本文實現(xiàn)的原理很簡單，優(yōu)化方法是用的梯度下降。后面有測試結(jié)果。

先來看看實現(xiàn)的示例代碼：

# coding=utf-8from math import expimport matplotlib.pyplot as pltimport numpy as npfrom sklearn.datasets.samples_generator import make_blobsdef sigmoid(num): ''' :param num: 待計算的x :return: sigmoid之后的數(shù)值 ''' if type(num) == int or type(num) == float:  return 1.0 / (1 + exp(-1 * num)) else:  raise ValueError, 'only int or float data can compute sigmoid'class logistic(): def __init__(self, x, y):   if type(x) == type(y) == list:   self.x = np.array(x)   self.y = np.array(y)  elif type(x) == type(y) == np.ndarray:   self.x = x   self.y = y  else:   raise ValueError, 'input data error' def sigmoid(self, x):  '''  :param x: 輸入向量  :return: 對輸入向量整體進行simgoid計算后的向量結(jié)果  '''  s = np.frompyfunc(lambda x: sigmoid(x), 1, 1)  return s(x) def train_with_punish(self, alpha, errors, punish=0.0001):  '''  :param alpha: alpha為學習速率  :param errors: 誤差小于多少時停止迭代的閾值  :param punish: 懲罰系數(shù)  :param times: 最大迭代次數(shù)  :return:  '''  self.punish = punish  dimension = self.x.shape[1]  self.theta = np.random.random(dimension)  compute_error = 100000000  times = 0  while compute_error > errors:   res = np.dot(self.x, self.theta)   delta = self.sigmoid(res) - self.y   self.theta = self.theta - alpha * np.dot(self.x.T, delta) - punish * self.theta # 帶懲罰的梯度下降方法   compute_error = np.sum(delta)   times += 1 def predict(self, x):  '''  :param x: 給入新的未標注的向量  :return: 按照計算出的參數(shù)返回判定的類別  '''  x = np.array(x)  if self.sigmoid(np.dot(x, self.theta)) > 0.5:   return 1  else:   return 0def test1(): ''' 用來進行測試和畫圖，展現(xiàn)效果 :return: ''' x, y = make_blobs(n_samples=200, centers=2, n_features=2, random_state=0, center_box=(10, 20)) x1 = [] y1 = [] x2 = [] y2 = [] for i in range(len(y)):  if y[i] == 0:   x1.append(x[i][0])   y1.append(x[i][1])  elif y[i] == 1:   x2.append(x[i][0])   y2.append(x[i][1]) # 以上均為處理數(shù)據(jù)，生成出兩類數(shù)據(jù) p = logistic(x, y) p.train_with_punish(alpha=0.00001, errors=0.005, punish=0.01) # 步長是0.00001，最大允許誤差是0.005，懲罰系數(shù)是0.01 x_test = np.arange(10, 20, 0.01) y_test = (-1 * p.theta[0] / p.theta[1]) * x_test plt.plot(x_test, y_test, c='g', label='logistic_line') plt.scatter(x1, y1, c='r', label='positive') plt.scatter(x2, y2, c='b', label='negative') plt.legend(loc=2) plt.title('punish value = ' + p.punish.__str__()) plt.show()if __name__ == '__main__': test1()

運行結(jié)果如下圖

總結(jié)

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