[FIXED] How to project a new point to new basis using 'components_' attribute of PCA from sklearn.decomposition package?

Issue

I have some data points with 3 co-ordinates and using PCA function I converted it into a points having 2 co-ordinates by doing this

import numpy as np
from sklearn.decomposition import PCA
X = np.array([[-1, -1, -3], [-2, -1, -1], [-3, -2, -2], [1, 1, 1], [2, 1, 5], [3, 2, 6]]) #data
pca = PCA(n_components=2)
pca.fit(X)
PCA(copy=True, n_components=2, whiten=False)
XT = pca.fit_transform(X)
print XT
#output obtained
#[[-4.04510516 -1.24556106]
#[-2.92607624  0.61239898]
#[-4.55000611  1.13825234]
#[ 0.81687144 -1.11632484]
#[ 4.5401931   0.56854397]
#[ 6.16412297  0.04269061]]

The I got principal axes in feature space, representing the directions of maximum variance in the data using 'components_' attribute

W = (pca.components_)
print W
# output obtained
#[[ 0.49508794  0.3217835   0.80705843]
# [-0.67701709 -0.43930775  0.59047148]]

Now I wanted to project the first point [-1, -1, -3] (which is first point in X) onto 2D subspace using 'components_' attribute by doing this

projectedXT_0 = np.dot(W,X[0])
print projectedXT_0
#output obtained
#[-3.23804673 -0.65508959]

#expected output
#[-4.04510516 -1.24556106] 

I am not getting what I expected so, obviously I am doing something wrong while calculating projectedPoint using 'components_' attribute. Kindly demonstrate the use of 'components_' attribute to get projection of a point.

NOTE: I know 'transform' function does this but I want do using 'components_' attribute.

Solution

You forgot to substract the mean.

See the source of pca transform:

if self.mean_ is not None:
    X = X - self.mean_
X_transformed = fast_dot(X, self.components_.T)
if self.whiten:
    X_transformed /= np.sqrt(self.explained_variance_)
return X_transformed

Answered By - lejlot