131 lines
4.0 KiB
Python
131 lines
4.0 KiB
Python
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"""
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=========================
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Multilabel classification
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=========================
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This example simulates a multi-label document classification problem. The
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dataset is generated randomly based on the following process:
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- pick the number of labels: n ~ Poisson(n_labels)
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- n times, choose a class c: c ~ Multinomial(theta)
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- pick the document length: k ~ Poisson(length)
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- k times, choose a word: w ~ Multinomial(theta_c)
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In the above process, rejection sampling is used to make sure that n is more
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than 2, and that the document length is never zero. Likewise, we reject classes
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which have already been chosen. The documents that are assigned to both
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classes are plotted surrounded by two colored circles.
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The classification is performed by projecting to the first two principal
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components found by PCA and CCA for visualisation purposes, followed by using
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the :class:`~sklearn.multiclass.OneVsRestClassifier` metaclassifier using two
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SVCs with linear kernels to learn a discriminative model for each class.
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Note that PCA is used to perform an unsupervised dimensionality reduction,
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while CCA is used to perform a supervised one.
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Note: in the plot, "unlabeled samples" does not mean that we don't know the
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labels (as in semi-supervised learning) but that the samples simply do *not*
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have a label.
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"""
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# Authors: Vlad Niculae, Mathieu Blondel
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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.cross_decomposition import CCA
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from sklearn.datasets import make_multilabel_classification
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from sklearn.decomposition import PCA
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from sklearn.multiclass import OneVsRestClassifier
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from sklearn.svm import SVC
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def plot_hyperplane(clf, min_x, max_x, linestyle, label):
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# get the separating hyperplane
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w = clf.coef_[0]
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a = -w[0] / w[1]
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xx = np.linspace(min_x - 5, max_x + 5) # make sure the line is long enough
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yy = a * xx - (clf.intercept_[0]) / w[1]
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plt.plot(xx, yy, linestyle, label=label)
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def plot_subfigure(X, Y, subplot, title, transform):
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if transform == "pca":
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X = PCA(n_components=2).fit_transform(X)
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elif transform == "cca":
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X = CCA(n_components=2).fit(X, Y).transform(X)
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else:
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raise ValueError
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min_x = np.min(X[:, 0])
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max_x = np.max(X[:, 0])
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min_y = np.min(X[:, 1])
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max_y = np.max(X[:, 1])
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classif = OneVsRestClassifier(SVC(kernel="linear"))
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classif.fit(X, Y)
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plt.subplot(2, 2, subplot)
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plt.title(title)
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zero_class = np.where(Y[:, 0])
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one_class = np.where(Y[:, 1])
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plt.scatter(X[:, 0], X[:, 1], s=40, c="gray", edgecolors=(0, 0, 0))
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plt.scatter(
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X[zero_class, 0],
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X[zero_class, 1],
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s=160,
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edgecolors="b",
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facecolors="none",
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linewidths=2,
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label="Class 1",
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)
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plt.scatter(
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X[one_class, 0],
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X[one_class, 1],
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s=80,
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edgecolors="orange",
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facecolors="none",
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linewidths=2,
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label="Class 2",
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)
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plot_hyperplane(
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classif.estimators_[0], min_x, max_x, "k--", "Boundary\nfor class 1"
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)
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plot_hyperplane(
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classif.estimators_[1], min_x, max_x, "k-.", "Boundary\nfor class 2"
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)
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plt.xticks(())
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plt.yticks(())
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plt.xlim(min_x - 0.5 * max_x, max_x + 0.5 * max_x)
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plt.ylim(min_y - 0.5 * max_y, max_y + 0.5 * max_y)
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if subplot == 2:
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plt.xlabel("First principal component")
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plt.ylabel("Second principal component")
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plt.legend(loc="upper left")
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plt.figure(figsize=(8, 6))
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X, Y = make_multilabel_classification(
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n_classes=2, n_labels=1, allow_unlabeled=True, random_state=1
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)
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plot_subfigure(X, Y, 1, "With unlabeled samples + CCA", "cca")
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plot_subfigure(X, Y, 2, "With unlabeled samples + PCA", "pca")
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X, Y = make_multilabel_classification(
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n_classes=2, n_labels=1, allow_unlabeled=False, random_state=1
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)
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plot_subfigure(X, Y, 3, "Without unlabeled samples + CCA", "cca")
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plot_subfigure(X, Y, 4, "Without unlabeled samples + PCA", "pca")
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plt.subplots_adjust(0.04, 0.02, 0.97, 0.94, 0.09, 0.2)
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plt.show()
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