def initial_para(nums_feature):
? ? """initial the weights and bias which is zero"""
? ? #nums_feature是輸入數(shù)據(jù)的屬性數(shù)目，因此權(quán)重w是[1, nums_feature]維
? ? #且w和b均初始化為0
? ? w = np.zeros((1, nums_feature))
? ? b = 0
? ? return w, b

2.邏輯回歸方程

def activation(x, w , b):
? ? """a linear function and then sigmoid activation function:?
? ? x_ = w*x +b,y = 1/(1+exp(-x_))"""
? ? #線性方程，輸入的x是[batch, 2]維，輸出是[1, batch]維，batch是模型優(yōu)化迭代一次輸入數(shù)據(jù)的數(shù)目
? ? #[1, 2] * [2, batch] = [1, batch], 所以是w * x.T（x的轉(zhuǎn)置）
? ? #np.dot是矩陣乘法
? ? x_ = np.dot(w, x.T) + b
? ? #np.exp是實現(xiàn)e的x次冪
? ? sigmoid = 1 / (1 + np.exp(-x_))
? ? return sigmoid

3.梯度下降

def gradient_descent_batch(x, w, b, label, learning_rate):
? ? #獲取輸入數(shù)據(jù)的數(shù)目，即batch大小
? ? n = len(label)
? ? #進行邏輯回歸預(yù)測
? ? sigmoid = activation(x, w, b)
? ? #損失函數(shù)，np.sum是將矩陣求和
? ? cost = -np.sum(label.T * np.log(sigmoid) + (1-label).T * np.log(1-sigmoid)) / n
? ? #求對w和b的偏導(dǎo)(即梯度值)
? ? g_w = np.dot(x.T, (sigmoid - label.T).T) / n
? ? g_b = np.sum((sigmoid - label.T)) / n
? ? #根據(jù)梯度更新參數(shù)
? ? w = w - learning_rate * g_w.T
? ? b = b - learning_rate * g_b
? ? return w, b, cost

4.模型優(yōu)化

def optimal_model_batch(x, label, nums_feature, step=10000, batch_size=1):
? ? """train the model with batch"""
? ? length = len(x)
? ? w, b = initial_para(nums_feature)
? ? for i in range(step):
? ? ? ? #隨機獲取一個batch數(shù)目的數(shù)據(jù)
? ? ? ? num = randint(0, length - 1 - batch_size)
? ? ? ? x_batch = x[num:(num+batch_size), :]
? ? ? ? label_batch = label[num:num+batch_size]
? ? ? ? #進行一次梯度更新(優(yōu)化)
? ? ? ? w, b, cost = gradient_descent_batch(x_batch, w, b, label_batch, 0.0001)
? ? ? ? #每1000次打印一下?lián)p失值
? ? ? ? if i%1000 == 0:
? ? ? ? ? ? print('step is : ', i, ', cost is: ', cost)
? ? return w, b

5.讀取數(shù)據(jù)，數(shù)據(jù)預(yù)處理，訓(xùn)練模型，評估精度

import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from random import randint
from sklearn.preprocessing import StandardScaler
?
def _main():
? ? #讀取csv格式的數(shù)據(jù)data_path是數(shù)據(jù)的路徑
? ? data = pd.read_csv('data_path')
? ? #獲取樣本屬性和標簽
? ? x = data.iloc[:, 2:4].values
? ? y = data.iloc[:, 4].values
? ? #將數(shù)據(jù)集分為測試集和訓(xùn)練集
? ? x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.2, random_state=0)
? ? #數(shù)據(jù)預(yù)處理，去均值化
? ? standardscaler = StandardScaler()
? ? x_train = standardscaler.fit_transform(x_train)
? ? x_test = standardscaler.transform(x_test)
? ? #w, b = optimal_model(x_train, y_train, 2, 50000)
? ? #訓(xùn)練模型
? ? w, b = optimal_model_batch(x_train, y_train, 2, 50000, 64)
? ? print('trian is over')
? ? #對測試集進行預(yù)測，并計算精度
? ? predict = activation(x_test, w, b).T
? ? n = 0
? ? for i, p in enumerate(predict):
? ? ? ? if p >=0.5:
? ? ? ? ? ? if y_test[i] == 1:
? ? ? ? ? ? ? ? n += 1
? ? ? ? else:
? ? ? ? ? ? if y_test[i] == 0:
? ? ? ? ? ? ? ? n += 1
? ? print('accuracy is : ', n / len(y_test))

6.結(jié)果可視化

predict = np.reshape(np.int32(predict), [len(predict)])
? ? #將預(yù)測結(jié)果以散點圖的形式可視化
? ? for i, j in enumerate(np.unique(predict)):
? ? ? ? plt.scatter(x_test[predict == j, 0], x_test[predict == j, 1],?
? ? ? ? c = ListedColormap(('red', 'blue'))(i), label=j)
? ? plt.show()