PCA analysis example

In this example, we perform the PCA dimensionality reduction of the classical iris dataset (Ronald A. Fisher. “The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics, 7, pp.179-188, 1936).

First we laod the spectrochempy API package

import spectrochempy as scp

Upload a dataset form a distant server

try:
    dataset = scp.download_iris()
except (IOError, OSError):
    print("Could not load The `IRIS` dataset. Finishing here.")
    import sys

    sys.exit(0)

Create a PCA object

pca = scp.PCA(dataset, centered=True)

Reduce the data to a lower dimensionality. Here, the number of components is automatically determined using n_pc="auto". As indicated by the dimension of LT, 4 PC are found.

S, LT = pca.reduce(n_pc="auto")

print(LT)

NDDataset: [float64] cm (shape: (y:3, x:4))

The figures of merit (explained and cumulative variance) confirm that these 4 PC’s explain 100% of the variance:

pca.printev()

PC      Eigenvalue              %variance               %cumulative
         of cov(X)                 per PC                  variance
#1       1.449e+01                 92.462                    92.462
#2       3.469e+00                  5.302                    97.763
#3       1.975e+00                  1.719                    99.482
#4       1.085e+00                  0.518                   100.000

These figures of merit can also be displayed graphically

The ScreePlot

_ = pca.screeplot()

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The score plots can be used for classification purposes. The first one - in 2D for the 2 first PC’s - shows that the first PC allows distinguishing Iris-setosa (score of PC#1 < -1) from other species (score of PC#1 > -1), while more PC’s are required to distinguish versicolor from viginica.

_ = pca.scoreplot(1, 2, color_mapping="labels")

The second one - in 3D for the 3 first PC’s - indicates that a thid PC won’t allow better distinguishing versicolor from viginica.

ax = pca.scoreplot(1, 2, 3, color_mapping="labels")
ax.view_init(10, 75)

# scp.show()  # uncomment to show plot if needed (not necessary in jupyter notebook)