
+summary(arch2,na.rm=T)
+summary(prog2,na.rm=T)
+
+summary(downtime)
+
+# Graphical Displays: Boxplots
+
+boxplot(downtime)
+
+boxplot(downtime,xlab = "downtime",ylab = "minutes")
+
+# Graphical Displays: Multiple Boxplots
+
+boxplot(arch1, arch2,xlab="Architecture Semesters 1, and 2")
+
+# Graphical Displays: Multiple Boxplots
+
+boxplot(arch1~gender, xlab = "gender", ylab = "Marks (%)",main = "Architecture Semester 1")
+
+# par function
+
+par (mfrow = c(2,2))
+
+boxplot (arch1~gender, main = "Architecture Semester 1")
+boxplot(arch2~gender, main = "Architecture Semester 2")
+boxplot(prog1~gender, main = "Probability Semester 1")
+boxplot(prog2~gender, main = "Probability Semester 2")
+
+par (mfrow = c(1,1)) restores full screen.
+
+# Histograms
+
+hist(arch1, breaks = 5,xlab ="Marks(%)",ylab = "Number of students",
+main = "Architecture Semester 1")
+
+hist(prog1, "breaks = 5",xlab ="marks(%)",ylab = "Number of Students",
+main = "Architecture Semester 1")
+
+bins <-c(0,40,60,80,100)
+hist(arch1, breaks=bins)
+
+par (mfrow = c(2,2))
+
+hist(arch1, xlab = "Architecture",main = " Semester 1", ylim = c(0, 35))
+hist(arch2, xlab = "Architecture",main = " Semester 2", ylim = c(0, 35))
+hist(prog1, xlab = "Programming",main = " ", ylim = c(0, 35))
+hist(prog2, xlab = "Programming",main = " ", ylim = c(0, 35))
+
+# Stem and Leaf
+
+stem(downtime, scale = 2)
+
+stem(prog1)
+
+# Scatter Plots
+
+plot(prog1, prog2,xlab = "Programming, Semester 1",
+ylab = "Programming, Semester 2")
+
+# Pairs
+
+pairs(results[2:5])
+
+# First read the data into separate vectors:
+x1=c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5)
+y1=c(8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68)
+x2=c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5)
+y2=c(9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74)
+x3=c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5)
+y3=c(7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42,5.73)
+x4=c(8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8)
+y4=c(6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91,6.89)
+
+# Calculate the means
+mean (data.frame(x1, x2, x3, x4))
+
+mean (data.frame(y1, y2, y3, y4))
+
+# the standard deviations:
+
+sd(data.frame(x1, x2, x3, x4))
+
+sd(data.frame(y1, y2, y3, y4))
+
+# Everything seems the same! But when we plot
+
+par(mfrow = c(2, 2))
+plot(x1,y1, xlim=c(0, 20), ylim =c(0, 13))
+plot(x2,y2, xlim=c(0, 20), ylim =c(0, 13))
+plot(x3,y3, xlim=c(0, 20), ylim =c(0, 13))
+plot(x4,y4, xlim=c(0, 20), ylim =c(0, 13))
+
+# Everything seems different!
+
+
+# ctrl+L clears the screen....
\ No newline at end of file
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@@ -0,0 +1,48 @@
+Q1,Q2,Q3,Q4,Q5,Q6,Q7,Q8,Q9,Q10,Q11,Q12,Q13,Q13a,Q13b,Q13c,Q13d,Q14,Q14a,Q14b,Q15a,Q15b,Q16,Q17,Q17y,Q18,Q18y,Q19,Q19y
+1,167.64,60,1,1,0,1,15.2,37.6,35,1,2,2,,,,,2,,,NA,,2,2,,2,,1,10
+1,178,90,2,5,120,4,0.25,20,25,3,2,1,12,300,1500,1,1,15,9,NA,,NA,1,2,1,40,1,10
+1,177.8,72.55,1,1,50,3,2,15,70,1,2,1,16,360,1200,1,1,24,10,3,2,2,1,17,1,26,2,
+1,174,73,1,1,0,4,2,0,10,1,2,2,,,,,2,,,1,2,3,2,,1,12,2,
+1,176,64.5,1,5,120,4,0.5,12,45,2,2,1,1,370,0,3,2,,,1,2,1,2,,1,20,2,
+2,157,59,1,4,115,4,1.4,0,20,3,2,1,12,200,240,1,1,10,8.65,0,3,1,2,,1,2,2,
+1,176,84,1,1,0,1,14,16,15,1,1,1,12,160,0,1,1,12.5,11,0,0,1,2,,2,,1,7
+1,182,78,2,2,0,4,2,0,50,2,2,1,12,400,NA,1,2,,,0,3,2,2,,1,3,1,15
+2,180.34,75,2,1,0,1,2.5,10,10,1,2,1,9,150,200,3,2,,,1,5,1,1,2,1,20,1,3
+1,182.88,74.39,2,1,100,1,18.6,60,30,1,1,2,,,,,2,,,0,0,3,2,,2,,1,1
+1,180,81,1,1,0,3,10,27,40,1,2,1,6,520,250,3,2,,,2,16,3,2,,1,16,2,
+2,170,63,1,4,250,1,3.1,22,30,3,2,2,,,,,2,,,1,1,3,2,,NA,NA,2,
+1,182.88,76,1,1,0,3,3,40,4,1,2,1,12,150,100,1,2,,,3,7,3,2,,1,18,1,8
+2,175,NA,1,4,100,4,0.5,5,20,2,2,1,16,240,2500,1,1,14,10,1,3,3,2,,1,7,2,
+2,152.4,57,2,1,30,3,14.2,40,12,1,1,2,,,,,2,,,2,5,3,2,,1,5,1,5
+1,175,70,1,1,0,1,21,17,20,1,1,2,,,,,2,,,NA,1,2,2,,1,2,1,5
+1,187.96,83,2,1,0,3,4,5,40,1,2,1,12,400,100,3,1,12,8.65,2,5,3,2,,1,30,1,5.5
+1,187.96,75,1,4,105,4,0.8,0,35,3,1,1,30,250,2000,1,1,8,9,1,3,2,2,,1,20,1,10
+1,182.88,72.1,1,1,0,3,23.7,67,45,1,2,1,16,250,1000,1,1,32,9,2,3,3,2,,1,10,1,10
+1,180,76.2,1,5,130,4,0,0,50,3,2,1,15,325,3000,1,1,8,8.65,1,3,3,2,,1,25,1,9
+1,182.8,76.29,1,1,0,3,1.3,10,100,1,2,1,21,570,3000,1,1,16,11.5,4,12,3,2,,1,50,1,20
+1,180,70,1,4,75,4,0.7,30,50,2,2,1,2,200,0,1,1,NA,NA,1,3,1,2,,1,35,1,7
+2,170,53,1,1,0,1,3,16,20,1,1,1,4,150,0,1,1,NA,NA,2,2,2,2,,2,,2,
+2,160,48,1,4,100,1,7.5,11.5,30,3,1,1,NA,NA,NA,NA,1,12,8.65,0,5,3,2,,2,,2,
+1,188,83,1,4,110,4,0.8,0,40,3,1,1,8,130,1000,1,1,22,6.82,1,7,3,2,,1,25,1,10
+2,173,50,1,1,0,1,7.1,20,15,1,1,1,12,300,1500,1,1,25,9,4,7,3,2,,2,,1,10
+2,172,78,1,4,100,4,0.5,0,30,3,1,1,14,200,0,1,1,14,10,4,15,2,2,,1,3,2,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,1,NA,NA,NA
+1,178,64,1,1,0,3,5,40,40,1,1,1,11,900,3000,4,2,,,2,5,3,2,,1,20,1,3
+2,165,57.15,1,1,0,3,13.6,10,20,1,2,1,13,200,1000,1,1,20,9,1,6,NA,2,,1,8,2,
+1,180,80,1,NA,0,2,1.2,0,50,1,2,1,12,300,3000,3,1,17,11.45,NA,NA,NA,NA,NA,1,NA,1,NA
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,1,NA,1,NA
+1,177,69,2,1,9,1,8.4,24,20,1,2,1,12,210,400,1,1,9,9,1,2,3,2,,1,20,1,9
+1,182.9,82.5,1,4,120,4,0.5,35,50,3,2,1,10,350,2000,2,1,6,7.5,2,4,1,2,,1,15,1,10
+2,174,62,1,1,0,3,17,60,40,1,2,1,26,300,100,1,1,20,8.75,1,3,3,2,,1,1,NA,NA
+2,157.5,48,1,4,120,4,0,0,NA,3,2,1,NA,NA,NA,1,1,5,10,3,5,NA,2,,NA,NA,2,
+1,183,78,1,1,0,3,11,25,30,1,1,2,,,,,2,,,0,0,1,2,,2,,2,
+1,193,82,1,1,40,1,4,17.2,30,1,1,2,,,,,1,16,9.48,1,1,2,2,,1,8,1,6
+2,158,42,2,1,0,1,15.2,11.5,20,4,2,2,,,,,2,,,3,6,2,2,,2,,1,2
+2,132,47,1,4,87.5,4,2.6,0,15,1,1,2,,,,,1,18,8.65,1,3,3,2,,2,,2,
+1,185.42,114,2,4,337.5,4,1.3,0,20,2,2,1,10,200,2000,1,2,,,5,15,2,2,,1,50,1,10
+1,177.8,94,1,1,55,1,15.2,30,19,1,2,1,12,320,4000,1,1,32,9.75,3,14,3,2,,1,16,1,4
+1,180.34,60,1,4,67.5,1,2,17.2,20,1,1,2,,,,,1,12.5,9.7,1,1,2,2,,2,,2,
+1,185.42,87,1,1,0,3,11,40,60,1,2,1,14,300,1200,1,1,12,10,3,8,2,2,,1,25,1,5
+1,190.5,81.92,1,1,50,3,48,35,20,1,2,1,21,175,NA,1,1,20.5,8.65,1,2,3,2,,1,74,2,
+1,177.8,63.288,1,4,75,4,0.3,0,40,3,2,2,,,,,2,,,0,NA,1,2,,1,10,1,5
+2,160,NA,1,1,0,1,11.2,17.5,50,1,2,1,12,330,1000,1,1,16,9.46,3,7,3,1,5,1,10,2,
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+
+
+
+
+The Qualitative Paradigm
+
+
+
+
The Qualitative Paradigm
+
+
+
The design of a research study begins with the selection of a topic and a paradigm. A paradigm is essentially a worldview, a whole framework of beliefs, values and methods within which research takes place. It is this world view within which researchers work.
+
+
According to Cresswell (1994) "A qualitative study is defined as an inquiry process of understanding a social or human problem, based on building a complex, holistic picture, formed with words, reporting detailed views of informants, and conducted in a natural setting.
+
+
+
Alternatively a quantitative study, consistent with the quantitative paradigm, is an inquiry into a social or human problem, based on testing a theory composed of variables, measured with numbers, and analyzed with statistical procedures, in order to determine whether the predictive generalizations of the theory hold true."
+
+
The paradigm framework is made up of:
+
+
P Philosophy
+
O Ontology
+
E Epistemology
+
M Methodology
+
(Source: University of Sheffield)
+
+
+
A summary of the scientific paradigm (Quantitative) might be:
+
+
P Scientific materialism
+
O Laws of nature
+
E Measurable and observable proof
+
M Experiment, large scale data collection, quantitative analysis
+
+
+
A summary of the Humanistic/Post Modern paradigm might be summarized as:
+
+
P Homocentric reality as a social construct, contextual verities
+
O The nature of the psyche, of perception, creativity, intelligence
+
E self verified evidence, grounded theory, recorded testimony
+
M Phenomenology, ethnography, depth interviews
+
+
Key Distinctions between Qualitative and Quantitative Research
+
+
+
+
+
(1) Words and numbers
+
+
+
+
Qualitative research places emphasis on understanding through looking closely at people's words, actions and records. The traditional or quantitative approach to research looks past these words, actions and records to their mathematical significance. The traditional approach to research (quantifies) the results of these observations.
+
+
In contrast qualitative research examines the patterns of meaning which emerge from the data and these are often presented in the participants' own words. The task of the qualitative researcher is to find patterns within those words (and actions) and to present those patterns for others to inspect while at the same time staying as close to the construction of the world as the participants originally experienced it.
+
+
+
+
(2) Perspectival (Subjective) versus objective views
+
(3) Discovery versus proof
+
+
+
+
The goal of qualitative research is to discover patterns which emerge after close observation, careful documentation, and thoughtful analysis of the research topic. What can be discovered by qualitative research are not sweeping generalizations but contextual findings. This process of discovery is basic to the philosophic underpinning of the qualitative approach.
+
+
+
Definitions of Qualitative Research
+
+
Denzin and Lincoln (1994) define qualitative research:
+
+
+
Qualitative research is multi-method in focus, involving an interpretive, naturalistic approach to its subject matter. This means that qualitative researchers study things in their natural settings, attempting to make sense of or interpret phenomena in terms of the meanings people bring to them. Qualitative research involves the studied use and collection of a variety of empirical materials case study, personal experience, introspective, life story interview, observational, historical, interactional, and visual texts-that describe routine and problematic moments and meaning in individuals' lives.
+
+
+
Cresswell (1994) defines it as:
+
+
+
Qualitative research is an inquiry process of understanding based on distinct methodological traditions of inquiry that explore a social or human problem. The researcher builds a complex, holistic picture, analyzes words, reports detailed views of informants, and conducts the study in a natural setting.
+
+
+
Characteristics of Qualitative Research
+
+
+
+
+
+
An exploratory and Descriptive focus
+
Emergent Design
+
Data Collection in the natural setting
+
Emphasis on human-as-instrument
+
Qualitative methods of data collection
+
Early and On-going inductive analysis
+
+
+
Cresswell (1994) divides qualitative research into five main Qualitative Research Types and identifies the key challenges of each mode of inquiry.
+
+
+
+
The Biography
+
Phenomenology
+
Grounded Theory
+
Ethnography
+
Case Study
+
+
+
+
+
Challenges of Each Type
+
+
Biography
+
+
+
+
+
The researcher needs to collect extensive information from and about the subject of the biography.
+
+
+
+
+
The investigator needs to have a clear understanding of historical, contextual material to position the subject within the larger trends in society or in the culture.
+
+
+
+
+
It takes a keen eye to determine the particular stories, slant, or angle that "works" in writing a biography and to uncover the "figure under the carpet" (Edel, 1984) that explains the multilayered context of a life.
+
+
+
+
+
The writer, using an interpretive approach, needs to be able to bring himself or herself into the narrative.
+
+
+
A phenomenologicalstudy may be challenging to use \because
+
+
+
·
+ The researcher requires a solid grounding in the philosophical precepts of phenomenology.
+
+
·
+ The participants in the study need to be carefully chosen to be individuals who have experienced the phenomenon
+
+
+
+
+
Bracketing personal experiences by the researcher may be difficult.
+
+
+
+
·
+ The researcher needs to decide how and in what way his or her personal experiences will be introduced into the study.
+
+
+
A grounded theory study challenges researchers for the following reasons:
+
+
+
·
+ The investigator needs to set aside, as much as possible, theoretical ideas or notions so that the analytic, substantive theory can emerge.
+
+
·
+ Despite the evolving, inductive nature of this form of qualitative inquiry, the researcher must recognize that this is a systematic approach to research with specific steps in data analysis.
+
+
·
+ The researcher faces the difficulty of determining when categories are saturated or when the theory is sufficiently detailed.
+
+
+
+
+
The researcher needs to recognize that the primary outcome of this study is a theory with specific components: a central phenomenon, causal conditions, strategies, conditions and context, and consequences. These are prescribed categories of information in the theory.
+
+
+
+
+
The ethnography is challenging to use for the following reasons:
+
+
+
·
+ The researcher needs to have grounding in cultural anthropology and the meaning of a social-cultural system as well as the concepts typically explored by ethnographers.
+
+
+
+
+
The time to collect data is extensive, involving prolonged time in the field.
+
+
+
+
·
+ In many ethnographies, the narratives are written in a literary, almost storytelling approach, an approach that may limit the audience for the work and may be challenging for authors accustomed to traditional approaches to writing social and human science research.
+
+
·
+ There is a possibility that the researcher will "go native" and be unable to complete the study or be compromised in the study. This is but one issue in the complex array of fieldwork issues facing ethnographers who venture into an unfamiliar cultural group or system.
+
+
+
The Case study poses the following challenges
+
+
+
+
The researcher must identify his or her case. He or she must decide what bounded system to study, recognizing that several might be possible candidates for this selection and realizing that either the case itself or an issue, for which a case or cases are selected to illustrate, is worthy of study.
+
+
+
+
·
+ The researcher must consider whether to study a single case or multiple cases. The study of more than one case dilutes the overall analysis; the more cases an individual studies, the greater the lack of depth in any single case. When a researchers chooses multiple cases, the issue becomes "How many?"- Typically, however, the researcher chooses no more than four cases. What motivates the researcher to consider a large number of cases is the idea of generalizability, a term that holds little meaning for most qualitative researchers.
+
+
+
+
Qualitative Methods of Data Collection
+
+
+
Peoples words and actions represent the data of qualitative inquiry and this requires methods that allow the researcher to capture language and behavior. The key ways of capturing these are:
+
+
+
+
Observation both participant and direct
+
In-depth interviews
+
Group Interviews
+
The collection of relevant documents
+
Photographs and Video Tapes
+
+
+
+
The Interview
+
+
The interview is one of the major sources of data collection, and it is also one of the most difficult ones to get right. In qualitative research the interview is a form of discourse. According to Mischler (1986) its particular features reflect the distinctive structure and aims of interviewing, namely, that it is discourse shaped and organized by asking and answering questions. An interview is a joint product of what interviewees and interviewers talk about together and how they talk with each other. The record of an interview that we researchers make and then use in our work of analysis and interpretation is a representation of that talk.
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Interview Probes
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One of the key techniques in good interviewing is the use of probes.
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Patton (1990) identifies three types of probes:
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+
+
+
detail-oriented probes
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elaboration probes,
+
clarification probes.
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1. Detail-oriented probes. In our natural conversations we ask each other questions to get more detail. These types of follow-up questions are designed to fill out the picture of whatever it is we are trying to understand. We easily ask these questions when we are genuinely curious.
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Who was with you?
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What was it like being there
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Where did you go then?
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When did this happen in your life?
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How are you going to try to deal with the situation?
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2. Elaboration probes. Another type of probe is designed to encourage the interviewee to tell us more. We indicate our desire to know more by such things as gently nodding our head as the person talks, softly voicing 'un-huh' every so often, and sometimes by just remaining silent but attentive. We can also ask for the interviewee to simply continue talking.
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·
+ Tell me more about that.
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Can you give me an example of what you are talking about?
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·
+ I think I understand what you mean.
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·
+ Talk more about that, will you?
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·
+ I'd like to hear you talk more about that.
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3. Clarification probes. There are likely to be times in an interview when the interviewer is unsure of what the interviewee is talking about, what she or he means. In these situations the interviewer can gently ask for clarification, making sure to communicate that it is the interviewer's difficulty in understanding and not the fault of the interviewee.
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+
I'm not sure I understand what you mean by 'hanging out'. Can you help me understand what that means?
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I'm having trouble understanding the problem you've described. Can you talk a little more about that?
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I want to make sure I understand what you mean. Would you describe it for me again?
+
I'm sorry. I don't quite get. Tell me again, would you?
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+
Characteristics of Good Qualitative Research
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We use a tradition of inquiry. This means that the researcher identifies, studies, and employs one or more traditions of inquiry.
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We begin with a single focus. The project starts with a single idea/
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Problem that the researcher seeks to understand, not a causal relationship of variables or a comparison of groups Although relationships might evolve or comparisons might be made these emerge late in the study after we describe a single idea
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The study includes detailed methods, a rigorous approach to data collection, data analysis, and report writing. This means, too, that the researcher verifies the accuracy of the account using one of the many procedures for verification.
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We write persuasively so that the reader experiences "being there."
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We analyze data using multiple levels of abstraction. Often, writers present their studies in stages (e.g., the multiple themes that can be combined into larger themes or perspectives) or layer their analyses from the particular to the general reflecting all the complexities that exist in real life. The best qualitative studies engage the reader.
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+
REASONS FOR CONDUCTING
+
QUALITATIVE RESEARCH
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+
Given these distinctions and definitions of a qualitative study, why does a person engage in such a rigorous design? To undertake qualitative research requires a strong commitment to study a problem and demands time and resources. Qualitative research shares good company with the most rigorous quantitative research, and it should not be viewed as an easy substitute for a "statistical" or quantitative study. Qualitative inquiry is for the researcher who is willing to do the following:
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Commit to extensive time in the field. The investigator spends many hours in the field, collects extensive data, and labors over field issues of trying to gain access, rapport, and an "insider" perspective.
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engage in the complex, time-consuming process of data analysis the ambitious task of sorting through large amounts of data and reducing them to a few themes or categories. For a multidisciplinary team of qualitative researchers, this task can be shared; for most researchers, it is a lonely, isolated time of struggling with the data. The task is challenging, especially because the database consists of complex texts and images.
+
+
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Write long passages, because the evidence must substantiate claims and the writer needs to show multiple perspectives. The incorporation of quotes to provide participants' perspectives also lengthens the study.
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Participate in a form of social and human science research that does not have firm guidelines or specific procedures and is evolving and changing constantly. This complicates telling others how one plans to conduct a study and how others might judge it when the study is done.
+
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+
+
If an individual is willing to engage in qualitative inquiry, then the person needs to determine whether a strong rationale exists for choosing a qualitative approach, and there are compelling reasons to undertake a qualitative study . In this respect Cresswell (1994) offers the following advice:
+
+
First select a qualitative study because of the nature of the research question. Ina qualitative study, the research question often starts with a how or a what so that initial forays into the topic describe what is going on. This is in contrast to quantitative questions that ask why and look for a comparison of groups (e.g., Is Group 1 better at something than Group 2) or a relationship between variables, with the intent of establishing an association, relationship, or cause and effect (e.g., Did Variable explain what happened in Variable Y)
+
+
Second choose a qualitative, study because the topic needs to be explored. 'By this, I mean that variables cannot be easily identified, theories are not available to explain behavior of participants or their population of study, and theories need to be developed.
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+
Third use a qualitative study because of the need to present a detailed view of the topic. The side angle lens of the distant panoramic shot will not suffice to present answers to the problem, or the close-up view does not exist.
+
+
Fourth, choose a qualitative approach in order to study individuals in their natural setting. This involves going out to the setting or field of study, gaining access, and gathering material. If participants are removed from their setting, it leads to contrived findings that are out of context.
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+
. .
+
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Fifth, select a qualitative approach because of interest in writing in a literary style; the writer brings himself or herself into the study, the personal pronoun "I" is used, or perhaps the writer engages a storytelling form of narration.
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Sixth, employ a qualitative study because of sufficient time and resources to spend on extensive data collection in the field and detailed data analysis of "text" information.
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Seventh, select a qualitative approach because audiences are receptive to qualitative research. This audience might be a graduate adviser or committee, a discipline inclusive of multiple research methodologies, or publication outlets with editors receptive to qualitative approaches.
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Eighth, and finally, employ a qualitative approach to emphasize the researcher's role as an active learner who can tell the story from the participants' view rather than as an "expert" who passes judgment on participants.
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++Emre Uan 1001090035
++Tolga Akan 1001090024
++Taner Kayaca 1001090006
++Erdogan Yildirim 1001090115
++Sema Arslan 1001090015
++Reyhan Gl Dzen 16812
+
+***************************************************
+Derse Katilanlar:
+
+
+************** 20 Mays 2011 (Levene ve Ortalama testi)
+
+
++lknur Kk (yars)
++Merve Sava (yars)
++Fatmagl Kker (yars)
++Derya Ayazolu (yars)
++Cansu alk (yars)
++zgl Erbay (yars)
++Demet Yildiz 1001090329
+
+zmen Alpaslan 16616
+
++Seluk akir 1001080158
++Koray Korkmaz 1001090151
++Zuhal
+Demet
+Nazli
++Kbra
++Ceren Dere
++Emrah oban
+
++Mevlt Zeren (yars)
+-Mahmut Emin evik (yars)
++Kerem Aydnl (yars)
++Mehtap elik (yars)
++Elif Kurupnar (yars)
+-Adem Dursun (yars)
++Erkan Yatkn (tamam)
++enay Ayan (tamam)
++Ceren Dere (tamam)
+
+
diff --git a/english/courses/StatisticalAnalysis/statisticalAnalysis.html b/english/courses/StatisticalAnalysis/statisticalAnalysis.html
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+
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+Statistical Analysis
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+
1500 öğrencisi olan bir fakültede 50 kişiyle bir anket çalışması yapacaksanız ve basit tesadüfi örnekleme türünü kullanacaksanız 50 adet rassal sayıyı Excel'de herhangi bir hücreye aşağıdaki formülün yazılmasıyla elde edebilirsiniz. Ancak bu formülün 50 adet Excel hücresinde tekrar edilmesi gerekmektedir. Aksi durumda sadece 1 tane tesadüfi sayı elde edersiniz!:
+
+ =RANDBETWEEN(1,1500)
+
+
+
+
\ No newline at end of file
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+
+
+
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+
+R programında sample fonksiyonu
+
+
+
+
+
+
1500 öğrencisi olan bir fakültede 50 kişiyle bir anket çalışması yapacaksanız ve basit tesadüfi örnekleme türünü kullanacaksanız 50 adet rassal sayıyı R programında sample fonksiyonunu kullanarak aşağıdaki gibi elde edebilirsiniz:
+
+
+
\ No newline at end of file
diff --git a/english/courses/StatisticalAnalysis/w1/dice.html b/english/courses/StatisticalAnalysis/w1/dice.html
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+
+
+
+
+
+
+Dice Roll - Probability Theory
+
+
+
+
+
+
+
+
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+
+
+
+
+
+
+
+
+
+
+
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+% Options for packages loaded elsewhere
+\PassOptionsToPackage{unicode}{hyperref}
+\PassOptionsToPackage{hyphens}{url}
+%
+\documentclass[
+]{book}
+\usepackage{lmodern}
+\usepackage{amssymb,amsmath}
+\usepackage{ifxetex,ifluatex}
+\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
+ \usepackage[T1]{fontenc}
+ \usepackage[utf8]{inputenc}
+ \usepackage{textcomp} % provide euro and other symbols
+\else % if luatex or xetex
+ \usepackage{unicode-math}
+ \defaultfontfeatures{Scale=MatchLowercase}
+ \defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
+\fi
+% Use upquote if available, for straight quotes in verbatim environments
+\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
+\IfFileExists{microtype.sty}{% use microtype if available
+ \usepackage[]{microtype}
+ \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
+}{}
+\makeatletter
+\@ifundefined{KOMAClassName}{% if non-KOMA class
+ \IfFileExists{parskip.sty}{%
+ \usepackage{parskip}
+ }{% else
+ \setlength{\parindent}{0pt}
+ \setlength{\parskip}{6pt plus 2pt minus 1pt}}
+}{% if KOMA class
+ \KOMAoptions{parskip=half}}
+\makeatother
+\usepackage{xcolor}
+\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
+\IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}}
+\hypersetup{
+ pdftitle={Unsupervised Learning Methods},
+ pdfauthor={Dr Sebnem Er},
+ hidelinks,
+ pdfcreator={LaTeX via pandoc}}
+\urlstyle{same} % disable monospaced font for URLs
+\usepackage{color}
+\usepackage{fancyvrb}
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+\makesavenoteenv{longtable}
+\usepackage{graphicx,grffile}
+\makeatletter
+\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
+\def\maxheight{\ifdim\Gin@nat@height>\textheight\textheight\else\Gin@nat@height\fi}
+\makeatother
+% Scale images if necessary, so that they will not overflow the page
+% margins by default, and it is still possible to overwrite the defaults
+% using explicit options in \includegraphics[width, height, ...]{}
+\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio}
+% Set default figure placement to htbp
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+\def\fps@figure{htbp}
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+\setlength{\emergencystretch}{3em} % prevent overfull lines
+\providecommand{\tightlist}{%
+ \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
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+\usepackage{booktabs}
+\usepackage{amsthm}
+\makeatletter
+\def\thm@space@setup{%
+ \thm@preskip=8pt plus 2pt minus 4pt
+ \thm@postskip=\thm@preskip
+}
+\makeatother
+\usepackage[]{natbib}
+\bibliographystyle{apalike}
+
+\title{Unsupervised Learning Methods}
+\author{Dr Sebnem Er}
+\date{2020-10-02}
+
+\begin{document}
+\maketitle
+
+{
+\setcounter{tocdepth}{1}
+\tableofcontents
+}
+\hypertarget{introduction}{%
+\chapter{Introduction}\label{introduction}}
+
+This book will guide you through the R codes for the following Unsupervised Learning methods:
+
+\begin{itemize}
+\tightlist
+\item
+ Association Rules
+\item
+ Cluster Analysis
+\item
+ Self Organising Maps
+\end{itemize}
+
+The chapters will be made available on Tuesdays when we start a new topic. So please update your browser to access the codes for the relevant chapter.
+
+\hypertarget{association-rules}{%
+\chapter{Association Rules}\label{association-rules}}
+
+\hypertarget{prerequisites}{%
+\section{Prerequisites}\label{prerequisites}}
+
+You need to have the following R packages installed and recalled into your library:
+
+\begin{Shaded}
+\begin{Highlighting}[]
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+\end{Shaded}
+
+\hypertarget{the-groceries-dataset}{%
+\section{The Groceries Dataset}\label{the-groceries-dataset}}
+
+We shall mine Groceries dataset for association rules using the Apriori Algorithm. The Groceries dataset can be loaded from R. The steps for doing so are shown below. Note that you will only be able to load the data set once the package \texttt{arules} has been loaded into R. The Groceries dataset contains a collection of receipts with each line representing 1 receipt and the items purchased. Each line is called a transaction and each column in a row represents an item.
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{data}\NormalTok{(Groceries)}
+\KeywordTok{summary}\NormalTok{(Groceries)}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## transactions as itemMatrix in sparse format with
+## 9835 rows (elements/itemsets/transactions) and
+## 169 columns (items) and a density of 0.02609146
+##
+## most frequent items:
+## whole milk other vegetables rolls/buns soda
+## 2513 1903 1809 1715
+## yogurt (Other)
+## 1372 34055
+##
+## element (itemset/transaction) length distribution:
+## sizes
+## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
+## 2159 1643 1299 1005 855 645 545 438 350 246 182 117 78 77 55 46
+## 17 18 19 20 21 22 23 24 26 27 28 29 32
+## 29 14 14 9 11 4 6 1 1 1 1 3 1
+##
+## Min. 1st Qu. Median Mean 3rd Qu. Max.
+## 1.000 2.000 3.000 4.409 6.000 32.000
+##
+## includes extended item information - examples:
+## labels level2 level1
+## 1 frankfurter sausage meat and sausage
+## 2 sausage sausage meat and sausage
+## 3 liver loaf sausage meat and sausage
+\end{verbatim}
+
+As you can see, the data is in ``transactions'' format with a density of 0.0261 (check slides to remember what this value means). There are 9835 transactions with 169 distinct items that can be bought in this database (\(D\)).
+
+The summary function also provides the distribution of number items per transaction and the most popular items.
+
+Now let us examine the first 3 transactions in \(D\).
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{inspect}\NormalTok{(}\KeywordTok{head}\NormalTok{(Groceries, }\DecValTok{3}\NormalTok{))}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## items
+## [1] {citrus fruit,
+## semi-finished bread,
+## margarine,
+## ready soups}
+## [2] {tropical fruit,
+## yogurt,
+## coffee}
+## [3] {whole milk}
+\end{verbatim}
+
+The first customer bought {\{citrus fruit,semi-finished bread,margarine,ready soups\}}, whereas the third customer bought only {\{whole milk\}}.
+
+We can also find how many items each transaction contains, for the first 10 transactions:
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{head}\NormalTok{(}\KeywordTok{size}\NormalTok{(Groceries), }\DecValTok{10}\NormalTok{)}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## [1] 4 3 1 4 4 5 1 5 1 2
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{hist}\NormalTok{(}\KeywordTok{size}\NormalTok{(Groceries), }\DataTypeTok{main =} \StringTok{"Distribution of the number of items purchased"}\NormalTok{, }\DataTypeTok{xlab =} \StringTok{"Number of items"}\NormalTok{, }\DataTypeTok{ylab=}\StringTok{"Number of Transactions"}\NormalTok{)}
+\end{Highlighting}
+\end{Shaded}
+
+\includegraphics{Unsupervised-Learning_files/figure-latex/unnamed-chunk-4-1.pdf}
+
+As it is clear, the distribution of the number of items is skewed to right, clearly most transactions inlcude fewer number of items, only very few have more than 10 items purchased together.
+
+\hypertarget{support-count-item-frequencies-and-item-frequency-plot}{%
+\section{Support Count (Item Frequencies) and Item Frequency Plot}\label{support-count-item-frequencies-and-item-frequency-plot}}
+
+We can check the support count (\(freq(A)\)) for the top 25 products with the following R code:
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{itemSupportCount =}\StringTok{ }\KeywordTok{itemFrequency}\NormalTok{(Groceries, }\DataTypeTok{type =} \StringTok{"absolute"}\NormalTok{) }\CommentTok{# obtain the counts for individual items}
+\NormalTok{itemSupportCount =}\StringTok{ }\KeywordTok{sort}\NormalTok{(itemSupportCount, }\DataTypeTok{decreasing =} \OtherTok{TRUE}\NormalTok{) }\CommentTok{# sort the counts in descending order}
+\KeywordTok{head}\NormalTok{(itemSupportCount, }\DecValTok{25}\NormalTok{) }\CommentTok{# check the support count for the top 25 items}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## whole milk other vegetables rolls/buns
+## 2513 1903 1809
+## soda yogurt bottled water
+## 1715 1372 1087
+## root vegetables tropical fruit shopping bags
+## 1072 1032 969
+## sausage pastry citrus fruit
+## 924 875 814
+## bottled beer newspapers canned beer
+## 792 785 764
+## pip fruit fruit/vegetable juice whipped/sour cream
+## 744 711 705
+## brown bread domestic eggs frankfurter
+## 638 624 580
+## margarine coffee pork
+## 576 571 567
+## butter
+## 545
+\end{verbatim}
+
+We can also plot the support count, it is possible to change the colours of the bars as well.
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{itemFrequencyPlot}\NormalTok{(Groceries, }\DataTypeTok{topN =} \DecValTok{25}\NormalTok{, }\DataTypeTok{type=}\StringTok{"absolute"}\NormalTok{)}
+\end{Highlighting}
+\end{Shaded}
+
+\includegraphics{Unsupervised-Learning_files/figure-latex/unnamed-chunk-6-1.pdf}
+
+We can see that top purchased product is \{whole milk\} and it appears in 2513 transactions out of 9835. Therefore the support count for \{whole milk\} is 2513.
+
+\hypertarget{support}{%
+\section{Support}\label{support}}
+
+Remember the support (\(S(A)\)) is calculated as follows:
+
+\[S(A)=\frac{\texttt{freq({A})}}{n}\]
+The support for \{whole milk\} would be
+
+\[S(\texttt{{whole milk}})=\frac{\texttt{freq({whole milk})}}{n}=\frac{2513}{9835}=25.55\%\]
+
+It is possible to obtain this information with the same code as shown previously by simply replacing \(\texttt{type="absolute"}\) with the \(\texttt{type="relative"}\) option:
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{itemSupport =}\StringTok{ }\KeywordTok{itemFrequency}\NormalTok{(Groceries, }\DataTypeTok{type =} \StringTok{"relative"}\NormalTok{) }\CommentTok{# obtain the counts for individual items}
+\NormalTok{itemSupport =}\StringTok{ }\KeywordTok{sort}\NormalTok{(itemSupport, }\DataTypeTok{decreasing =} \OtherTok{TRUE}\NormalTok{) }\CommentTok{# sort the counts in descending order}
+\KeywordTok{head}\NormalTok{(itemSupport, }\DecValTok{25}\NormalTok{) }\CommentTok{# check the support count for the top 25 items}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## whole milk other vegetables rolls/buns
+## 0.25551601 0.19349263 0.18393493
+## soda yogurt bottled water
+## 0.17437722 0.13950178 0.11052364
+## root vegetables tropical fruit shopping bags
+## 0.10899847 0.10493137 0.09852567
+## sausage pastry citrus fruit
+## 0.09395018 0.08896797 0.08276563
+## bottled beer newspapers canned beer
+## 0.08052872 0.07981698 0.07768175
+## pip fruit fruit/vegetable juice whipped/sour cream
+## 0.07564820 0.07229283 0.07168277
+## brown bread domestic eggs frankfurter
+## 0.06487036 0.06344687 0.05897306
+## margarine coffee pork
+## 0.05856634 0.05805796 0.05765125
+## butter
+## 0.05541434
+\end{verbatim}
+
+We can also plot the support.
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{itemFrequencyPlot}\NormalTok{(Groceries, }\DataTypeTok{topN =} \DecValTok{25}\NormalTok{, }\DataTypeTok{type=}\StringTok{"relative"}\NormalTok{)}
+\end{Highlighting}
+\end{Shaded}
+
+\includegraphics{Unsupervised-Learning_files/figure-latex/unnamed-chunk-8-1.pdf}
+
+Note that the maximum support is low. To ensure that the top 25 frequent items are included in the analysis the minimum support would have to be less than 0.10! (\(10\%\)) Suppose we set the minimum support to 0.001 and minimum confidence to 0.8. We can mine some rules by executing the following R code:
+
+\hypertarget{rule-generation-with-apriori-algorithm}{%
+\section{Rule Generation with Apriori Algorithm}\label{rule-generation-with-apriori-algorithm}}
+
+\begin{itemize}
+\item
+ We are going to use the Apriori algorithm within the \(\texttt{arules}\) library to mine frequent itemsets and association rules..
+\item
+ Assume that we want to generate all the rules that satisfy the support threshold of \(0.1\%\) and confidence threshold of \(80\%\), then we need to enter \(\texttt{supp=0.001}\) and \(\texttt{conf=0.8}\) values in the \(\texttt{apriori()}\) function. If you want stronger rules, you can increase the value of \(\texttt{conf}\) and for more extended rules give higher value to \(\texttt{maxlen}\).
+\item
+ It might be desirable to sort the rules according either confidence or support, here we chose sorting according to confidence in a descending manner.
+\item
+ Finally we can examine the rules using \(\texttt{summary()}\) function.
+\end{itemize}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{rules <-}\StringTok{ }\KeywordTok{apriori}\NormalTok{(Groceries, }\DataTypeTok{parameter =} \KeywordTok{list}\NormalTok{(}\DataTypeTok{supp=}\FloatTok{0.001}\NormalTok{, }\DataTypeTok{conf=}\FloatTok{0.8}\NormalTok{))}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## Apriori
+##
+## Parameter specification:
+## confidence minval smax arem aval originalSupport maxtime support minlen
+## 0.8 0.1 1 none FALSE TRUE 5 0.001 1
+## maxlen target ext
+## 10 rules TRUE
+##
+## Algorithmic control:
+## filter tree heap memopt load sort verbose
+## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
+##
+## Absolute minimum support count: 9
+##
+## set item appearances ...[0 item(s)] done [0.00s].
+## set transactions ...[169 item(s), 9835 transaction(s)] done [0.03s].
+## sorting and recoding items ... [157 item(s)] done [0.00s].
+## creating transaction tree ... done [0.00s].
+## checking subsets of size 1 2 3 4 5 6 done [0.02s].
+## writing ... [410 rule(s)] done [0.00s].
+## creating S4 object ... done [0.00s].
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{rules <-}\StringTok{ }\KeywordTok{sort}\NormalTok{(rules, }\DataTypeTok{by=}\StringTok{'confidence'}\NormalTok{, }\DataTypeTok{decreasing =} \OtherTok{TRUE}\NormalTok{)}
+\KeywordTok{summary}\NormalTok{(rules)}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## set of 410 rules
+##
+## rule length distribution (lhs + rhs):sizes
+## 3 4 5 6
+## 29 229 140 12
+##
+## Min. 1st Qu. Median Mean 3rd Qu. Max.
+## 3.000 4.000 4.000 4.329 5.000 6.000
+##
+## summary of quality measures:
+## support confidence coverage lift
+## Min. :0.001017 Min. :0.8000 Min. :0.001017 Min. : 3.131
+## 1st Qu.:0.001017 1st Qu.:0.8333 1st Qu.:0.001220 1st Qu.: 3.312
+## Median :0.001220 Median :0.8462 Median :0.001322 Median : 3.588
+## Mean :0.001247 Mean :0.8663 Mean :0.001449 Mean : 3.951
+## 3rd Qu.:0.001322 3rd Qu.:0.9091 3rd Qu.:0.001627 3rd Qu.: 4.341
+## Max. :0.003152 Max. :1.0000 Max. :0.003559 Max. :11.235
+## count
+## Min. :10.00
+## 1st Qu.:10.00
+## Median :12.00
+## Mean :12.27
+## 3rd Qu.:13.00
+## Max. :31.00
+##
+## mining info:
+## data ntransactions support confidence
+## Groceries 9835 0.001 0.8
+\end{verbatim}
+
+In this output we are provided with the following information:
+
+\begin{itemize}
+\tightlist
+\item
+ There are 410 rules based on 0.001 support and 0.8 confidence thresholds.
+\item
+ The distribution of the number of items in each rule (rule length distribution): Most rules are 4 items long.
+\end{itemize}
+
+We need use the \(\texttt{inspect()}\) function to see the actual rules.
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{inspect}\NormalTok{(rules[}\DecValTok{1}\OperatorTok{:}\DecValTok{5}\NormalTok{])}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## lhs rhs support confidence coverage lift count
+## [1] {rice,
+## sugar} => {whole milk} 0.001220132 1 0.001220132 3.913649 12
+## [2] {canned fish,
+## hygiene articles} => {whole milk} 0.001118454 1 0.001118454 3.913649 11
+## [3] {root vegetables,
+## butter,
+## rice} => {whole milk} 0.001016777 1 0.001016777 3.913649 10
+## [4] {root vegetables,
+## whipped/sour cream,
+## flour} => {whole milk} 0.001728521 1 0.001728521 3.913649 17
+## [5] {butter,
+## soft cheese,
+## domestic eggs} => {whole milk} 0.001016777 1 0.001016777 3.913649 10
+\end{verbatim}
+
+If we look at the confidence we see that for the top 5 rules it is \(1\), this indicates \(100\%\) confidence:
+
+\begin{itemize}
+\item
+ \(100\%\) customers who bought ``\{rice, sugar\}'' end up buying ``\{whole milk\}'' as well.
+\item
+ \(100\%\) customers who bought ``\{canned fish, hygiene articles\}'' end up buying ``\{whole milk\}'' as well.
+\end{itemize}
+
+In the following section we will look at visualizing the rules.
+
+\hypertarget{visualisation-of-the-rules}{%
+\subsection{Visualisation of the Rules}\label{visualisation-of-the-rules}}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{topRules <-}\StringTok{ }\NormalTok{rules[}\DecValTok{1}\OperatorTok{:}\DecValTok{10}\NormalTok{]}
+\KeywordTok{plot}\NormalTok{(topRules)}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
+\end{verbatim}
+
+\includegraphics{Unsupervised-Learning_files/figure-latex/unnamed-chunk-11-1.pdf}
+
+The scatter plot of support and confidence of the top ten rules shows us that high confidence rules have low support values.
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{plot}\NormalTok{(rules)}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
+\end{verbatim}
+
+\includegraphics{Unsupervised-Learning_files/figure-latex/unnamed-chunk-12-1.pdf}
+
+In the following section we will look at removing redundant rules.
+
+\hypertarget{removing-redundant-rules}{%
+\subsection{Removing redundant rules}\label{removing-redundant-rules}}
+
+You may want to remove rules that are subsets of larger rules. Use the code below to remove such rules:
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{subset.rules <-}\StringTok{ }\KeywordTok{which}\NormalTok{(}\KeywordTok{colSums}\NormalTok{(}\KeywordTok{is.subset}\NormalTok{(rules, rules)) }\OperatorTok{>}\StringTok{ }\DecValTok{1}\NormalTok{) }\CommentTok{# get subset rules in vector}
+\CommentTok{# is.subset() determines if elements of one vector contain all the elements of other}
+\KeywordTok{length}\NormalTok{(subset.rules)}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## [1] 91
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{subset.rules <-}\StringTok{ }\NormalTok{rules[}\OperatorTok{-}\NormalTok{subset.rules] }\CommentTok{# remove subset rules.}
+\end{Highlighting}
+\end{Shaded}
+
+\hypertarget{finding-rules-related-to-given-items}{%
+\subsection{Finding rules related to given items}\label{finding-rules-related-to-given-items}}
+
+In the case of specific product in interest, either as a precedent (LHS) or as a consequent (RHS) in the rule, you need to set the ``\(\texttt{appearance=}\)'' parameter in the apriori rule generating function:
+
+Let us say we are interested in those transactions that end up in buying ``root vegetables'':
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{rveg.rules <-}\StringTok{ }\KeywordTok{apriori}\NormalTok{(Groceries, }\DataTypeTok{parameter =} \KeywordTok{list}\NormalTok{(}\DataTypeTok{supp=}\FloatTok{0.001}\NormalTok{, }\DataTypeTok{conf=}\FloatTok{0.8}\NormalTok{),}\DataTypeTok{appearance =} \KeywordTok{list}\NormalTok{(}\DataTypeTok{default=}\StringTok{"lhs"}\NormalTok{,}\DataTypeTok{rhs=}\StringTok{"root vegetables"}\NormalTok{))}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## Apriori
+##
+## Parameter specification:
+## confidence minval smax arem aval originalSupport maxtime support minlen
+## 0.8 0.1 1 none FALSE TRUE 5 0.001 1
+## maxlen target ext
+## 10 rules TRUE
+##
+## Algorithmic control:
+## filter tree heap memopt load sort verbose
+## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
+##
+## Absolute minimum support count: 9
+##
+## set item appearances ...[1 item(s)] done [0.00s].
+## set transactions ...[169 item(s), 9835 transaction(s)] done [0.01s].
+## sorting and recoding items ... [157 item(s)] done [0.00s].
+## creating transaction tree ... done [0.01s].
+## checking subsets of size 1 2 3 4 5 6 done [0.03s].
+## writing ... [5 rule(s)] done [0.00s].
+## creating S4 object ... done [0.00s].
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{inspect}\NormalTok{(}\KeywordTok{head}\NormalTok{(rveg.rules))}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## lhs rhs support confidence coverage lift count
+## [1] {other vegetables,
+## whole milk,
+## yogurt,
+## rice} => {root vegetables} 0.001321810 0.8666667 0.001525165 7.951182 13
+## [2] {tropical fruit,
+## other vegetables,
+## whole milk,
+## oil} => {root vegetables} 0.001321810 0.8666667 0.001525165 7.951182 13
+## [3] {beef,
+## citrus fruit,
+## tropical fruit,
+## other vegetables} => {root vegetables} 0.001016777 0.8333333 0.001220132 7.645367 10
+## [4] {citrus fruit,
+## other vegetables,
+## soda,
+## fruit/vegetable juice} => {root vegetables} 0.001016777 0.9090909 0.001118454 8.340400 10
+## [5] {tropical fruit,
+## other vegetables,
+## whole milk,
+## yogurt,
+## oil} => {root vegetables} 0.001016777 0.9090909 0.001118454 8.340400 10
+\end{verbatim}
+
+\hypertarget{using-your-own-dataset-stored-as-a-csv-file}{%
+\section{Using your own dataset stored as a csv file}\label{using-your-own-dataset-stored-as-a-csv-file}}
+
+You might want to use a dataset from a csv file. The format of this file should be as follows:
+
+\begin{itemize}
+\tightlist
+\item
+ Transactions in the rows (remember in our small example, we had 5 transactions.)
+\item
+ Items per transaction should be entered separately in different columns (items were A, B, C, D, E, and F)
+\end{itemize}
+
+\begin{figure}
+\centering
+\includegraphics{example.png}
+\caption{How the data looks like in csv format:}
+\end{figure}
+
+\begin{itemize}
+\tightlist
+\item
+ The data should be extracted using the \(\texttt{read.transactions()}\) function.
+\end{itemize}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{slideExample <-}\StringTok{ }\KeywordTok{read.transactions}\NormalTok{(}\StringTok{'C:/Users/01438475/Google Drive/UCTcourses/Analytics/UnsupervisedLearning/Arules/example.csv'}\NormalTok{, }\DataTypeTok{format =} \StringTok{'basket'}\NormalTok{, }\DataTypeTok{sep=}\StringTok{','}\NormalTok{)}
+\NormalTok{slideExample}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## transactions in sparse format with
+## 5 transactions (rows) and
+## 6 items (columns)
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{inspect}\NormalTok{(}\KeywordTok{head}\NormalTok{(slideExample, }\DecValTok{6}\NormalTok{))}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## items
+## [1] {A,D}
+## [2] {A,B,C,E}
+## [3] {B,C,D,F}
+## [4] {A,B,C,D}
+## [5] {A,B,D,F}
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\KeywordTok{size}\NormalTok{(}\KeywordTok{head}\NormalTok{(slideExample))}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## [1] 2 4 4 4 4
+\end{verbatim}
+
+I will leave all the rest for you to obtain.
+
+\hypertarget{references}{%
+\section{References:}\label{references}}
+
+\begin{itemize}
+\tightlist
+\item
+ \href{http://www.rdatamining.com/examples/association-rules}{R and Data Mining}
+\item
+ \href{https://github.com/susanli2016/Data-Analysis-with-R/blob/master/Market_Basket_Analysis.Rmd}{Susan Li - MBA}
+\item
+ \href{https://www.datacamp.com/community/tutorials/market-basket-analysis-r}{Datacamp}
+\item
+ Dr Juwa Nyirenda's lecture notes
+\end{itemize}
+
+\hypertarget{cluster-analysis}{%
+\chapter{Cluster Analysis}\label{cluster-analysis}}
+
+For this section, please update your browser on the 13th of October Tuesday.
+
+\hypertarget{self-organising-maps}{%
+\chapter{Self Organising Maps}\label{self-organising-maps}}
+
+For this section, please update your browser on the 20th of October Tuesday.
+
+ \bibliography{book.bib,packages.bib}
+
+\end{document}
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+ Chapter 5 A. Visualisation - Map Weights onto Colors | Unsupervised Learning Methods
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Chapter 5 A. Visualisation - Map Weights onto Colors
+
+
5.1 Vis - 1) Training Process
+
As the SOM training iterations progress, the distance from each node’s weights to the samples represented by that node is reduced. Ideally, this distance should reach a minimum plateau.
+This plot option shows the progress over time.
+If the curve is continually decreasing, more iterations are required.
+
plot(som_model, type="changes")
+
+
+
+
5.2 Vis - 2) Node Counts
+
The Kohonen packages allows us to visualise the count of how many samples are mapped to each node on the map.
+This metric can be used as a measure of map quality - ideally the sample distribution is relatively uniform.
+Large values in some map areas suggests that a larger map would be benificial.
+Empty nodes indicate that your map size is too big for the number of samples.
+Aim for at least 5-10 samples per node when choosing map size.
We shall mine Groceries dataset for association rules using the Apriori Algorithm. The Groceries dataset can be loaded from R. The steps for doing so are shown below. Note that you will only be able to load the data set once the package arules has been loaded into R. The Groceries dataset contains a collection of receipts with each line representing 1 receipt and the items purchased. Each line is called a transaction and each column in a row represents an item.
+
data(Groceries)
+summary(Groceries)
+
## transactions as itemMatrix in sparse format with
+## 9835 rows (elements/itemsets/transactions) and
+## 169 columns (items) and a density of 0.02609146
+##
+## most frequent items:
+## whole milk other vegetables rolls/buns soda
+## 2513 1903 1809 1715
+## yogurt (Other)
+## 1372 34055
+##
+## element (itemset/transaction) length distribution:
+## sizes
+## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
+## 2159 1643 1299 1005 855 645 545 438 350 246 182 117 78 77 55 46
+## 17 18 19 20 21 22 23 24 26 27 28 29 32
+## 29 14 14 9 11 4 6 1 1 1 1 3 1
+##
+## Min. 1st Qu. Median Mean 3rd Qu. Max.
+## 1.000 2.000 3.000 4.409 6.000 32.000
+##
+## includes extended item information - examples:
+## labels level2 level1
+## 1 frankfurter sausage meat and sausage
+## 2 sausage sausage meat and sausage
+## 3 liver loaf sausage meat and sausage
+
As you can see, the data is in “transactions” format with a density of 0.0261 (check slides to remember what this value means). There are 9835 transactions with 169 distinct items that can be bought in this database (\(D\)).
+
The summary function also provides the distribution of number items per transaction and the most popular items.
+
Now let us examine the first 3 transactions in \(D\).
The first customer bought {citrus fruit,semi-finished bread,margarine,ready soups}, whereas the third customer bought only {whole milk}.
+
We can also find how many items each transaction contains, for the first 10 transactions:
+
head(size(Groceries), 10)
+
## [1] 4 3 1 4 4 5 1 5 1 2
+
hist(size(Groceries), main ="Distribution of the number of items purchased", xlab ="Number of items", ylab="Number of Transactions")
+
+
As it is clear, the distribution of the number of items is skewed to right, clearly most transactions inlcude fewer number of items, only very few have more than 10 items purchased together.
+
+
+
2.3 Support Count (Item Frequencies) and Item Frequency Plot
+
We can check the support count (\(freq(A)\)) for the top 25 products with the following R code:
+
itemSupportCount =itemFrequency(Groceries, type ="absolute") # obtain the counts for individual items
+itemSupportCount =sort(itemSupportCount, decreasing =TRUE) # sort the counts in descending order
+head(itemSupportCount, 25) # check the support count for the top 25 items
We can see that top purchased product is {whole milk} and it appears in 2513 transactions out of 9835. Therefore the support count for {whole milk} is 2513.
+
+
+
2.4 Support
+
Remember the support (\(S(A)\)) is calculated as follows:
+
\[S(A)=\frac{\texttt{freq({A})}}{n}\]
+The support for {whole milk} would be
It is possible to obtain this information with the same code as shown previously by simply replacing \(\texttt{type="absolute"}\) with the \(\texttt{type="relative"}\) option:
+
itemSupport =itemFrequency(Groceries, type ="relative") # obtain the counts for individual items
+itemSupport =sort(itemSupport, decreasing =TRUE) # sort the counts in descending order
+head(itemSupport, 25) # check the support count for the top 25 items
Note that the maximum support is low. To ensure that the top 25 frequent items are included in the analysis the minimum support would have to be less than 0.10! (\(10\%\)) Suppose we set the minimum support to 0.001 and minimum confidence to 0.8. We can mine some rules by executing the following R code:
+
+
+
2.5 Rule Generation with Apriori Algorithm
+
+
We are going to use the Apriori algorithm within the \(\texttt{arules}\) library to mine frequent itemsets and association rules..
+
Assume that we want to generate all the rules that satisfy the support threshold of \(0.1\%\) and confidence threshold of \(80\%\), then we need to enter \(\texttt{supp=0.001}\) and \(\texttt{conf=0.8}\) values in the \(\texttt{apriori()}\) function. If you want stronger rules, you can increase the value of \(\texttt{conf}\) and for more extended rules give higher value to \(\texttt{maxlen}\).
+
It might be desirable to sort the rules according either confidence or support, here we chose sorting according to confidence in a descending manner.
+
Finally we can examine the rules using \(\texttt{summary()}\) function.
If we look at the confidence we see that for the top 5 rules it is \(1\), this indicates \(100\%\) confidence:
+
+
\(100\%\) customers who bought “{rice, sugar}” end up buying “{whole milk}” as well.
+
\(100\%\) customers who bought “{canned fish, hygiene articles}” end up buying “{whole milk}” as well.
+
+
In the following section we will look at visualizing the rules.
+
+
2.5.1 Visualisation of the Rules
+
topRules <-rules[1:10]
+plot(topRules)
+
## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
+
+
The scatter plot of support and confidence of the top ten rules shows us that high confidence rules have low support values.
+
plot(rules)
+
## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
+
+
In the following section we will look at removing redundant rules.
+
+
+
2.5.2 Removing redundant rules
+
You may want to remove rules that are subsets of larger rules. Use the code below to remove such rules:
+
subset.rules <-which(colSums(is.subset(rules, rules)) >1) # get subset rules in vector
+# is.subset() determines if elements of one vector contain all the elements of other
+length(subset.rules)
In the case of specific product in interest, either as a precedent (LHS) or as a consequent (RHS) in the rule, you need to set the “\(\texttt{appearance=}\)” parameter in the apriori rule generating function:
+
Let us say we are interested in those transactions that end up in buying “root vegetables”:
plot(hc, labels = F,-1)
+rect.hclust(hc, k =2, border =2:3) # Add rectangle around 3 groups
+
+
+
+
4.0.3 Centroid
+
+
+
4.1 Methods for determining number of clusters
+
+
4.1.1 Elbow method for k-means clustering
+
set.seed(123)
+# Compute and plot wss for k = 2 to k = 15
+k.max <-15# Maximal number of clusters
+df.out <-df
+wss <-sapply(1:k.max,
+function(k){kmeans(df.out, k, nstart=10 )$tot.withinss})
+plot(1:k.max, wss, type="b", pch =19, frame =FALSE, xlab="Number of clusters K", ylab="Total within-clusters sum of squares")
+abline(v =3, lty =2)
+
+
According to the elbow method, the optimal number of clusters suggested for the K-means algorithm is 3.
+
+
+
4.1.2 Average silhouette method for k-means clustering
+
k.max <-15
+data.out <-df
+sil <-rep(0, k.max)
+# Compute the average silhouette width for
+# k = 2 to k = 15
+for(i in2:k.max){
+km.res <-kmeans(df.out, centers = i, nstart =25)
+ss <-silhouette(km.res$cluster, dist(df.out))
+sil[i] <-mean(ss[, 3])
+}
+
# Plot the average silhouette width
+plot(1:k.max, sil, type ="b", pch =19,
+frame =FALSE, xlab ="Number of clusters k")
+abline(v =which.max(sil), lty =2)
+
+
According to the silhouette method the optimal number of clusters suggested for the Kmeans algorithm is 2.
+
+
+
4.1.3 Average silhouette method for PAM clustering
+
#clusplot(pam.out, main = "Cluster plot, k = 2", color = TRUE)
+plot(pam.out)
+
+
These two components explain 86.75% of the point variability.
+
This table shows how to use the average silhouette width value:
+
Range of SC : Interpretation
+0.71-1.0 : A strong structure has been found
+0.51-0.70 : A reasonable structure has been found
+0.26-0.50 : The structure is weak and could be artificial
+< 0.25 : No substantial structure has been found
+
According to the table, the fit is weak.
+
+
+
4.1.4 Average silhouette method for hierarchical clustering
+
plot(silhouette(cutree(hc,2),dist.out))
+
+
Average silhouette width : 0.4
+
This table shows how to use the average silhouette width value:
+
Range of SC: Interpretation
+0.71-1.0 : A strong structure has been found
+0.51-0.70 : A reasonable structure has been found
+0.26-0.50 : The structure is weak and could be artificial
+< 0.25 : No substantial structure has been found
+
The result for hierarchical clustering is similar to that of PAM. The conclusion we can make is that fit is weak.
+
+
+
4.1.5 Gap Statistic for K means clustering
+
# Compute gap statistic
+gap_stat <-clusGap(df, FUN = kmeans, nstart =25, K.max =10, B =50)
+# Print the result
+plot(gap_stat, frame =FALSE, xlab ="Number of clusters k")
+abline(v =4, lty =2)
+
+
According to the Gap Statistic the ’optimal number of clusters chosen for the Kmeans algorithm is 4!
+
Using the NbClust package which uses a vote to chose the number of clusters.
+The following example determine the number of clusters using all statistics:
## *** : The Hubert index is a graphical method of determining the number of clusters.
+## In the plot of Hubert index, we seek a significant knee that corresponds to a
+## significant increase of the value of the measure i.e the significant peak in Hubert
+## index second differences plot.
+##
+
+
## *** : The D index is a graphical method of determining the number of clusters.
+## In the plot of D index, we seek a significant knee (the significant peak in Dindex
+## second differences plot) that corresponds to a significant increase of the value of
+## the measure.
+##
+## *******************************************************************
+## * Among all indices:
+## * 9 proposed 2 as the best number of clusters
+## * 4 proposed 3 as the best number of clusters
+## * 6 proposed 4 as the best number of clusters
+## * 2 proposed 5 as the best number of clusters
+## * 1 proposed 8 as the best number of clusters
+## * 1 proposed 10 as the best number of clusters
+##
+## ***** Conclusion *****
+##
+## * According to the majority rule, the best number of clusters is 2
+##
+##
+## *******************************************************************
+
When all statistics in the NbClust package are allowed to vote, the majority (in this case 9 out of 23) propose
+that the ‘optimal’ number of clusters should be 2.
You can label chapter and section titles using {#label} after them, e.g., we can reference Chapter 2. If you do not manually label them, there will be automatic labels anyway, e.g., Chapter 4.
+
Figures and tables with captions will be placed in figure and table environments, respectively.
+
par(mar =c(4, 4, .1, .1))
+plot(pressure, type ='b', pch =19)
+
+
+
+Figure 2.1: Here is a nice figure!
+
+
+
Reference a figure by its code chunk label with the fig: prefix, e.g., see Figure 2.1. Similarly, you can reference tables generated from knitr::kable(), e.g., see Table 2.1.
+
knitr::kable(
+head(iris, 20), caption ='Here is a nice table!',
+booktabs =TRUE
+)
+
+
Table 2.1: Here is a nice table!
+
+
+
Sepal.Length
+
Sepal.Width
+
Petal.Length
+
Petal.Width
+
Species
+
+
+
+
+
5.1
+
3.5
+
1.4
+
0.2
+
setosa
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+
+
4.9
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3.0
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1.4
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0.2
+
setosa
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+
+
4.7
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3.2
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1.3
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0.2
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setosa
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+
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4.6
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3.1
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1.5
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0.2
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setosa
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5.0
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3.6
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1.4
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0.2
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setosa
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5.4
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3.9
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1.7
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0.4
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setosa
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+
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4.6
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3.4
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1.4
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0.3
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setosa
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+
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5.0
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3.4
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1.5
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0.2
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setosa
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+
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4.4
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2.9
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1.4
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0.2
+
setosa
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+
+
4.9
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3.1
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1.5
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0.1
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setosa
+
+
+
5.4
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3.7
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1.5
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0.2
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setosa
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+
+
4.8
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3.4
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1.6
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0.2
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setosa
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+
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4.8
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3.0
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1.4
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0.1
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setosa
+
+
+
4.3
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3.0
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1.1
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0.1
+
setosa
+
+
+
5.8
+
4.0
+
1.2
+
0.2
+
setosa
+
+
+
5.7
+
4.4
+
1.5
+
0.4
+
setosa
+
+
+
5.4
+
3.9
+
1.3
+
0.4
+
setosa
+
+
+
5.1
+
3.5
+
1.4
+
0.3
+
setosa
+
+
+
5.7
+
3.8
+
1.7
+
0.3
+
setosa
+
+
+
5.1
+
3.8
+
1.5
+
0.3
+
setosa
+
+
+
+
You can write citations, too. For example, we are using the bookdown package (Xie 2020) in this sample book, which was built on top of R Markdown and knitr(Xie 2015).
+
+
+
References
+
+
+
Xie, Yihui. 2015. Dynamic Documents with R and Knitr. 2nd ed. Boca Raton, Florida: Chapman; Hall/CRC. http://yihui.name/knitr/.
'
+ + '
'
+ + ''
+ + ''
+ + ''
+ + ''
+ + '
'
+ + ''
+ + ''
+ + ' {Date} - {Time} | #'
+ + '
'
+ + '{Name}'
+ + '{IP}'
+ + '
{Label:addPicText}'
+ + '
'
+ + ''
+ + ' ('
+ + '{Label:retry}/'
+ + '{Label:cancel}'
+ +')'
+ + '
' +
+ '
';
+}
+
+JSCC.prototype.textSmiles2Graphical = function(text, reverse) {
+ var s = this;
+ if(window.tinyMCE) tinyMCE.settings.smiley = false;
+ var flag = true;
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+ JSKitLib.fmap(s.smiles, function(el, i){
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+
+