重庆大学机器学习三实验-对数几率回归分类鸢尾花、决策树、BP算法

import pandas as pd import numpy as np import datetime import matplotlib.pyplot as plt from pandas.plotting import radviz hide_num=22#隐藏层节点数量 feature=13#特征数量 label=3#标签数量 test_path='wine_test.csv' train_path='wine_training.csv' draw=False learning_rate=0.0001 learning_num=100000 # 分类鸢尾花数据集时取消下列的注释 hide_num=10 feature=4 test_path='iris_test.csv' train_path='iris_training.csv' draw=True learning_rate=0.4 learning_num=10000 # 1.初始化参数 def initialize_parameters(n_x, n_h, n_y): np.random.seed(2) # 权重和偏置矩阵 w1 = np.random.randn(n_h, n_x) * 0.01 b1 = np.zeros(shape=(n_h, 1)) w2 = np.random.randn(n_y, n_h) * 0.01 b2 = np.zeros(shape=(n_y, 1)) # 通过字典存储参数 parameters = {'w1': w1, 'b1': b1, 'w2': w2, 'b2': b2} return parameters # 2.前向传播 def forward_propagation(X, parameters): w1 = parameters['w1'] b1 = parameters['b1'] w2 = parameters['w2'] b2 = parameters['b2'] # 通过前向传播来计算a2 z1 = np.dot(w1, X) + b1 a1 = np.tanh(z1) # 使用tanh作为第一层的激活函数 z2 = np.dot(w2, a1) + b2 a2 = 1 / (1 + np.exp(-z2)) # 使用sigmoid作为第二层的激活函数 # 通过字典存储参数 cache = {'z1': z1, 'a1': a1, 'z2': z2, 'a2': a2} return a2, cache # 3.计算代价函数 def compute_cost(a2, Y): m = Y.shape[1] # Y的列数即为总的样本数 # 采用交叉熵（cross-entropy）作为代价函数 logprobs = np.multiply(np.log(a2), Y) + np.multiply((1 - Y), np.log(1 - a2)) cost = - np.sum(logprobs) / m return cost # 4.反向传播（计算代价函数的导数） def backward_propagation(parameters, cache, X, Y): m = 120 w2 = parameters['w2'] a1 = cache['a1'] a2 = cache['a2'] # 反向传播，计算dw1、db1、dw2、db2 dz2 = a2 - Y dw2 = (1 / m) * np.dot(dz2, a1.T) db2 = (1 / m) * np.sum(dz2, axis=1, keepdims=True) dz1 = np.multiply(np.dot(w2.T, dz2), 1 - np.power(a1, 2)) dw1 = (1 / m) * np.dot(dz1, X.T) db1 = (1 / m) * np.sum(dz1, axis=1, keepdims=True) grads = {'dw1': dw1, 'db1': db1, 'dw2': dw2, 'db2': db2} return grads # 5.更新参数 def update_parameters(parameters, grads, learning_rate): w1 = parameters['w1'] b1 = parameters['b1'] w2 = parameters['w2'] b2 = parameters['b2'] dw1 = grads['dw1'] db1 = grads['db1'] dw2 = grads['dw2'] db2 = grads['db2'] # 更新参数 w1 = w1 - dw1 * learning_rate b1 = b1 - db1 * learning_rate w2 = w2 - dw2 * learning_rate b2 = b2 - db2 * learning_rate parameters = {'w1': w1, 'b1': b1, 'w2': w2, 'b2': b2} return parameters # 建立神经网络 def nn_model(X, Y, n_h, n_input, n_output, num_iterations,learning_rate): np.random.seed(3) n_x = n_input # 输入层节点数 n_y = n_output # 输出层节点数 # 1.初始化参数 parameters = initialize_parameters(n_x, n_h, n_y) # 梯度下降循环 for i in range(0, num_iterations): # 2.前向传播 a2, cache = forward_propagation(X, parameters) # 3.计算代价函数 cost = compute_cost(a2, Y) # 4.反向传播 grads = backward_propagation(parameters, cache, X, Y) # 5.更新参数 parameters = update_parameters(parameters, grads,learning_rate) # 每1000次迭代，输出一次代价函数 if i % 1000 == 0: print('迭代第%i次，代价函数为：%f' % (i, cost)) return parameters # 6.模型评估 def predict(parameters, x_test, y_test): w1 = parameters['w1'] b1 = parameters['b1'] w2 = parameters['w2'] b2 = parameters['b2'] z1 = np.dot(w1, x_test) + b1 a1 = np.tanh(z1) z2 = np.dot(w2, a1) + b2 a2 = 1 / (1 + np.exp(-z2)) # 结果的维度 n_rows = y_test.shape[0] n_cols = y_test.shape[1] # 预测值结果存储 output = np.empty(shape=(n_rows, n_cols), dtype=int) for i in range(n_rows): for j in range(n_cols): if a2[i][j] > 0.5: output[i][j] = 1 else: output[i][j] = 0 print('预测结果：', output) print('真实结果：', y_test) count = 0 for k in range(0, n_cols): if output[0][k] == y_test[0][k] and output[1][k] == y_test[1][k] and output[2][k] == y_test[2][k]: count = count + 1 else: print('错误分类样本的序号：', k + 1) acc = count / int(y_test.shape[1]) * 100 print('准确率：%.2f%%' % acc) return output # 特征有4个维度，类别有1个维度，一共5个维度，故采用了RadViz图 def result_visualization(x_test, y_test, result): cols = y_test.shape[1] y = [] pre = [] # 反转换类别的独热编码 for i in range(cols): if y_test[0][i] == 0 and y_test[1][i] == 0 and y_test[2][i] == 1: y.append('setosa') elif y_test[0][i] == 0 and y_test[1][i] == 1 and y_test[2][i] == 0: y.append('versicolor') elif y_test[0][i] == 1 and y_test[1][i] == 0 and y_test[2][i] == 0: y.append('virginica') for j in range(cols): if result[0][j] == 0 and result[1][j] == 0 and result[2][j] == 1: pre.append('setosa') elif result[0][j] == 0 and result[1][j] == 1 and result[2][j] == 0: pre.append('versicolor') elif result[0][j] == 1 and result[1][j] == 0 and result[2][j] == 0: pre.append('virginica') else: pre.append('未知种类') # 将特征和类别矩阵拼接起来 real = np.column_stack((x_test.T, y)) prediction = np.column_stack((x_test.T, pre)) df_real = pd.DataFrame(real, index=None, columns=['萼片长度', '萼片宽度', '花瓣长度', '花瓣宽度', '种类']) df_prediction = pd.DataFrame(prediction, index=None, columns=['萼片长度', '萼片宽度', '花瓣长度', '花瓣宽度', '种类']) df_real[['萼片长度', '萼片宽度', '花瓣长度', '花瓣宽度']] = df_real[ ['萼片长度', '萼片宽度', '花瓣长度', '花瓣宽度']].astype(float) df_prediction[['萼片长度', '萼片宽度', '花瓣长度', '花瓣宽度']] = df_prediction[ ['萼片长度', '萼片宽度', '花瓣长度', '花瓣宽度']].astype(float) # 绘图 plt.figure('真实分类') radviz(df_real, '种类', color=['blue', 'green', 'red', 'yellow']) plt.figure('预测分类') radviz(df_prediction, '种类', color=['blue', 'green', 'red', 'yellow']) plt.rcParams['font.sans-serif'] = ['SimHei'] # 显示中文标签 plt.rcParams['axes.unicode_minus'] = False plt.show() if __name__ == "__main__": # 读取数据 data_set = pd.read_csv(train_path, header=None) X = data_set.iloc[:, 0:feature].values.T Y = data_set.iloc[:, feature:].values.T Y = Y.astype('uint8') # 开始训练 parameters = nn_model(X, Y, n_h=hide_num, n_input=feature, n_output=label, num_iterations=learning_num,learning_rate=learning_rate) # 对模型进行测试 data_test = pd.read_csv(test_path, header=None) x_test = data_test.iloc[:, 0:feature].values.T y_test = data_test.iloc[:, feature:].values.T y_test = y_test.astype('uint8') result = predict(parameters, x_test, y_test) # 分类结果可视化(红酒数据集特征数量过多，不绘制) if draw: result_visualization(x_test, y_test, result)