Kernel Perceptron

perceptron.py

# Mathieu Blondel, October 2010
# License: BSD 3 clause

import numpy as np
from numpy import linalg

def linear_kernel(x1, x2):
    return np.dot(x1, x2)

def polynomial_kernel(x, y, p=3):
    return (1 + np.dot(x, y)) ** p

def gaussian_kernel(x, y, sigma=5.0):
    return np.exp(-linalg.norm(x-y)**2 / (2 * (sigma ** 2)))


class Perceptron(object):

    def __init__(self, T=1):
        self.T = T

    def fit(self, X, y):
        n_samples, n_features = X.shape
        self.w = np.zeros(n_features, dtype=np.float64)
        self.b = 0.0

        for t in range(self.T):
            for i in range(n_samples):
                if self.predict(X[i])[0] != y[i]:
                    self.w += y[i] * X[i]
                    self.b += y[i]

    def project(self, X):
        return np.dot(X, self.w) + self.b

    def predict(self, X):
        X = np.atleast_2d(X)
        return np.sign(self.project(X))

class KernelPerceptron(object):

    def __init__(self, kernel=linear_kernel, T=1):
        self.kernel = kernel
        self.T = T

    def fit(self, X, y):
        n_samples, n_features = X.shape
        #np.hstack((X, np.ones((n_samples, 1))))
        self.alpha = np.zeros(n_samples, dtype=np.float64)

        # Gram matrix
        K = np.zeros((n_samples, n_samples))
        for i in range(n_samples):
            for j in range(n_samples):
                K[i,j] = self.kernel(X[i], X[j])

        for t in range(self.T):
            for i in range(n_samples):
                if np.sign(np.sum(K[:,i] * self.alpha * y)) != y[i]:
                    self.alpha[i] += 1.0

        # Support vectors
        sv = self.alpha > 1e-5
        ind = np.arange(len(self.alpha))[sv]
        self.alpha = self.alpha[sv]
        self.sv = X[sv]
        self.sv_y = y[sv]
        print "%d support vectors out of %d points" % (len(self.alpha),
                                                       n_samples)

    def project(self, X):
        y_predict = np.zeros(len(X))
        for i in range(len(X)):
            s = 0
            for a, sv_y, sv in zip(self.alpha, self.sv_y, self.sv):
                s += a * sv_y * self.kernel(X[i], sv)
            y_predict[i] = s
        return y_predict

    def predict(self, X):
        X = np.atleast_2d(X)
        n_samples, n_features = X.shape
        #np.hstack((X, np.ones((n_samples, 1))))
        return np.sign(self.project(X))

if __name__ == "__main__":
    import pylab as pl

    def gen_lin_separable_data():
        # generate training data in the 2-d case
        mean1 = np.array([0, 2])
        mean2 = np.array([2, 0])
        cov = np.array([[0.8, 0.6], [0.6, 0.8]])
        X1 = np.random.multivariate_normal(mean1, cov, 100)
        y1 = np.ones(len(X1))
        X2 = np.random.multivariate_normal(mean2, cov, 100)
        y2 = np.ones(len(X2)) * -1
        return X1, y1, X2, y2

    def gen_non_lin_separable_data():
        mean1 = [-1, 2]
        mean2 = [1, -1]
        mean3 = [4, -4]
        mean4 = [-4, 4]
        cov = [[1.0,0.8], [0.8, 1.0]]
        X1 = np.random.multivariate_normal(mean1, cov, 50)
        X1 = np.vstack((X1, np.random.multivariate_normal(mean3, cov, 50)))
        y1 = np.ones(len(X1))
        X2 = np.random.multivariate_normal(mean2, cov, 50)
        X2 = np.vstack((X2, np.random.multivariate_normal(mean4, cov, 50)))
        y2 = np.ones(len(X2)) * -1
        return X1, y1, X2, y2

    def gen_lin_separable_overlap_data():
        # generate training data in the 2-d case
        mean1 = np.array([0, 2])
        mean2 = np.array([2, 0])
        cov = np.array([[1.5, 1.0], [1.0, 1.5]])
        X1 = np.random.multivariate_normal(mean1, cov, 100)
        y1 = np.ones(len(X1))
        X2 = np.random.multivariate_normal(mean2, cov, 100)
        y2 = np.ones(len(X2)) * -1
        return X1, y1, X2, y2

    def split_train(X1, y1, X2, y2):
        X1_train = X1[:90]
        y1_train = y1[:90]
        X2_train = X2[:90]
        y2_train = y2[:90]
        X_train = np.vstack((X1_train, X2_train))
        y_train = np.hstack((y1_train, y2_train))
        return X_train, y_train

    def split_test(X1, y1, X2, y2):
        X1_test = X1[90:]
        y1_test = y1[90:]
        X2_test = X2[90:]
        y2_test = y2[90:]
        X_test = np.vstack((X1_test, X2_test))
        y_test = np.hstack((y1_test, y2_test))
        return X_test, y_test

    def plot_margin(X1_train, X2_train, clf):
        def f(x, w, b, c=0):
            # given x, return y such that [x,y] in on the line
            # w.x + b = c
            return (-w[0] * x - b + c) / w[1]

        pl.plot(X1_train[:,0], X1_train[:,1], "ro")
        pl.plot(X2_train[:,0], X2_train[:,1], "bo")

        # w.x + b = 0
        a0 = -4; a1 = f(a0, clf.w, clf.b)
        b0 = 4; b1 = f(b0, clf.w, clf.b)
        pl.plot([a0,b0], [a1,b1], "k")

        pl.axis("tight")
        pl.show()

    def plot_contour(X1_train, X2_train, clf):
        pl.plot(X1_train[:,0], X1_train[:,1], "ro")
        pl.plot(X2_train[:,0], X2_train[:,1], "bo")
        pl.scatter(clf.sv[:,0], clf.sv[:,1], s=100, c="g")

        X1, X2 = np.meshgrid(np.linspace(-6,6,50), np.linspace(-6,6,50))
        X = np.array([[x1, x2] for x1, x2 in zip(np.ravel(X1), np.ravel(X2))])
        Z = clf.project(X).reshape(X1.shape)
        pl.contour(X1, X2, Z, [0.0], colors='k', linewidths=1, origin='lower')

        pl.axis("tight")
        pl.show()

    def test_linear():
        X1, y1, X2, y2 = gen_lin_separable_data()
        #X1, y1, X2, y2 = gen_lin_separable_overlap_data()
        X_train, y_train = split_train(X1, y1, X2, y2)
        X_test, y_test = split_test(X1, y1, X2, y2)

        clf = Perceptron(T=3)
        clf.fit(X_train, y_train)

        y_predict = clf.predict(X_test)
        correct = np.sum(y_predict == y_test)
        print "%d out of %d predictions correct" % (correct, len(y_predict))

        plot_margin(X_train[y_train==1], X_train[y_train==-1], clf)

    def test_kernel():
        X1, y1, X2, y2 = gen_non_lin_separable_data()
        X_train, y_train = split_train(X1, y1, X2, y2)
        X_test, y_test = split_test(X1, y1, X2, y2)

        clf = KernelPerceptron(gaussian_kernel, T=20)
        clf.fit(X_train, y_train)

        y_predict = clf.predict(X_test)
        correct = np.sum(y_predict == y_test)
        print "%d out of %d predictions correct" % (correct, len(y_predict))

        plot_contour(X_train[y_train==1], X_train[y_train==-1], clf)

    test_linear()

Nice! BTW, shouldn't the * in polynomial kernel be a ** ?

Good catch, fixed :)

I want that in the scikit :)

self.alpha[i] += 1.0
should be self.alpha[i] += y[i]?