79 lines
2.3 KiB
Python
79 lines
2.3 KiB
Python
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"""
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===============================================================
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Factor Analysis (with rotation) to visualize patterns
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===============================================================
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Investigating the Iris dataset, we see that sepal length, petal
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length and petal width are highly correlated. Sepal width is
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less redundant. Matrix decomposition techniques can uncover
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these latent patterns. Applying rotations to the resulting
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components does not inherently improve the predictive value
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of the derived latent space, but can help visualise their
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structure; here, for example, the varimax rotation, which
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is found by maximizing the squared variances of the weights,
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finds a structure where the second component only loads
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positively on sepal width.
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"""
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# Authors: Jona Sassenhagen
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# License: BSD 3 clause
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.datasets import load_iris
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from sklearn.decomposition import PCA, FactorAnalysis
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from sklearn.preprocessing import StandardScaler
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# %%
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# Load Iris data
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data = load_iris()
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X = StandardScaler().fit_transform(data["data"])
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feature_names = data["feature_names"]
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# %%
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# Plot covariance of Iris features
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ax = plt.axes()
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im = ax.imshow(np.corrcoef(X.T), cmap="RdBu_r", vmin=-1, vmax=1)
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ax.set_xticks([0, 1, 2, 3])
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ax.set_xticklabels(list(feature_names), rotation=90)
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ax.set_yticks([0, 1, 2, 3])
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ax.set_yticklabels(list(feature_names))
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plt.colorbar(im).ax.set_ylabel("$r$", rotation=0)
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ax.set_title("Iris feature correlation matrix")
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plt.tight_layout()
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# %%
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# Run factor analysis with Varimax rotation
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n_comps = 2
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methods = [
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("PCA", PCA()),
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("Unrotated FA", FactorAnalysis()),
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("Varimax FA", FactorAnalysis(rotation="varimax")),
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]
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fig, axes = plt.subplots(ncols=len(methods), figsize=(10, 8), sharey=True)
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for ax, (method, fa) in zip(axes, methods):
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fa.set_params(n_components=n_comps)
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fa.fit(X)
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components = fa.components_.T
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print("\n\n %s :\n" % method)
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print(components)
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vmax = np.abs(components).max()
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ax.imshow(components, cmap="RdBu_r", vmax=vmax, vmin=-vmax)
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ax.set_yticks(np.arange(len(feature_names)))
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ax.set_yticklabels(feature_names)
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ax.set_title(str(method))
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ax.set_xticks([0, 1])
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ax.set_xticklabels(["Comp. 1", "Comp. 2"])
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fig.suptitle("Factors")
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plt.tight_layout()
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plt.show()
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