不确定 sklearn 中的 PCA

Question

I need to do some PCA using sklearn and I want to make sure I do it the right way. Here is my code:

from sklearn.decomposition import PCA
pca = PCA(n_components=5)
pca_result = pca.fit_transform(data)

eigenvalues = pca.singular_values_
print(eigenvalues)

x = pca_result[:,0]
y = pca_result[:,1]

The data looks like this:

[[ -6.4186, -14.3534,  18.1296,  -2.8110,  14.0298],
[ -7.1220, -17.1501,  21.2807,  -3.5025,  16.4489],
[ -8.4652, -18.9316,  25.0303,  -4.1773,  18.5066],
...,
[ -4.7054,   6.1389,   3.5146,  -0.1036,  -0.7332],
[ -5.8533,   9.9087,   4.1178,  -0.5211,  -2.2415],
[ -6.2969,  13.8951,   3.4365,  -0.9207,  -4.2024]]

These are the eigenvalues: [1005.2761 , 853.5491 , 65.058365, 49.994457, 10.277865] . I am not totally sure about the last 2 lines. I want to plot the data projected in the 2D space that seems to make up for most of the variation in the data (basically make a 2D plot of the 5D data, as it seems like it lives on a 2D manifold). Am I doing it right? Thank you!

Answer 1

Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables (entities each of which takes on various numerical values) into a set of values of linearly uncorrelated variables called principal components

Such dimensionality reduction can be a very useful step for visualising and processing high-dimensional datasets, while still retaining as much of the variance in the dataset as possible. For example, selecting L = 2 and keeping only the first two principal components finds the two-dimensional plane through the high-dimensional dataset in which the data is most spread out, so if the data contains clusters these too may be most spread out, and therefore most visible to be plotted out in a two-dimensional diagram; whereas if two directions through the data (or two of the original variables) are chosen at random, the clusters may be much less spread apart from each other, and may in fact be much more likely to substantially overlay each other, making them indistinguishable.

https://en.wikipedia.org/wiki/Principal_component_analysis

So you need to run:

from sklearn.decomposition import PCA
pca = PCA(n_components=2)
pca_result = pca.fit_transform(data)

x = pca_result[:,0]
y = pca_result[:,1]

Then you have a two dimensional space.