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Comparison of LDA and PCA 2D projection of Iris dataset#
The Iris dataset represents 3 kind of Iris flowers (Setosa, Versicolour and Virginica) with 4 attributes: sepal length, sepal width, petal length and petal width.
Principal Component Analysis (PCA) applied to this data identifies the combination of attributes (principal components, or directions in the feature space) that account for the most variance in the data. Here we plot the different samples on the 2 first principal components.
Linear Discriminant Analysis (LDA) tries to identify attributes that account for the most variance between classes. In particular, LDA, in contrast to PCA, is a supervised method, using known class labels.
explained variance ratio (first two components): [0.92461872 0.05306648]
# Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import matplotlib.pyplot as plt from sklearn import datasets from sklearn.decomposition import PCA from sklearn.discriminant_analysis import LinearDiscriminantAnalysis iris = datasets.load_iris() X = iris.data y = iris.target target_names = iris.target_names pca = PCA(n_components=2) X_r = pca.fit(X).transform(X) lda = LinearDiscriminantAnalysis(n_components=2) X_r2 = lda.fit(X, y).transform(X) # Percentage of variance explained for each components print( "explained variance ratio (first two components): %s" % str(pca.explained_variance_ratio_) ) plt.figure() colors = ["navy", "turquoise", "darkorange"] lw = 2 for color, i, target_name in zip(colors, [0, 1, 2], target_names): plt.scatter( X_r[y == i, 0], X_r[y == i, 1], color=color, alpha=0.8, lw=lw, label=target_name ) plt.legend(loc="best", shadow=False, scatterpoints=1) plt.title("PCA of IRIS dataset") plt.figure() for color, i, target_name in zip(colors, [0, 1, 2], target_names): plt.scatter( X_r2[y == i, 0], X_r2[y == i, 1], alpha=0.8, color=color, label=target_name ) plt.legend(loc="best", shadow=False, scatterpoints=1) plt.title("LDA of IRIS dataset") plt.show()
Total running time of the script: (0 minutes 0.193 seconds)
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Principal Component Analysis (PCA) on Iris Dataset
Dimensionality Reduction with Neighborhood Components Analysis
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