PCA example (iris dataset)

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).

Load the SpectroChemPy API package

import spectrochempy as scp

Load the Iris dataset

dataset = scp.load_iris()

Fit a PCA model with automatic component selection

Using n_components="mle", the optimal number of components is determined automatically. Note: "mle" cannot be used when n_observations < n_features.

pca = scp.PCA(n_components="mle")
_ = pca.fit(dataset)

The number of components found is 3:

pca.n_components

It explains 99.5% of the variance:

pca.cumulative_explained_variance[-1].value

Fit a PCA model with a variance threshold

We can also specify the amount of explained variance directly:

pca = scp.PCA(n_components=0.999)
_ = pca.fit(dataset)

This time 4 components are found:

pca.n_components

Inspect the loadings and scores

The 4 components (loadings) are accessible via pca.components:

loadings = pca.components
loadings

or equivalently via pca.loadings:

pca.loadings

To reduce the data to a lower dimensionality, use transform:

scores = pca.transform()
scores

The scores are also available directly via pca.scores:

scores = pca.scores
scores

The explained and cumulative variance can be printed:

pca.printev()

Visualize the results

The scree plot shows the explained variance per component:

_ = pca.plot_scree()

The 2D score plot (first 2 PCs) separates Iris-setosa from the other species:

_ = pca.plot_score(color_mapping="labels")

The 3D score plot (first 3 PCs) shows that a third PC does not further distinguish versicolor from virginica:

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

Uncomment the following line to display all figures when running the script directly with Python.

# scp.show()