In [1]:

    

import numpy as np
from numpy import linalg
import numpy.random as npr
import pylab as pl
%matplotlib inline


    

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# example of what should come out: PCA


    

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import sklearn


    

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from sklearn import datasets


    

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X = datasets.make_swiss_roll(1000,0.05)[0]


    

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X.shape


    

    
Out[10]:





(1000, 3)

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from sklearn.decomposition import PCA


    

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pca = PCA(2)


    

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y = pca.fit_transform(X)


    

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X2 = pca.inverse_transform(y)


    

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np.sum(np.abs(X2-X))


    

    
Out[29]:





7537.6674630939006

In [30]:

    

np.mean(X,0)


    

    
Out[30]:





array([  2.19610597,  10.42289769,   0.13858269])

In [34]:

    

cov = np.cov(X,rowvar=0)
cov.shape


    

    
Out[34]:





(3, 3)

In [39]:

    

W = linalg.eig(cov)[1]
W


    

    
Out[39]:





array([[-0.33264407, -0.89430932,  0.2992637 ],
       [ 0.17698896, -0.37089915, -0.91165165],
       [-0.92629522,  0.25028915, -0.28166028]])

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y = W.dot(X.T)


    

In [79]:

    

def transform(X,dim=2):
    #mean = np.mean(X,0)
    cov = np.cov(X,rowvar=0)
    evals,evecs = linalg.eig(cov)
    W = evecs[:dim]
    return W.dot(X.T).T


    

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X = npr.randn(1000,2)
X[:,0] += npr.rand(1000)*20-10
X[:,1] += X[:,0] + 0.05*X[:,0]**2
pl.scatter(X[:,0],X[:,1])


    

    
Out[107]:





<matplotlib.collections.PathCollection at 0x1166bbbd0>






    

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y = transform(X)


    

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y.shape


    

    
Out[109]:





(1000, 2)

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pl.scatter(y[:,0],y[:,1])


    

    
Out[110]:





<matplotlib.collections.PathCollection at 0x11691e890>






    

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dim=2
evecs[:dim].shape


    

    
Out[111]:





(2, 2)

In [112]:

    

cov = np.cov(X,rowvar=0)
evals,evecs = linalg.eig(cov)
W = evecs[:dim]
y = W.dot(X.T).T


    

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X2 = W[:1].dot(y.T).T


    

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pl.scatter(X2[::-1,0],-X2[::-1,1])


    

    




---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-125-5c603559aab3> in <module>()
----> 1 pl.scatter(X2[::-1,0],-X2[::-1,1])

IndexError: index 1 is out of bounds for axis 1 with size 1

In [126]:

    

X2.shape


    

    
Out[126]:





(1000, 1)

In [127]:

    

pl.scatter(range(len(X2)),X2)


    

    
Out[127]:





<matplotlib.collections.PathCollection at 0x1173fff90>






    

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