统计机器学习笔记(一)---感知机模型

代码

一、公共绘图部分

import numpy as npfrom matplotlib import pyplot as pltfrom matplotlib import animationfrom functools import partial# first set up the figure, the axis, and the plot element we want to animate__FIG = plt.figure()__AX = plt.axes(xlim=(0, 2), ylim=(-2, 2))__LINE, = __AX.plot([], [], 'g', lw = 2)__LABEL = __AX.text([], [], '')# initialization function: plot the background of each framedef __init(trains):    __LINE.set_data([], [])    x, y, x_, y_ = [], [], [], []    for p in trains:        if p[1] > 0:            x.append(p[0][0])            y.append(p[0][1])        else:            x_.append(p[0][0])            y_.append(p[0][1])    plt.plot(x, y, 'bo', x_, y_, 'rx')    plt.axis([-6, 6, -6, 6])    plt.grid(True)    plt.xlabel('x')    plt.ylabel('y')    plt.title('Prceptron Algorithm(wendale.cn)')    return __LINE, __LABEL# animation function.  this is called sequentiallydef __animate(history, i):    global __AX, __LINE, __LABEL    w = history[i][0]    b = history[i][1]    if w[1] == 0:        return __LINE, __LABEL    x1 = -7    y1 = -(b + w[0]*x1)/w[1]    x2 = 7    y2 = -(b + w[0]*x2)/w[1]    __LINE.set_data([x1, x2], [y1, y2])    x1 = 0    y1 = -(b + w[0] * x1) / w[1]    __LABEL.set_text(history[i])    __LABEL.set_position([x1, y1])    return __LINE, __LABELdef show(trains, history, save=False, name=''):    # call the animator.  blit=true means only re-draw the parts that have changed.    anim = animation.FuncAnimation(__FIG, partial(__animate, history), init_func=partial(__init, trains),                                   frames=len(history), interval=1000, repeat=True, blit=True)    plt.show()    if save:        anim.save(name, fps=2, writer='imagemagick')if __name__ == '__main__':    trains = np.array([[(3, 3), 1], [(4, 3), 1], [(1, 1), -1]])    history = [[[1.0, 0.0, -0.0], 1], [[1.0, 0.0, -1.0], 0], [[1.0, 0.0, -2.0], -1], [[1.0, 0.0, -3.0], -2], [[2.0, 0.0, -3.0], -1], [[2.0, 0.0, -4.0], -2], [[2.0, 0.0, -5.0], -3]]    show(trains, history)

二、原始形式

import copyimport drawHISTORY = []TRAINS = [[(3, 3), 1], [(4, 3), 1], [(1, 1), -1]]def update(w, b, item):    for i in range(len(item[0])):        w[i] += item[1] * item[0][i]    b += item[1]    return w, bdef cal(item):    res = 0    for i in range(len(item[0])):        res += item[0][i] * w[i]    res += b    res *= item[1]    return resdef iterComp(w, b, trains):    global HISTORY         flag = False    for item in trains:        if cal(item) <= 0:            flag = True            (w, b) = update(w, b, item)            HISTORY.append([copy.copy(w), b])    if not flag:        print "RESULT:w:" + str(w) + "b:" + str(b)    return flag, w, bif __name__ == "__main__":    w = [0, 0]    b = 0       while True:        (flag, w, b) = iterComp(w, b, TRAINS)        if not flag:            break    draw.show(TRAINS, HISTORY, True, 'perceptron.gif')

效果

三、对偶形式

__author__ = 'wendale'import numpy as npimport drawdef __cal_gram(trains):    gram = np.empty((len(trains), len(trains)), np.int)    for i in range(len(trains)):        for j in range(len(trains)):            gram[i][j] = np.dot(trains[i][0], trains[j][0])    return gramdef __check(trains, gram, alpha, b):    y = np.array(trains[:,1])    for i in range(len(trains)):        if (np.dot(alpha * y, gram[i]) + b) * y[i] <= 0:            return False, i    return True, -1def find(trains):    gram = __cal_gram(trains)    alpha = np.zeros(len(trains))    b = 0    x = np.array(trains[:,0].tolist()).reshape(3,2)    y = np.array(trains[:,1])    history = []    while True:        (flag, i) = __check(trains, gram, alpha, b)        if flag:            break        #update        alpha[i] += 1        b += trains[i][1]        history.append([np.dot(alpha * y, x).tolist(), b])    return alpha, b, historyif __name__ == '__main__':    trains = np.array([[[3, 3], 1], [[4, 3], 1], [[1, 1], -1]])    (a, b, history) = find(trains)    draw.show(trains, history, True, 'duality_perceptron.gif')

效果

参考

参考1