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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]

    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 0.128 seconds)

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