梯度下降学习笔记

# encoding:utf8

import numpy as np
import matplotlib.pyplot as plt
import time


class Logistic:
    def __init__(self):
        self._data_set = None
        self._labels = None
        self._weight = None
        self.axs = plt.subplots(nrows=1, ncols=2, sharex=True)[1]

    def load_data_set(self):
        with open('data/testSet.txt') as f:
            data_set = []
            labels = []
            for line in f.readlines():
                feat_array = line.strip().split()
                data_set.append([1.0, float(feat_array[0]), float(feat_array[1])])
                labels.append(float(feat_array[-1]))
            self._data_set = data_set
            self._labels = labels

    def sig(self, x):
        '''
        将数字映射成0到1区间的数字
        :param x: 
        :return: 
        '''
        return 1 / (1 + np.exp(-x))

    def gradDescent(self, a, max_itera):
        '''
        使用全部数据
        :param a: 
        :param max_itera: 最大迭代次数
        :return: 
        '''
        data_matrix = np.mat(self._data_set)
        label_matrix = np.mat(self._labels).transpose()
        m, n = np.shape(data_matrix)
        weights = np.ones((n, 1))
        for i in range(max_itera):
            h = self.sig(data_matrix * weights)
            e = (h - label_matrix)
            # θ=θ−αXT(Xθ−Y）
            weights = weights - a * data_matrix.transpose() * e

        self._weight = weights

    def randomGradDescent(self, max_itera):
        '''
        随机梯度下降，每次迭代，随机选择一行数据
        :param max_itera: 
        :return: 
        '''
        data_matrix = np.mat(self._data_set)
        labels = self._labels
        m, n = np.shape(data_matrix)
        weights = np.ones((n, 1))
        for i in range(max_itera):
            data_index = range(m)
            for j in range(m):
                a = 4 / (1.0 + j + i) + 0.0001
                rand_index = int(np.random.uniform(0, len(data_index)))
                h = self.sig((data_matrix[rand_index] * weights).sum())
                e = (h - labels[rand_index])
                weights = weights - a * e * data_matrix[rand_index].transpose()
                del (data_index[rand_index])

        self._weight = weights

    def classify(self, vec):
        vec_matrix = np.mat(vec)
        v = self.sig(vec_matrix * self._weight).sum()
        print 'cls is {}'.format(v)
        return 1.0 if v > 0.5 else 0.0

    def draw(self, ax_index, title):
        ax = self.axs[ax_index]
        ax.set_title(title)
        ax.grid(True)
        data_set = self._data_set
        labes = self._labels
        data_matrix = np.array(data_set)
        x1 = []
        x2 = []
        y1 = []
        y2 = []
        for i in range(len(data_set)):
            lb = labes[i]
            if lb == 0:
                x1.append(data_set[i][1])
                y1.append(data_set[i][2])
            else:
                x2.append(data_set[i][1])
                y2.append(data_set[i][2])
        # 绘制所有的数据点         
        ax.scatter(x1, y1, s=60, c='red', marker='s')
        ax.scatter(x2, y2, s=60, c='blue')
        # 绘制 wx = 0时，w1和w2的线性关系
        min_val = data_matrix[:, 1].min()
        max_val = data_matrix[:, 1].max()
        x = np.arange(min_val, max_val, 0.1)
        y = (-self._weight[0].sum() - x * self._weight[1].sum()) / self._weight[2].sum()
        ax.plot(x, y)

    def show(self):
        plt.show()


if __name__ == '__main__':
    lg = Logistic()
    lg.load_data_set()
    st = time.time()
    max_itera = 300
    lg.gradDescent(0.01, max_itera)
    cost = time.time() - st
    lg.draw(0, u'梯度下降,{}次迭代,耗时{}s'.format(max_itera, cost * 1000))
    st = time.time()
    max_itera = 5
    lg.randomGradDescent(max_itera)
    cost = time.time() - st
    lg.draw(1, u'随机梯度下降,{}次迭代,耗时{}s'.format(max_itera, cost * 1000))
    lg.show()
    lb = lg.classify([1, 1.78592, 7.718645])
    print lb

测试数据
-0.017612 14.053064 0
-1.395634 4.662541 1
-0.752157 6.538620 0
-1.322371 7.152853 0
0.423363 11.054677 0
0.406704 7.067335 1
0.667394 12.741452 0
-2.460150 6.866805 1
0.569411 9.548755 0
-0.026632 10.427743 0
0.850433 6.920334 1
1.347183 13.175500 0
1.176813 3.167020 1
-1.781871 9.097953 0
-0.566606 5.749003 1
0.931635 1.589505 1
-0.024205 6.151823 1
-0.036453 2.690988 1
-0.196949 0.444165 1
1.014459 5.754399 1
1.985298 3.230619 1
-1.693453 -0.557540 1
-0.576525 11.778922 0
-0.346811 -1.678730 1
-2.124484 2.672471 1
1.217916 9.597015 0
-0.733928 9.098687 0
-3.642001 -1.618087 1
0.315985 3.523953 1
1.416614 9.619232 0
-0.386323 3.989286 1
0.556921 8.294984 1
1.224863 11.587360 0
-1.347803 -2.406051 1
1.196604 4.951851 1
0.275221 9.543647 0
0.470575 9.332488 0
-1.889567 9.542662 0
-1.527893 12.150579 0
-1.185247 11.309318 0
-0.445678 3.297303 1
1.042222 6.105155 1
-0.618787 10.320986 0
1.152083 0.548467 1
0.828534 2.676045 1
-1.237728 10.549033 0
-0.683565 -2.166125 1
0.229456 5.921938 1
-0.959885 11.555336 0
0.492911 10.993324 0
0.184992 8.721488 0
-0.355715 10.325976 0
-0.397822 8.058397 0
0.824839 13.730343 0
1.507278 5.027866 1
0.099671 6.835839 1
-0.344008 10.717485 0
1.785928 7.718645 1
-0.918801 11.560217 0
-0.364009 4.747300 1
-0.841722 4.119083 1
0.490426 1.960539 1
-0.007194 9.075792 0
0.356107 12.447863 0
0.342578 12.281162 0
-0.810823 -1.466018 1
2.530777 6.476801 1
1.296683 11.607559 0
0.475487 12.040035 0
-0.783277 11.009725 0
0.074798 11.023650 0
-1.337472 0.468339 1
-0.102781 13.763651 0
-0.147324 2.874846 1
0.518389 9.887035 0
1.015399 7.571882 0
-1.658086 -0.027255 1
1.319944 2.171228 1
2.056216 5.019981 1
-0.851633 4.375691 1
-1.510047 6.061992 0
-1.076637 -3.181888 1
1.821096 10.283990 0
3.010150 8.401766 1
-1.099458 1.688274 1
-0.834872 -1.733869 1
-0.846637 3.849075 1
1.400102 12.628781 0
1.752842 5.468166 1
0.078557 0.059736 1
0.089392 -0.715300 1
1.825662 12.693808 0
0.197445 9.744638 0
0.126117 0.922311 1
-0.679797 1.220530 1
0.677983 2.556666 1
0.761349 10.693862 0
-2.168791 0.143632 1
1.388610 9.341997 0
0.317029 14.739025 0