Author: 相忠良(Zhong-Liang Xiang)
Email: ugoood@163.com
Date: Sep. 23st, 2017
根据 Andrew Ng 老师的深度学习课程课后作业及指导，参照吴老师代码完成了这个LR的coding．
(重要)吴老师建议,数据应组织成下列形式，有利于扫除编程bug：
- X.shape = (n_x, m), n_x是样本维度，m是样本个数
- Y.shape = (1, m)
- w, b应该分开，其中:
- b is a scaler
- w.shape = (n_x, 1)
- A = sigmoid(np.dot(w.T, X)+b), A.shape = (1, m)
- dw.shape = (n_x, 1)
- db is a scaler
- dZ = A - Y, dZ.shape = A.shape = Y.shape = (1, m)
- 重要建议:
- 勇于使用 reshape, 使之成为我们需要的维度, 要始终使用明确维度的行、列向量和 matrix;
- 绝不使用 a = np.random.randn(5), a.shape = (5,)这种"rank 1 array".因为这东西使用时不符合直觉;
- 应该用 a = np.random.randn(5,1) 或者 (1,5) 这种非常明确的列或行向量(very important)!
- 若出现2所示内容，解决办法是：a = a.reshape(5,1) 或者 (1,5)重新明确shape!;
- 要经常并随意使用 assert(a.shape == (5,1)) 这种断言;
- 要仔细检查我们的 matrix, vector的维度.
符合上述规则和自己的总结，编出个机器学习算法就很简单了．
我整合吴老师的课后作业，加了少许修改，做出 Logisitc Regression 算法的代码, 如下:
# !/usr/bin/python
# -*- coding:utf-8 -*-
"""
Re-implement Logistic Regression algorithm as a practice
使用该 LR re-implement 的前提：
Due to the binary classifier of LR
The label of a sample must be as probability
train data 的标签必须转成0,1的形式
"""
# Author: 相忠良(Zhong-Liang Xiang) <ugoood@163.com>
# Finished on September 23rd, 2017
import h5py
import numpy as np
def load_dataset():
train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")
train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features
train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels
test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")
test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features
test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels
classes = np.array(test_dataset["list_classes"][:]) # the list of classes
train_set_y_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))
test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))
return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes
def load_data():
train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes = load_dataset()
train_X = (train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T) / 255. # flatten and divide 255
test_X = (test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T) / 255. # flatten and divide 255
return train_X, train_set_y_orig, test_X, test_set_y_orig, classes
def sigmoid(z):
"""
Compute the sigmoid of z
Arguments:
z -- A scalar or numpy array of any size.
Return:
s -- sigmoid(z)
"""
s = 1.0 / (1 + np.exp(-z))
return s
def init_with_zeros(dim):
"""
This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.
Argument:
dim -- size of the w vector we want (or number of parameters in this case)
Returns:
w -- initialized vector of shape (dim, 1)
b -- initialized scalar (corresponds to the bias)
"""
w = np.zeros((dim, 1))
b = 0
assert (w.shape == (dim, 1))
assert (isinstance(b, float) or isinstance(b, int))
return w, b
def propagate(w, b, X, Y):
"""
Implement the cost function and its gradient for the propagation
Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of size (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)
Return:
cost -- negative log-likelihood cost for logistic regression
dw -- gradient of the loss with respect to w, thus same shape as w
db -- gradient of the loss with respect to b, thus same shape as b
"""
# FORWARD PROPAGATION(FROM X TO COST)
m = X.shape[1] # 样本个数
A = sigmoid(np.dot(w.T, X) + b) # activation (1 * m)
cost = (np.dot(np.log(A), Y.T) + np.dot(np.log(1 - A), (1 - Y).T)) / -m # a scaler
# BACKWARD PROPAGATION (TO FIND GRAD)
dZ = A - Y # (1 * m)
dw = np.dot(X, dZ.T) / m # (n_x, 1) n_x 是 样本的维度
db = np.sum(dZ) / m # a scaler
# ASSERT
assert (dw.shape == w.shape)
assert (db.dtype == float)
cost = np.squeeze(cost) # 变成个数字
assert (cost.shape == ())
grads = {"dw": dw,
"db": db}
return grads, cost
def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost):
"""
This function optimizes w and b by running a gradient descent algorithm
Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of shape (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
num_iterations -- number of iterations of the optimization loop
learning_rate -- learning rate of the gradient descent update rule
print_cost -- True to print the loss every 100 steps
Returns:
params -- dictionary containing the weights w and bias b
grads -- dictionary containing the gradients of the weights and bias with respect to the cost function
costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.
"""
costs = [] # 将迭代过程中算出的cost收集起来
for i in range(num_iterations):
# Cost and gradient calculation
grads, cost = propagate(w, b, X, Y)
# Retrieve derivatives from grads
dw = grads["dw"]
db = grads["db"]
# update dw, db
w = w - learning_rate * dw
b = b - learning_rate * db
# Record the costs
if i % 100 == 0:
costs.append(cost)
# Print the cost every 100 iterations
if print_cost and i % 100 == 0:
print("Cost after iteration %i: %f" % (i, cost))
params = {"w": w,
"b": b}
grads = {"dw": dw,
"db": db}
return params, grads, costs
class MyLogisticRegression:
costs = []
params = {} # w, b
grads = {} # dw, db
num_iterations = 0
learning_rate = 0.
print_cost = False
def __init__(self, num_iterations=1000, learning_rate=0.01, print_cost=False):
# 初始化超參數 num_iterations, learning_rate
self.num_iterations = num_iterations
self.learning_rate = learning_rate
self.print_cost = print_cost
return
def fit(self, X, Y):
n_x = X.shape[0] # dim of X
w, b = init_with_zeros(n_x) # initialize w,b with zeros, w.shape=(n_x, 1), b=0 a scaler.
# 前向传播获取cost,反向传播获取grads,并更新params．这种事情做了num_iterations次，学习率为learning_rate
self.params, self.grads, self.costs = optimize(w, b, X, Y, self.num_iterations, self.learning_rate,
self.print_cost)
# fit函数的结果是获取params.顺便得到了grads, costs, 便于我们查看并对costs画图，以检查模型是否学到了东西．
def predict(self, X):
m = X.shape[1] # the number of samples
Y_predict = np.zeros((1, m)) # initialize Y_predict
w = self.params["w"] # 获取已经训练好的 w
b = self.params["b"] # 获取已经训练好的 b
A = sigmoid(np.dot(w.T, X) + b) # 根据 训练好的w,b,计算 p(Y=1|X)
# 将预测概率p(Y=1|X)转换为标签值， 大于0.5的标签值为１，否则为０
for i in range(A.shape[1]):
Y_predict[0, i] = 1 if A[0, i] > 0.5 else 0
assert (Y_predict.shape == (1, m))
return Y_predict
def score(self, X, y):
pass
## 测试用例
train_X, train_y, test_X, test_y, classes = load_data()
cls = MyLogisticRegression(num_iterations=2000, learning_rate=0.005, print_cost=True)
cls.fit(train_X, train_y)
Y_predict_test = cls.predict(test_X)
Y_predict_train = cls.predict(train_X)
print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_predict_train - train_y)) * 100))
print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_predict_test - test_y)) * 100))
"""
运行结果
/usr/bin/python2.7 /home/xiang/桌面/ML_Course_20170314/xiang_code/Xiang_ml_in_practice/MyLogisticRegression.py
Cost after iteration 0: 0.693147
Cost after iteration 100: 0.584508
Cost after iteration 200: 0.466949
Cost after iteration 300: 0.376007
Cost after iteration 400: 0.331463
Cost after iteration 500: 0.303273
Cost after iteration 600: 0.279880
Cost after iteration 700: 0.260042
Cost after iteration 800: 0.242941
Cost after iteration 900: 0.228004
Cost after iteration 1000: 0.214820
Cost after iteration 1100: 0.203078
Cost after iteration 1200: 0.192544
Cost after iteration 1300: 0.183033
Cost after iteration 1400: 0.174399
Cost after iteration 1500: 0.166521
Cost after iteration 1600: 0.159305
Cost after iteration 1700: 0.152667
Cost after iteration 1800: 0.146542
Cost after iteration 1900: 0.140872
train accuracy: 99.043062201 %
test accuracy: 70.0 %
"""
