实现双层神经网络

1.工具文件帮助加载数据和画出决策边界，以及一些函数的辅助

import matplotlib.pyplot as plt
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model


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)



def sigmoid(x):
    s = 1/(1+np.exp(-x))
    return s

def load_planar_dataset():
    np.random.seed(1)
    m = 400 # number of examples
    N = int(m/2) # number of points per class
    D = 2 # dimensionality
    X = np.zeros((m,D)) # data matrix where each row is a single example
    Y = np.zeros((m,1), dtype='uint8') # labels vector (0 for red, 1 for blue)
    a = 4 # maximum ray of the flower

    for j in range(2):
        ix = range(N*j,N*(j+1))
        t = np.linspace(j*3.12,(j+1)*3.12,N) + np.random.randn(N)*0.2 # theta
        r = a*np.sin(4*t) + np.random.randn(N)*0.2 # radius
        X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
        Y[ix] = j

    X = X.T
    Y = Y.T

    return X, Y

def load_extra_datasets():  
    N = 200
    noisy_circles = sklearn.datasets.make_circles(n_samples=N, factor=.5, noise=.3)
    noisy_moons = sklearn.datasets.make_moons(n_samples=N, noise=.2)
    blobs = sklearn.datasets.make_blobs(n_samples=N, random_state=5, n_features=2, centers=6)
    gaussian_quantiles = sklearn.datasets.make_gaussian_quantiles(mean=None, cov=0.5, n_samples=N, n_features=2, n_classes=2, shuffle=True, random_state=None)
    no_structure = np.random.rand(N, 2), np.random.rand(N, 2)

    return noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure

2.实现双层神经网络的代码

#!/usr/bin/env python
# _*_ coding:utf-8 _*_

import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets

np.random.seed(1)  # 设置一个固定的随机种子，以保证接下来的步骤中我们的结果是一致的。

# 1.加载和查看数据集，x的维度为（2,400），y的维度为（1,400）
X, Y = load_planar_dataset()
# 查看数据集的代码
# z=np.squeeze(Y)变成秩为1的数组，才可以赋值给c
# plt.scatter(X[0,:],X[1,:],c=np.squeeze(Y),s=40,cmap=plt.cm.Spectral)
# plt.show()


# 2.查看逻辑回归的效果
clf = sklearn.linear_model.LogisticRegressionCV()
clf.fit(X.T, Y.T)


# 绘制决策边界
# plot_decision_boundary(lambda x: clf.predict(x),X,Y)
# plt.title("Logistic Regression")  # 图标题
# LR_predictions  = clf.predict(X.T)  # 预测结果
# print ("逻辑回归的准确性： %d " % float((np.dot(Y, LR_predictions) +
#         np.dot(1 - Y,1 - LR_predictions)) / float(Y.size) * 100) +
#        "% " + "(正确标记的数据点所占的百分比)")


# 3.搭建神经网络
# 3.1定义神经网络的结构
def layer_sizes(X, Y):
    n_x = X.shape[0]
    n_h = 4
    n_y = Y.shape[0]

    return (n_x, n_h, n_y)


# 3.2初始化模型参数
def initialize_parameters(n_x, n_h, n_y):
    np.random.seed(2)
    w1 = np.random.rand(n_h, n_x) * 0.01
    b1 = np.zeros(shape=(n_h, 1))
    w2 = np.random.rand(n_y, n_h) * 0.01
    b2 = np.zeros(shape=(n_y, 1))

    paramemters = {
        "W1": w1,
        "b1": b1,
        "W2": w2,
        "b2": b2
    }
    return paramemters


# 3.3向前传播
def forward_propagation(X, parameters):
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]

    # 计算
    Z1 = np.dot(W1, X) + b1
    A1 = np.tanh(Z1)
    Z2 = np.dot(W2, A1) + b2
    A2 = sigmoid(Z2)

    assert (A2.shape == (1, X.shape[1]))

    cache = {
        "Z1": Z1,
        "A1": A1,
        "Z2": Z2,
        "A2": A2
    }
    return (A2, cache)


# 3.3定义损失函数
def compute_cost(A2, Y, parameters):
    m = Y.shape[1]
    logprobs = np.multiply(np.log(A2), Y) + np.multiply(np.log(1 - A2), 1 - Y)
    cost = -np.sum(logprobs) / m
    cost = float(np.squeeze(cost))

    return cost


# 3.4定义后向传播函数
def backward_propagation(parameters, cache, X, Y):
    A2 = cache["A2"]
    A1 = cache["A1"]

    W2 = parameters["W2"]

    m = Y.shape[1]

    dz2 = A2 - Y
    dw2 = np.dot(dz2, A1.T) * (1 / m)
    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,
        "dw2": dw2,
        "db1": db1,
        "db2": db2
    }
    return grads


# 3.5定义更新函数
def update_parameters(parameters, grads, learning_rate=1.2):
    W1 = parameters["W1"]
    W2 = parameters["W2"]
    b1 = parameters["b1"]
    b2 = parameters["b2"]

    dw1, dw2 = grads["dw1"], grads["dw2"]
    db1, db2 = grads["db1"], grads["db2"]

    W1 = W1 - learning_rate * dw1
    b1 = b1 - learning_rate * db1
    W2 = W2 - learning_rate * dw2
    b2 = b2 - learning_rate * db2

    parameters = {
        "W1": W1,
        "W2": W2,
        "b1": b1,
        "b2": b2

    }
    return parameters


# 4.整合
def nn_model(X, Y, n_h, num_iterations, print_cost=False):
    np.random.seed(3)
    n_x = layer_sizes(X, Y)[0]
    n_y = layer_sizes(X, Y)[2]

    parameters = initialize_parameters(n_x, n_h, n_y)

    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]

    for i in range(num_iterations):
        A2, cache = forward_propagation(X, parameters)
        cost = compute_cost(A2, Y, parameters)
        grads = backward_propagation(parameters, cache, X, Y)
        parameters = update_parameters(parameters, grads, learning_rate=0.5)

        if print_cost:
            if i % 1000 == 0:
                print("第", i, "次循环，成本为：" + str(cost))

    return parameters


# 5.预测
def predict(parameters, X):
    A2, cache = forward_propagation(X, parameters)
    predictions = np.round(A2)
    return predictions


# 6.正式运行
# parameters = nn_model(X, Y, n_h=4, num_iterations=10000, print_cost=True)
#
# # 绘制边界
# plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
#
# predictions = predict(parameters, X)
# print("准确率：" + str(float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size) * 100)) + "%")


# 7.更改隐藏层节点数量
plt.figure(figsize=(16, 32))

hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 50]

for i, n_h in enumerate(hidden_layer_sizes):
    plt.subplot(5, 2, i + 1)
    plt.title("Hidden Layer of size %d" % n_h)
    parameters = nn_model(X, Y, n_h, num_iterations=5000)
    plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
    predictions = predict(parameters, X)
    accuracy = float(np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size) * 100
    print("隐藏层节点数量：{},准确率：{}".format(n_h, accuracy))

plt.show()

参考链接

https://blog.csdn.net/u013733326/article/details/79702148