Merge pull request #20 from MpoMp/master

DL Optimal String Alignment implementation

Author: tdebatty

README.md

@@ -45,7 +45,7 @@ The main characteristics of each implemented algorithm are presented below. The
 | [Normalized Levenshtein](#normalized-levenshtein)	|distance<br>similarity	| Yes 			| No 		| 	      | O(m*n) <sup>1</sup> |
 | [Weighted Levenshtein](#weighted-levenshtein)		|distance 				| No 			| No 		| 	      | O(m*n) <sup>1</sup> |
 | [Damerau-Levenshtein](#damerau-levenshtein) <sup>3</sup> 	|distance 				| No 			| Yes 		| 	      | O(m*n) <sup>1</sup> |
-| Optimal String Alignment <sup>3</sup> |not implemented yet | No 			| No 		| 	      | O(m*n) <sup>1</sup> |
+| [Optimal String Alignment](#optimal-string-alignment) <sup>3</sup> |distance | No 			| No 		| 	      | O(m*n) <sup>1</sup> |
 | [Jaro-Winkler](#jaro-winkler) 		|similarity<br>distance	| Yes  			| No 		| 	      | O(m*n) |
 | [Longest Common Subsequence](#longest-common-subsequence) 		|distance 				| No 			| No 		| 	      | O(m*n) <sup>1,2</sup> |
 | [Metric Longest Common Subsequence](#metric-longest-common-subsequence) |distance   			| Yes 			| Yes  		| 	      | O(m*n) <sup>1,2</sup> |
@@ -210,7 +210,31 @@ Will produce:
 6.0
 ```
 
+## Optimal String Alignment
+The Optimal String Alignment variant of Damerau–Levenshtein (sometimes called the restricted edit distance) computes the number of edit operations needed to make the strings equal under the condition that **no substring is edited more than once**, whereas the true Damerau–Levenshtein presents no such restriction.
+The difference from the algorithm for Levenshtein distance is the addition of one recurrence for the transposition operations.
 
+Note that for the optimal string alignment distance, the triangle inequality does not hold and so it is not a true metric.
+
+```java
+import info.debatty.java.stringsimilarity.*;
+
+public class MyApp {
+
+
+    public static void main(String[] args) {
+        OptimalStringAlignment osa = new OptimalStringAlignment();
+        
+        System.out.println(osa.distance("CA", "ABC"));;
+    }
+}
+```
+
+Will produce:
+
+```
+3.0
+```
 
 ## Jaro-Winkler
 Jaro-Winkler is a string edit distance that was developed in the area of record linkage (duplicate detection) (Winkler, 1990). The Jaro–Winkler distance metric is designed and best suited for short strings such as person names, and to detect typos.

src/main/java/info/debatty/java/stringsimilarity/OptimalStringAlignment.java

@@ -0,0 +1,102 @@
+/*
+ * The MIT License
+ *
+ * Copyright 2016 Thibault Debatty.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+package info.debatty.java.stringsimilarity;
+
+import info.debatty.java.stringsimilarity.interfaces.StringDistance;
+import net.jcip.annotations.Immutable;
+
+/**
+ * Implementation of the the Optimal String Alignment (sometimes called the
+ * restricted edit distance) variant of the Damerau-Levenshtein distance.
+ *
+ * The difference between the two algorithms consists in that the Optimal String
+ * Alignment algorithm computes the number of edit operations needed to make the
+ * strings equal under the condition that no substring is edited more than once,
+ * whereas Damerau-Levenshtein presents no such restriction.
+ *
+ * @author Michail Bogdanos
+ */
+@Immutable
+public final class OptimalStringAlignment implements StringDistance {
+
+    /**
+     * Compute the distance between strings: the minimum number of operations
+     * needed to transform one string into the other (insertion, deletion,
+     * substitution of a single character, or a transposition of two adjacent
+     * characters) while no substring is edited more than once.
+     *
+     * @param s1 the first input string
+     * @param s2 the second input string
+     * @return the OSA distance
+     */
+    public final double distance(final String s1, final String s2) {
+        int n = s1.length(), m = s2.length();
+        if (n == 0) return m;
+        if (m == 0) return n;
+        
+
+        // Create the distance matrix H[0 .. s1.length+1][0 .. s2.length+1]
+        int[][] d = new int[s1.length() + 2][s2.length() + 2];
+
+        //initialize top row and leftmost column
+        for (int i = 0; i <= n; i++) {
+            d[i][0] = i;
+        }
+        for (int j = 0; j <= m; j++) {
+            d[0][j] = j;
+        }
+
+        //fill the distance matrix
+        int cost;
+
+        for (int i = 1; i <= n; i++) {
+            for (int j = 1; j <= m; j++) {
+
+                //if s1[i - 1] = s2[j - 1] then cost = 0, else cost = 1
+                cost = (s1.charAt(i - 1) == s2.charAt(j - 1)) ? 0 : 1;
+
+                d[i][j] = min(
+                        d[i - 1][j - 1] + cost, // substitution
+                        d[i][j - 1] + 1,        // insertion
+                        d[i - 1][j] + 1         // deletion
+                );
+
+                //transposition check
+                if (i > 1 && j > 1 
+                        && s1.charAt(i - 1) == s2.charAt(j - 2) 
+                        && s1.charAt(i - 2) == s2.charAt(j - 1)
+                    ){
+                    d[i][j] = Math.min(d[i][j], d[i - 2][j - 2] + cost);
+                }
+            }
+        }
+
+        return d[n][m];
+    }
+
+    private static int min(
+            final int a, final int b, final int c) {
+        return Math.min(a, Math.min(b, c));
+    }
+}

src/main/java/info/debatty/java/stringsimilarity/examples/Examples.java

@@ -26,6 +26,7 @@
 import info.debatty.java.stringsimilarity.CharacterSubstitutionInterface;
 import info.debatty.java.stringsimilarity.Cosine;
 import info.debatty.java.stringsimilarity.Damerau;
+import info.debatty.java.stringsimilarity.OptimalStringAlignment;
 import info.debatty.java.stringsimilarity.Jaccard;
 import info.debatty.java.stringsimilarity.JaroWinkler;
 import info.debatty.java.stringsimilarity.KShingling;
@@ -49,13 +50,15 @@ public class Examples {
     public static void main(String[] args) {
         // Levenshtein
         // ===========
+        System.out.println("\nLevenshtein");
         Levenshtein levenshtein = new Levenshtein();
         System.out.println(levenshtein.distance("My string", "My $tring"));
         System.out.println(levenshtein.distance("My string", "M string2"));
         System.out.println(levenshtein.distance("My string", "My $tring"));
 
         // Jaccard index
         // =============
+        System.out.println("\nJaccard");
         Jaccard j2 = new Jaccard(2);
         // AB BC CD DE DF
         // 1  1  1  1  0
@@ -65,6 +68,7 @@ public static void main(String[] args) {
 
         // Jaro-Winkler
         // ============
+        System.out.println("\nJaro-Winkler");
         JaroWinkler jw = new JaroWinkler();
 
         // substitution of s and t : 0.9740740656852722
@@ -75,6 +79,7 @@ public static void main(String[] args) {
 
         // Cosine
         // ======
+        System.out.println("\nCosine");
         Cosine cos = new Cosine(3);
 
         // ABC BCE
@@ -93,6 +98,7 @@ public static void main(String[] args) {
 
         // Damerau
         // =======
+        System.out.println("\nDamerau");
         Damerau damerau = new Damerau();
 
         // 1 substitution
@@ -109,9 +115,20 @@ public static void main(String[] args) {
 
         // All different
         System.out.println(damerau.distance("ABCDEF", "POIU"));
-
+        
+        
+        // Optimal String Alignment
+        // =======
+        System.out.println("\nOptimal String Alignment");
+        OptimalStringAlignment osa = new OptimalStringAlignment();
+        
+        //Will produce 3.0
+        System.out.println(osa.distance("CA", "ABC"));
+        
+        
         // Longest Common Subsequence
         // ==========================
+        System.out.println("\nLongest Common Subsequence");
         LongestCommonSubsequence lcs = new LongestCommonSubsequence();
 
         // Will produce 4.0
@@ -123,6 +140,7 @@ public static void main(String[] args) {
         // NGram
         // =====
         // produces 0.416666
+        System.out.println("\nNGram");
         NGram twogram = new NGram(2);
         System.out.println(twogram.distance("ABCD", "ABTUIO"));
 
@@ -134,6 +152,7 @@ public static void main(String[] args) {
 
         // Normalized Levenshtein
         // ======================
+        System.out.println("\nNormalized Levenshtein");
         NormalizedLevenshtein l = new NormalizedLevenshtein();
 
         System.out.println(l.distance("My string", "My $tring"));
@@ -142,6 +161,7 @@ public static void main(String[] args) {
 
         // QGram
         // =====
+        System.out.println("\nQGram");
         QGram dig = new QGram(2);
 
         // AB BC CD CE
@@ -158,6 +178,7 @@ public static void main(String[] args) {
 
         // Sorensen-Dice
         // =============
+        System.out.println("\nSorensen-Dice");
         SorensenDice sd = new SorensenDice(2);
 
         // AB BC CD DE DF FG
@@ -168,6 +189,7 @@ public static void main(String[] args) {
 
         // Weighted Levenshtein
         // ====================
+        System.out.println("\nWeighted Levenshtein");
         WeightedLevenshtein wl = new WeightedLevenshtein(
                 new CharacterSubstitutionInterface() {
                     public double cost(char c1, char c2) {
@@ -188,6 +210,7 @@ public double cost(char c1, char c2) {
         System.out.println(wl.distance("String1", "Srring2"));
 
         // K-Shingling
+        System.out.println("\nK-Shingling");
         s1 = "my string,  \n  my song";
         s2 = "another string, from a song";
         KShingling ks = new KShingling(4);

src/test/java/info/debatty/java/stringsimilarity/OptimalStringAlignmentTest.java

@@ -0,0 +1,64 @@
+/*
+ * The MIT License
+ *
+ * Copyright 2016 Thibault Debatty.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+package info.debatty.java.stringsimilarity;
+
+import static org.junit.Assert.assertEquals;
+import org.junit.Test;
+
+/**
+ *
+ * @author Michail Bogdanos
+ */
+public class OptimalStringAlignmentTest {
+
+    /**
+     * Test of distance method, of class OptimalStringAlignment.
+     */
+    @Test
+    public final void testDistance() {
+        System.out.println("distance");
+        OptimalStringAlignment instance = new OptimalStringAlignment();
+        
+        //zero length
+        assertEquals(6.0, instance.distance("", "ABDCEF"), 0.0);
+        assertEquals(6.0, instance.distance("ABDCEF", ""), 0.0);
+        assertEquals(0.0, instance.distance("", ""), 0.0);
+        
+        //equality
+        assertEquals(0.0, instance.distance("ABDCEF", "ABDCEF"), 0.0);
+        
+        //single operation
+        assertEquals(1.0, instance.distance("ABDCFE", "ABDCEF"), 0.0);
+        assertEquals(1.0, instance.distance("BBDCEF", "ABDCEF"), 0.0);
+        assertEquals(1.0, instance.distance("BDCEF", "ABDCEF"), 0.0);
+        assertEquals(1.0, instance.distance("ABDCEF", "ADCEF"), 0.0);
+        
+        //other
+        assertEquals(3.0, instance.distance("CA", "ABC"), 0.0);
+        assertEquals(2.0, instance.distance("BAC", "CAB"), 0.0);
+        assertEquals(4.0, instance.distance("abcde", "awxyz"), 0.0);
+        assertEquals(5.0, instance.distance("abcde", "vwxyz"), 0.0);
+
+    }
+}