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PCA in Matlab vs Python sklearn


Prometheus

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Can someone give me sanity check. I've been doing PCA in matlab and python with sklearn and been getting slightly different results. Here's a toy dataset to illustrate:

In Matlab:

ty =

  -1.383405780000000   0.293578700000000
  -2.221898020000000  -0.251334840000000
   3.605303800000000   0.042243850000000
   1.383405780000000  -0.293578700000000
   2.221898020000000   0.251334840000000
   3.605303800000000  -0.042243850000000

[~, ty_sc] = pca(ty)

ty_sc =

   -2.5821    0.3192
   -3.4260   -0.2174
    2.4038    0.0184
    0.1787   -0.2954
    1.0226    0.2412
    2.4030   -0.0661

In python with sklearn:

from sklearn import decomposition
ty = np.array([(-1.38340578,  0.2935787),
          (-2.22189802, -0.25133484),
          (3.6053038,   0.04224385),
          (1.38340578, -0.2935787),
          (2.22189802,  0.25133484),
          (3.6053038,  -0.04224385)])
pca = PCA(n_components=2)
ty_pc = pca.fit_transform(ty)
ty_pc

array([[ 2.58213714,  0.31918546],
       [ 3.42598874, -0.21739117],
       [-2.40383649,  0.01842077],
       [-0.17871932, -0.29536446],
       [-1.02257092,  0.24121217],
       [-2.40299915, -0.06606278]])
 

Notice how the scores in the first columns are identical but for the sign. If all the signs were flipped i could understand, and it would make no difference to follow-up analyses, but just having one column flipped seems weird. This makes a huge difference when you feed these scores into an LDA classifier which i'm doing with the real data. 

As far as i can tell both techniques are centering and scaling the data in the same way. Any ideas what's going on to produce the difference?

 

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