Various PCA Results

[ykmd]

I applied tapkee PCA and opencv PCA to the same data and I got different results.
So I wonder if the methods are different in detail.

[lisitsyn]

This could be caused by whitening. Could you please attach these different projections so I can plot and analyze them?

[ykmd]

Code:
image = imread(filename, IMREAD_COLOR);
imageCV = image.reshape(1,image.rows_image.cols);
DenseMatrix imageE = DenseMatrix(imageCV.cols,imageCV.rows);
cv2eigen(imageCV.t(),imageE);
TapkeeOutput output = initialize()
.withParameters((method=tapkee::PCA,
target_dimension=3))
.embedUsing(imageE);
eigen2cv(output.embedding, imagePCA);
cv::PCA pca(imageCV, Mat(), CV_PCA_DATA_AS_COL, 3);
imshow("tapkeePCA", norm_0_255(imagePCA.t()).reshape(1, image.rows_3));
imshow("cvPCA", norm_0_255(pca.eigenvectors).reshape(1, image.rows*3));
Result:

[lisitsyn]

What bothers me is the case itself. Could you please explain what would be the meaning of such projection?

[ykmd]

PCA in opencv is to maximize the variance with the top dimension.
Data is in the form of RGB, result is treated in gray scale.
I followed the description in this note.
http://www.math.tau.ac.il/~turkel/notes/K-L.pdf

Date: Thu, 31 Jul 2014 10:09:50 -0700
From: notifications@github.com
To: tapkee@noreply.github.com
CC: yaukmd@hotmail.com
Subject: Re: [tapkee] Various PCA Results (#21)

What bothers me is the case itself. Could you please explain what would be the meaning of such projection?

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[lisitsyn]

Okay I see. Tapkee's PCA does the same thing as described. OpenCV is a bit different due to normalization.

[ykmd]

Somehow this data set cannot be solved by PCA with ARPACK solver, and kPCA with ARPACK produces a more alike result.

Date: Thu, 31 Jul 2014 11:41:14 -0700
From: notifications@github.com
To: tapkee@noreply.github.com
CC: yaukmd@hotmail.com
Subject: Re: [tapkee] Various PCA Results (#21)

Okay I see. Tapkee's PCA does the same thing as described. OpenCV is a bit different due to normalization.

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[lisitsyn]

Actually it could be due to numerical stability of ARPACK. This case is pretty singular as such 1-vector covariance could lead to ill-posed eigenproblem.