Linear_regression与 Logistic_regression简单比较与python实现
好久没写博客了，在度厂实习期间更是天天累成了狗的节奏，最近有幸蹭到隔壁组老大小黑黑关于machine learning这块的培训（以下图片均摘自小黑黑的PPT），甚是感动，决定好好学习下这块的东西。
Linear_regression 和 Logistic_regression 其实是非常相似的两种算法。它们都属于监督学习，都可以用梯度下降等方法进行参数的迭代学习等等。
他们最大的不同应该说是 估价函数的不同。
此外Linear_regression 的 cost function：
Logistic_regression 的 cost function ：
即我们的最终目标是要求出使得 J(theta)最小时theta的值。采取的方法均为类似梯度下降法的方法。
最后给出两种算法的python实现：
Linear_regression
import sysMAX_FEATURE_DIMENSION = 1024MAX_SAMPLE_NUMBER = 1024MAX_ITERATE_NUMBER = 1024##求导def compute_gradient(x,y,theta,feature_number,feature_pos,sample_number): sum = 0.0 for i in range(sample_number): res = 0.0 for j in range(feature_number+1): res += x[i][j] * theta[j] sum += (res - y[i])*x[i][feature_pos] return sum/sample_number##估价函数def compute_cost(x,y,theta,feature_number,sample_number): sum = 0.0 for i in range(sample_number): res = 0.0 for j in range(feature_number+1): res += x[i][j] * theta[j] sum += (res - y[i]) * (res - y[i]) return sum/(2*sample_number)##梯度下降法def gradient_descent(x,y,theta,feature_number,sample_number,alpha,iterate_number): for i in range(iterate_number): tmp = [] for j in range(MAX_FEATURE_DIMENSION): tmp.append(0) for j in range(feature_number+1): tmp[j] = theta[j] - alpha * compute_gradient(x,y,theta,feature_number,j,sample_number) for j in range(feature_number+1): theta[j] = tmp[j]##测试 def predict(theta,x,feature_number): sum = 0.0 for i in range(feature_number+1): sum += theta[i]*x[i] return sumif __name__ == '__main__': x = [ [1,96.79,2,1,2], [1,110.39,3,1,0], [1,70.25,1,0,2], [1,99.96,2,1,1], [1,118.15,3,1,0], [1,115.08,3,1,2] ] y = [287,343,199,298,340,350] sample_number = 6 alpha = 0.0001 iterate_number = 1500 feature_number = 4 theta = [] for i in range(101): theta.append(0) gradient_descent(x,y,theta,feature_number,sample_number,alpha,iterate_number) print compute_cost(x,y,theta,feature_number,sample_number) testx1 = [1,112,3,1,0] testx2 = [1,110,3,1,1] print predict(theta, testx1, 4) print predict(theta, testx2, 4)Logistic_regression
import sysimport mathMAX_FEATURE_DIMENSION = 1024MAX_SAMPLE_NUMBER = 1024MAX_ITERATE_NUMBER = 1024##估价函数def sigmoid(z): return 1 / (1.0 + math.exp(-z))def hypothesis(x, theta, feature_number): h = 0.0 for i in range(feature_number+1): h += x[i] * theta[i] return sigmoid(h)##计算偏导数def compute_gradient(x, y, theta, feature_number, feature_pos, sample_number): sum = 0.0 for i in range(sample_number): h = hypothesis(x[i], theta, feature_number) sum += (h - y[i]) * x[i][feature_pos] return sum/sample_number##代价def compute_cost(x, y, theta, feature_number, sample_number): sum = 0.0 for i in range(sample_number): h = hypothesis(x[i], theta, feature_number) sum += -y[i] * math.log(h) - (1 - y[i]) * math.log(1 - h) return sum / sample_number##梯度下降def gradient_descent(x, y, theta, feature_number, sample_number, alpha, iterate_number): for i in range(iterate_number): tmp = [] for j in range(MAX_FEATURE_DIMENSION): tmp.append(0) for j in range(feature_number + 1): tmp[j] = theta[j] - alpha * compute_gradient(x, y ,theta, feature_number, j, sample_number) for j in range(feature_number + 1): theta[j] = tmp[j] print compute_cost(x, y, theta, feature_number, sample_number)if __name__ == '__main__': feature_number = 2 sample_number = 12 alpha = 0.001 iterate_number = 10 x = [ [1, 34.6, 78.0], [1, 30.2, 43.8], [1, 35.8, 72.9], [1, 60.1, 86.3], [1, 79.0, 75.3], [1, 45.0, 56.3], [1, 61.1, 96.5], [1, 75.0, 46.5], [1, 76.0, 87.4], [1, 84.4, 43.5], [1, 95.8, 38.2], [1, 75.0, 30.6] ] y = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0] theta = [] for i in range(MAX_FEATURE_DIMENSION): theta.append(0) gradient_descent(x, y, theta, feature_number, sample_number, alpha, iterate_number) outstr = "" for i in range(3): outstr += "\t".join([str(theta[i])]) print outstr