使用BP神经网络完成对数据集分类，完整代码
分步讲解代码见：手动实现BP神经网络
'''搭建一个可以运行在不同优化器模式下的 3 层神经网络模型（网络层节点数 目分别为：5,2,1），对“月亮”数据集进行分类。
1) 在不使用优化器的情况下对数据集分类，并可视化表示。
2) 将优化器设置为具有动量的梯度下降算法，可视化表示分类结果。
3) 将优化器设置为 Adam 算法，可视化分类结果。
4) 总结不同算法的分类准确度以及代价曲线的平滑度。
注：以上算法均手动实现，提供数据集读取代码及相关方法代码。'''
# 导入需要的库
import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
import math
# 定义列表，用于存储cost值，方便后期画曲线
loss = []
accuracy = []
################################################## 以下是题给代码 ###########################################
def sigmoid(x):
"""
Compute the sigmoid of x
Arguments:
x -- A scalar or numpy array of any size.
Return:
s -- sigmoid(x)
"""
s = 1 / (1 + np.exp(-x))
return s
def relu(x):
"""
Compute the relu of x
Arguments:
x -- A scalar or numpy array of any size.
Return:
s -- relu(x)
"""
s = np.maximum(0, x)
return s
def forward_propagation(X, parameters):
"""
Implements the forward propagation (and computes the loss) presented in Figure 2.
Arguments:
X -- input dataset, of shape (input size, number of examples)
parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
W1 -- weight matrix of shape ()
b1 -- bias vector of shape ()
W2 -- weight matrix of shape ()
b2 -- bias vector of shape ()
W3 -- weight matrix of shape ()
b3 -- bias vector of shape ()
Returns:
loss -- the loss function (vanilla logistic loss)
"""
# retrieve parameters
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
W3 = parameters["W3"]
b3 = parameters["b3"]
# LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID
z1 = np.dot(W1, X) + b1
a1 = relu(z1)
z2 = np.dot(W2, a1) + b2
a2 = relu(z2)
z3 = np.dot(W3, a2) + b3
a3 = sigmoid(z3)
cache = (z1, a1, W1, b1, z2, a2, W2, b2, z3, a3, W3, b3)
return a3, cache
def predict(X, y, parameters):
"""
This function is used to predict the results of a n-layer neural network.
Arguments:
X -- data set of examples you would like to label
parameters -- parameters of the trained model
Returns:
p -- predictions for the given dataset X
"""
m = X.shape[1]
p = np.zeros((1, m), dtype=int)
# Forward propagation
a3, caches = forward_propagation(X, parameters)
# convert probas to 0/1 predictions
for i in range(0, a3.shape[1]):
if a3[0, i] > 0.5:
p[0, i] = 1
else:
p[0, i] = 0
# print results
# print ("predictions: " + str(p[0,:]))
# print ("true labels: " + str(y[0,:]))
print("Accuracy: " + str(np.mean((p[0, :] == y[0, :]))))
return p
def predict_dec(X, parameters):
"""
Used for plotting decision boundary.
Arguments:
parameters -- python dictionary containing your parameters
X -- input data of size (m, K)
Returns
predictions -- vector of predictions of our model (red: 0 / blue: 1)
"""
# Predict using forward propagation and a classification threshold of 0.5
a3, cache = forward_propagation(X, parameters)
predictions = (a3 > 0.5)
return predictions
def load_dataset(is_plot=True):
np.random.seed(3)
train_X, train_Y = sklearn.datasets.make_moons(n_samples=300, noise=.2) # 300 #0.2
# Visualize the data
if is_plot:
plt.scatter(train_X[:, 0], train_X[:, 1], c=train_Y, s=40, cmap=plt.cm.Spectral)
plt.show() # 显示“月亮”数据
train_X = train_X.T
train_Y = train_Y.reshape((1, train_Y.shape[0]))
return train_X, train_Y
##可视化分割线
def plot_decision_boundary(model, X, y):
# Set min and max values and give it some padding
x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1
y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1
h = 0.01
# Generate a grid of points with distance h between them
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
# Predict the function value for the whole grid
Z = model(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
# Plot the contour and training examples
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
plt.ylabel('x2')
plt.xlabel('x1')
plt.scatter(X[0, :], X[1, :], c=np.squeeze(y), cmap=plt.cm.Spectral)
plt.show()
############################################## 以上是题给代码 ###########################################
# 初始化模型的参数
def initialize_parameters(n_x, n1, n2, n_y):
"""
参数：
n_x - 输入层节点的数量 2
n1,n2 - 隐藏层节点的数量 5 2
n_y - 输出层节点的数量 1
返回：
parameters - 包含参数的字典
说明：如果允许将节点数改变，似效果更好些
"""
np.random.seed(3) # 指定一个随机种子
W1 = np.random.randn(n1, n_x) * 1.0
b1 = np.zeros((n1, 1))
W2 = np.random.randn(n2, n1) * 2.0
b2 = np.zeros((n2, 1))
W3 = np.random.randn(n_y, n2) * 1.0
b3 = np.zeros((n_y, 1))
parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2,
"W3": W3,
"b3": b3}
return parameters
# 反向传播，得到梯度
def backward_propagation(cache, X, Y):
m = X.shape[1]
(Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3) = cache
dZ3 = 1./ m * (A3 - Y)
dW3 = np.dot(dZ3, A2.T)
db3 = np.sum(dZ3, axis=1, keepdims=True)
dA2 = np.dot(W3.T, dZ3)
dZ2 = np.multiply(dA2, np.int64(A2 > 0))
dW2 = np.dot(dZ2, A1.T)
db2 = np.sum(dZ2, axis=1, keepdims=True)
dA1 = np.dot(W2.T, dZ2)
dZ1 = np.multiply(dA1, np.int64(A1 > 0))
dW1 = np.dot(dZ1, X.T)
db1 = np.sum(dZ1, axis=1, keepdims=True)
grads = {"dW3": dW3, "db3": db3,
"dW2": dW2, "db2": db2,
"dW1": dW1, "db1": db1}
return grads
# 计算cost值
def cost_computing(A, Y):
m = Y.shape[1]
logloss = np.multiply(np.log(A), Y) + np.multiply((1 - Y), np.log(1 - A))
cost = - np.sum(logloss) / m
return cost
# SGD优化器
def sgd(parameters, grads, learning_rate):
W1, W2, W3 = parameters["W1"], parameters["W2"], parameters["W3"]
b1, b2, b3 = parameters["b1"], parameters["b2"], parameters["b3"]
dW1, dW2, dW3 = grads["dW1"], grads["dW2"], grads["dW3"]
db1, db2, db3 = grads["db1"], grads["db2"], grads["db3"]
W1 = W1 - learning_rate * dW1
b1 = b1 - learning_rate * db1
W2 = W2 - learning_rate * dW2
b2 = b2 - learning_rate * db2
W3 = W3 - learning_rate * dW3
b3 = b3 - learning_rate * db3
parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2,
"W3": W3,
"b3": b3}
return parameters
# 随机批次分配 本段参考csdn其他博主文章
def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):
"""
Creates a list of random minibatches from (X, Y)
Arguments:
X -- input data, of shape (input size, number of examples)
Y -- true "label" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)
mini_batch_size -- size of the mini-batches, integer
Returns:
mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)
"""
np.random.seed(seed) # To make your "random" minibatches the same as ours
m = X.shape[1] # number of training examples
mini_batches = []
# Step 1: Shuffle (X, Y)
permutation = list(np.random.permutation(m))
shuffled_X = X[:, permutation]
shuffled_Y = Y[:, permutation].reshape((1,m))
# Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.
num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning
for k in range(0, num_complete_minibatches):
### START CODE HERE ### (approx. 2 lines)
mini_batch_X = shuffled_X[:, k*mini_batch_size : (k+1)*mini_batch_size]
mini_batch_Y = shuffled_Y[:, k*mini_batch_size : (k+1)*mini_batch_size]
### END CODE HERE ###
mini_batch = (mini_batch_X, mini_batch_Y)
mini_batches.append(mini_batch)
# Handling the end case (last mini-batch < mini_batch_size)
if m % mini_batch_size != 0:
### START CODE HERE ### (approx. 2 lines)
mini_batch_X = shuffled_X[:, num_complete_minibatches*mini_batch_size : m]
mini_batch_Y = shuffled_Y[:, num_complete_minibatches*mini_batch_size : m]
### END CODE HERE ###
mini_batch = (mini_batch_X, mini_batch_Y)
mini_batches.append(mini_batch)
return mini_batches
# SGDM优化器（包含两个函数：初始化和参数更新迭代）
def initialize_sgdm(parameters):
dW1 = np.zeros(parameters["W1"].shape)
db1 = np.zeros(parameters["b1"].shape)
dW2 = np.zeros(parameters["W2"].shape)
db2 = np.zeros(parameters["b2"].shape)
dW3 = np.zeros(parameters["W3"].shape)
db3 = np.zeros(parameters["b3"].shape)
v = {"dW1": dW1, "db1": db1,
"dW2": dW2, "db2": db2,
"dW3": dW3, "db3": db3}
return v
def sgdm(parameters, grads, v, beta, learning_rate):
v["dW1"] = beta * v["dW1"] + (1-beta) * grads["dW1"]
v["db1"] = beta * v["db1"] + (1-beta) * grads["db1"]
v["dW2"] = beta * v["dW2"] + (1-beta) * grads["dW2"]
v["db2"] = beta * v["db2"] + (1-beta) * grads["db2"]
v["dW3"] = beta * v["dW3"] + (1-beta) * grads["dW3"]
v["db3"] = beta * v["db3"] + (1-beta) * grads["db3"]
parameters["W1"] = parameters["W1"] - learning_rate * v["dW1"]
parameters["b1"] = parameters["b1"] - learning_rate * v["db1"]
parameters["W2"] = parameters["W2"] - learning_rate * v["dW2"]
parameters["b2"] = parameters["b2"] - learning_rate * v["db2"]
parameters["W3"] = parameters["W3"] - learning_rate * v["dW3"]
parameters["b3"] = parameters["b3"] - learning_rate * v["db3"]
return parameters, v
# ADAM优化器（包含两个函数：初始化和参数更新迭代）
def initialize_adam(parameters) :
v = {}
s = {}
v["dW1"] = np.zeros(parameters["W1"].shape)
v["db1"] = np.zeros(parameters["b1"].shape)
s["dW1"] = np.zeros(parameters["W1"].shape)
s["db1"] = np.zeros(parameters["b1"].shape)
v["dW2"] = np.zeros(parameters["W2"].shape)
v["db2"] = np.zeros(parameters["b2"].shape)
s["dW2"] = np.zeros(parameters["W2"].shape)
s["db2"] = np.zeros(parameters["b2"].shape)
v["dW3"] = np.zeros(parameters["W3"].shape)
v["db3"] = np.zeros(parameters["b3"].shape)
s["dW3"] = np.zeros(parameters["W3"].shape)
s["db3"] = np.zeros(parameters["b3"].shape)
return v, s
# 本段程序关于v和s的更新参考优快云他人代码，其中，ADAM优化器中参数的取值为ADAM算法作者建议的取值
def adam(parameters, grads, v, s, t, learning_rate, epsilon, beta1 = 0.9, beta2 = 0.999):
v_t = {}
s_t = {} # ADAM中包含了两个动量字典，要分别初始化，分别建立校正
v["dW1"] = beta1 * v["dW1"] + (1 - beta1) * grads['dW1']
v["db1"] = beta1 * v["db1"] + (1 - beta1) * grads['db1']
v["dW2"] = beta1 * v["dW2"] + (1 - beta1) * grads['dW2']
v["db2"] = beta1 * v["db2"] + (1 - beta1) * grads['db2']
v["dW3"] = beta1 * v["dW3"] + (1 - beta1) * grads['dW3']
v["db3"] = beta1 * v["db3"] + (1 - beta1) * grads['db3']
v_t["dW1"] = v["dW1"] / (1 - beta1 ** t)
v_t["db1"] = v["db1"] / (1 - beta1 ** t)
v_t["dW2"] = v["dW2"] / (1 - beta1 ** t)
v_t["db2"] = v["db2"] / (1 - beta1 ** t)
v_t["dW3"] = v["dW3"] / (1 - beta1 ** t)
v_t["db3"] = v["db3"] / (1 - beta1 ** t)
s["dW1"] = s["dW1"] + (1 - beta2) * (grads['dW1'] ** 2)
s["db1"] = s["db1"] + (1 - beta2) * (grads['db1'] ** 2)
s["dW2"] = s["dW2"] + (1 - beta2) * (grads['dW2'] ** 2)
s["db2"] = s["db2"] + (1 - beta2) * (grads['db2'] ** 2)
s["dW3"] = s["dW3"] + (1 - beta2) * (grads['dW3'] ** 2)
s["db3"] = s["db3"] + (1 - beta2) * (grads['db3'] ** 2)
s_t["dW1"] = s["dW1"] / (1 - beta2 ** t)
s_t["db1"] = s["db1"] / (1 - beta2 ** t)
s_t["dW2"] = s["dW2"] / (1 - beta2 ** t)
s_t["db2"] = s["db2"] / (1 - beta2 ** t)
s_t["dW3"] = s["dW3"] / (1 - beta2 ** t)
s_t["db3"] = s["db3"] / (1 - beta2 ** t)
mdW1 = v_t["dW1"] / (np.sqrt(s_t["dW1"]) + epsilon)
mdb1 = v_t["db1"] / (np.sqrt(s_t["db1"]) + epsilon)
mdW2 = v_t["dW2"] / (np.sqrt(s_t["dW2"]) + epsilon)
mdb2 = v_t["db2"] / (np.sqrt(s_t["db2"]) + epsilon)
mdW3 = v_t["dW3"] / (np.sqrt(s_t["dW3"]) + epsilon)
mdb3 = v_t["db3"] / (np.sqrt(s_t["db3"]) + epsilon)
parameters["W1"] = parameters["W1"] - learning_rate * mdW1
parameters["b1"] = parameters["b1"] - learning_rate * mdb1
parameters["W2"] = parameters["W2"] - learning_rate * mdW2
parameters["b2"] = parameters["b2"] - learning_rate * mdb2
parameters["W3"] = parameters["W3"] - learning_rate * mdW3
parameters["b3"] = parameters["b3"] - learning_rate * mdb3
return parameters, v, s
def model(Xtrain, Ytrain, n1, n2, EPOCHS, optimizer, learning_rate, epsilon, mompara, beta2):
"""
参数：
X - 数据集
Y - 标签
n1, n2 - 隐藏层节点数
iterations - 梯度下降循环中的迭代次数
optimizer - 优化器选择
learning_rate - 学习率
mompara - 动量系数
accplot - 绘图开关
返回：
parameters - 模型学习的参数，它们可以用来进行预测。
"""
global s
np.random.seed(3) # 指定随机种子
n_x, n_y = Xtrain.shape[0], Ytrain.shape[0]
t = 0
v = {}
seed = 10
cost = 0
parameters = initialize_parameters(n_x, n1, n2, n_y)
# 初始化动量
if optimizer == 'SGDM':
v = initialize_sgdm(parameters)
elif optimizer == 'ADAM':
v, s = initialize_adam(parameters)
else: pass # SGD不需要初始化动量
print("================== 训练神经网络 ======================")
for i in range(EPOCHS):
seed = seed + 1
minibatches = random_mini_batches(Xtrain, Ytrain, 64, seed)
for minibatch in minibatches:
(minibatch_X, minibatch_Y) = minibatch
A, cache = forward_propagation(minibatch_X, parameters)
cost = cost_computing(A, minibatch_Y)
predictions = predict(Xtest, Ytest, parameters)
accuracy.append(float((np.dot(Ytest, predictions.T) + np.dot(1 - Ytest, 1 - predictions.T)) / float(Ytest.size) * 100))
loss.append(cost)
grads = backward_propagation(cache, minibatch_X, minibatch_Y)
# 根据optimizer选择合适的优化器
if optimizer == "SGD":
parameters = sgd(parameters, grads, learning_rate)
elif optimizer == "SGDM":
parameters, v = sgdm(parameters, grads, v, mompara, learning_rate)
elif optimizer == "ADAM":
t = t + 1 # Adam counter
parameters, v, s = adam(parameters, grads, v, s, t, learning_rate, epsilon, mompara, beta2)
if i % (EPOCHS/10) == 0:
print("第 ", i, " 次循环，cost为：" + str(cost))
return parameters
##读取数据集代码
train_X, train_Y = load_dataset(is_plot=True) # 获取数据集
print(train_X.shape, train_Y.shape)
# 分割数据集为训练集和测试集
Xtrain = train_X[0:2, 0:270]
Ytrain = train_Y[0:1, 0:270]
Xtest = train_X[0:2 , 271:300]
Ytest = train_Y[0:1 , 271:300]
# 题目要求的层节点数量，输出是一个向量，默认就是1了，可以通过 Ytrain.shape[0] 求得
n1 = 5
n2 = 2
# 设置参数：迭代总数，使用的优化器，学习率，动量系数，所有的参数请在这里修改
EPOCHS = 1000
optimizer = 'ADAM' # 修改这里为'SGD' 'SGDM' 'ADAM' 以使用不同的优化器
learning_rate = 0.1
mompara = 0.9
beta2 = 0.999
epsilon = 1e-8
# 训练网络
parameters = model(Xtrain, Ytrain, n1, n2, EPOCHS, optimizer, learning_rate, epsilon, mompara, beta2)
# 绘制损失函数曲线
plt.plot(np.array(loss))
plt.title('Loss function plot with ' + optimizer)
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.show()
# 绘制准确率曲线
plt.plot(np.array(accuracy))
plt.title('Accuracy plot with ' + optimizer)
plt.xlabel('Epoch')
plt.ylabel('Accuracy')
plt.show()
# 绘制边界
print("=================================== 绘制边界 ===================================")
axes = plt.gca()
plot_decision_boundary(lambda x: predict_dec(x.T,parameters), train_X, train_Y)
predictions = predict(Xtest, Ytest, parameters)
print('准确率: %d' % float((np.dot(Ytest, predictions.T) + np.dot(1 - Ytest, 1 - predictions.T)) / float(Ytest.size) * 100) + '%')
运行结果（以Adam为例）：
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