吴恩达 机器学习第二周 logistic_regression 单层网络梯度下降法实现

import numpy as npimport matplotlib.pyplot as plt#--------------------------------------------------------------------def signomid(z):    '''    This function is used as the activation function    by the logistic regression method     math formula is:    f(z) = 1.0/[1.0+exp(-z)]        input: z   real num or array like structure        output: y  real or array like structure       '''    z =np.array(z)    y = 1.0/(1.0 + np.exp(-z))    #y += 1.0e-30    assert(y.shape == z.shape)    return y#--------------------------------------------------------------------   def signomid_backprop(y_label, z):    '''    This is function calculate the dy/dz value,    the deviation of dy/dz    input: y_label, labeled data    input: gz, internal data    output: dy/dz    '''    y_label = np.array(y_label)    gz = signomid(z)    dydz = y_label - gz    assert(dydz.shape == y_label.shape)    assert(dydz.shape == gz.shape)    return dydz# y = np.array([0,0,1,1,1]).reshape(5,1)# dz = signomid_backprop(y,a)# print(dz)#--------------------------------------------------------------------def backprop(x,y_label,w,b):    '''    This function do the calculation of all backprop calculation:    input: y_label   labeled data    x: features data    w: the weighted values    b:  the interception , real number    '''    y_label = np.array(y_label).reshape(-1,1)   # shape of m*1    x       = np.array(x)         #(n,m)    w       = np.array(w).reshape(-1,1)       # shape(n,1)    m = x.shape[1]    z = np.dot(w.T,x)+b        # shape = (1,n)    z = z.reshape(-1,1)        # shape = (n,1)    #print(z,z.shape)    dz = signomid_backprop(y_label, z)    dzdw = np.dot(x,dz).reshape(-1,1)    dzdw = dzdw /np.float(m)    dzdb = np.sum(dz)    return -dzdw,-dzdb#--------------------------------------------------------------------   def get_loss(x,y,w,b):    y = y.reshape(-1,1)    w = w.reshape(-1,1)    z = np.dot(w.T,x) + b   # shape = (1,m)    z.reshape(x.shape[1],1)  # shape = (m,1)    h = signomid(z).reshape(-1,1)    #h += 1.0e-30    m = x.shape[1]           # x.shape = (n,m)    gz1 = np.log(h)    gz2 = np.log(1.0-h)    loss = np.dot(y.T,gz1) + np.dot((1.0 - y).T,gz2)    loss = loss / np.float(m)    return loss#--------------------------------------------------------------------def parameter_learning(x,y,w,b,learning_rate):    '''    This is the total learning function    '''    num_iter = 10000    for i in range(num_iter):        loss = get_loss(x,y,w,b)        loss_temp = loss        dw, db = backprop(x,y,w,b)        #print(dw,db)        #print(w,b)        w  += -learning_rate*dw        b  += -learning_rate*db        loss = get_loss(x,y,w,b)        dloss = abs(loss-loss_temp)        # if dloss <= 1.0e-6:            # print('this is the needed values of w,b', w,b)            # return w,b    print('this is the needed values of w,b', w,b)    return w,b,dloss# function used to predict  def predict(x,y,w,b):    error_count = 0    m = x.shape[1]    z = np.dot(w.T,x) + b    props = signomid(z).reshape(-1,1)    predictions = np.arange(m)    for i in range(m):        if props[i] >= 0.5:             predictions[i] =1        else:            predictions[i] = 0    #print(predictions,predictions.shape)    #print('this is out of y',y)    for i in range(m):        if predictions[i] != y[i]:            error_count += 1    accuracy =1.0-np.float(error_count)/np.float(m)    print('this accuracy of signomid is:',accuracy)    return accuracy# the main function learning_rate = 0.01from sklearn.datasets import load_irisfrom sklearn.model_selection  import train_test_splitiris = load_iris()train = iris.datalabel = iris.targetfor i in range(len(label)):    if label[i] == 2 :        label[i] = 1#print(label)x_train,x_test,y_train,y_test = train_test_split(train,label, test_size=0.1)m,n = x_train.shape[0],x_train.shape[1]print('this is sample, and col:',m,n)y_train = y_train.reshape(-1,1)y_test = y_test.reshape(-1,1)x_train = x_train.Tx_test  = x_test.Tmax_feature = x_train.max(axis=1)max_feature = max_feature.reshape(-1,1)x_train = x_train/max_featurew = np.random.randn(n).reshape(-1,1)b = 0.0001new_w,new_b,dloss = parameter_learning(x_train,y_train, w,b,learning_rate)print('this is new w:',new_w)print('this is new b:',new_b)print('this is dloss:',dloss)accuracy = predict(x_train,y_train,new_w,new_b)