Multi-Label Document Classification

Introduction

This lab demonstrates a multi-label document classification problem using scikit-learn. The dataset is generated randomly based on the following process:

• Pick the number of labels: n ~ Poisson(n_labels)
• N times, choose a class c: c ~ Multinomial(theta)
• Pick the document length: k ~ Poisson(length)
• K times, choose a word: w ~ Multinomial(theta_c)

In this process, rejection sampling is used to ensure that n is more than 2, and that the document length is never zero. Likewise, classes that have already been chosen are rejected. The documents that are assigned to both classes are plotted surrounded by two colored circles.

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Skills Graph

Import Libraries

In this step, we import the necessary libraries: numpy, matplotlib, make_multilabel_classification from sklearn.datasets, OneVsRestClassifier and SVC from sklearn.multiclass, PCA and CCA from sklearn.decomposition.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_multilabel_classification
from sklearn.multiclass import OneVsRestClassifier
from sklearn.svm import SVC
from sklearn.decomposition import PCA
from sklearn.cross_decomposition import CCA

Define Plotting Function

In this step, we define the plot_hyperplane and plot_subfigure functions. plot_hyperplane function is used to get the separating hyperplane while plot_subfigure function is used to plot the subplots.

def plot_hyperplane(clf, min_x, max_x, linestyle, label):
    ## get the separating hyperplane
    w = clf.coef_[0]
    a = -w[0] / w[1]
    xx = np.linspace(min_x - 5, max_x + 5)  ## make sure the line is long enough
    yy = a * xx - (clf.intercept_[0]) / w[1]
    plt.plot(xx, yy, linestyle, label=label)


def plot_subfigure(X, Y, subplot, title, transform):
    if transform == "pca":
        X = PCA(n_components=2).fit_transform(X)
    elif transform == "cca":
        X = CCA(n_components=2).fit(X, Y).transform(X)
    else:
        raise ValueError

    min_x = np.min(X[:, 0])
    max_x = np.max(X[:, 0])

    min_y = np.min(X[:, 1])
    max_y = np.max(X[:, 1])

    classif = OneVsRestClassifier(SVC(kernel="linear"))
    classif.fit(X, Y)

    plt.subplot(2, 2, subplot)
    plt.title(title)

    zero_class = np.where(Y[:, 0])
    one_class = np.where(Y[:, 1])
    plt.scatter(X[:, 0], X[:, 1], s=40, c="gray", edgecolors=(0, 0, 0))
    plt.scatter(
        X[zero_class, 0],
        X[zero_class, 1],
        s=160,
        edgecolors="b",
        facecolors="none",
        linewidths=2,
        label="Class 1",
    )
    plt.scatter(
        X[one_class, 0],
        X[one_class, 1],
        s=80,
        edgecolors="orange",
        facecolors="none",
        linewidths=2,
        label="Class 2",
    )

    plot_hyperplane(
        classif.estimators_[0], min_x, max_x, "k--", "Boundary\nfor class 1"
    )
    plot_hyperplane(
        classif.estimators_[1], min_x, max_x, "k-.", "Boundary\nfor class 2"
    )
    plt.xticks(())
    plt.yticks(())

    plt.xlim(min_x - 0.5 * max_x, max_x + 0.5 * max_x)
    plt.ylim(min_y - 0.5 * max_y, max_y + 0.5 * max_y)
    if subplot == 2:
        plt.xlabel("First principal component")
        plt.ylabel("Second principal component")
        plt.legend(loc="upper left")

Generate Dataset

In this step, we generate the dataset using make_multilabel_classification function from sklearn.datasets.

X, Y = make_multilabel_classification(
    n_classes=2, n_labels=1, allow_unlabeled=True, random_state=1
)

Plot Subplots

In this step, we use plot_subfigure function to plot the subplots.

plt.figure(figsize=(8, 6))

plot_subfigure(X, Y, 1, "With unlabeled samples + CCA", "cca")
plot_subfigure(X, Y, 2, "With unlabeled samples + PCA", "pca")

X, Y = make_multilabel_classification(
    n_classes=2, n_labels=1, allow_unlabeled=False, random_state=1
)

plot_subfigure(X, Y, 3, "Without unlabeled samples + CCA", "cca")
plot_subfigure(X, Y, 4, "Without unlabeled samples + PCA", "pca")

plt.subplots_adjust(0.04, 0.02, 0.97, 0.94, 0.09, 0.2)
plt.show()

Summary

This lab demonstrated a multi-label document classification problem using scikit-learn. We used make_multilabel_classification function to generate the dataset and plot_subfigure function to plot the subplots.