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本文将学习如何利用Python的来实现具有一个隐藏层的平面数据分类问题。
本文的实践平台是Linux，Python3.4，基础库anaconda和spyder，
参考文章的实现平台是jupyter notebook：具有一个隐藏层的平面数据分类代码实战
理论知识学习请参看上篇deeplearning.ai 吴恩达网上课程学习（五）——浅层神经网络理论学习
目的：将创建的“花状”数据集分类
1.使用的数据集：
① 创造数据集是load_planar_dataset()函数，其内容如下：
def load_planar_dataset():np.random.seed(1)m = 400 # 样本数量N = int(m/2) # 每个类别的样本量D = 2 # 维度数X = np.zeros((m,D)) # 初始化XY = np.zeros((m,1), dtype='uint8') # 初始化Ya = 4 # 花儿的最大长度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 # thetar = a*np.sin(4*t) + np.random.randn(N)*0.2 # radiusX[ix] = np.c_[r*np.sin(t), r*np.cos(t)]Y[ix] = jX = X.TY = Y.Treturn X, Ynumpy.random.seed()的使用：https://blog.csdn.net/linzch3/article/details/58220569
作用：使得随机数据可预测。
关于此语句的测试：
import numpy as npnp.random.seed(5)
W1 = np.random.randn(5, 4) * 0.01
np.random.seed(5)
W2 = np.random.randn(5, 4) * 0.01 print ('w1 %d '+str( W1))
print ('w2 %d '+str( W2))
import numpy as npnp.random.seed(5)
W1 = np.random.randn(5, 4) * 0.01
W2 = np.random.randn(5, 4) * 0.01 print ('w1 %d '+str( W1))
print ('w2 %d '+str( W2))
import numpy as npnp.random.seed(5)
W1 = np.random.randn(5, 4) * 0.01
np.random.seed(6)
W2 = np.random.randn(5, 4) * 0.01 print ('w1 %d '+str( W1))
print ('w2 %d '+str( W2))
numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)
在指定的间隔内返回均匀间隔的数字。返回num均匀分布的样本，在[start, stop]。numpy.linspace使用详解：https://blog.csdn.net/you_are_my_dream/article/details/53493752
② 加载数据集，并用图像将其显示出来：
X, Y = load_planar_dataset()
plt.scatter(X[0, :], X[1, :], s=40,c=Y[0,:], cmap=plt.cm.Spectral); # 有修改cmatplotlib.pyplot.scatter(x, y, s=None, c=None, marker=None, cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, verts=None, edgecolors=None, hold=None, data=None, **kwargs)绘制散点图，其中x和y是相同长度的数组序列
matplotlib.pyplot.scatter使用详解：https://blog.csdn.net/anneqiqi/article/details/64125186
注意参数c：
显示结果：
图像像是一朵花儿，X是（2,400）的数组，表示的是位置，也就是有400个样本。y是（1,400）数组，表示的是颜色，对于y=0时，显示为红色的点；而当y=1时，显示的是蓝色的点。
我们的目的是希望建立一个模型可以将两种颜色的点区分开。
2.使用到的库：
import numpy as np
import matplotlib.pyplot as plt
from testCases import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary
from planar_utils import sigmoid
from planar_utils import load_planar_dataset
from planar_utils import load_extra_datasetsnp.random.seed(1) # 设置随机数的seed，保证每次获取的随机数固定3. 使用逻辑回归对上述数据分类：
可以使用我们前面文章的逻辑回归代码进行分类，也可以直接使用sklearn的内置函数来完成。
clf = sklearn.linear_model.LogisticRegressionCV();
clf.fit(X.T, Y.T.ravel());提醒是要对预测输出y做出ravel()转换
接下来，我们用图像来显示出来模型为分界线：
plot_decision_boundary(lambda x: clf.predict(x), X, Y)
plt.title("Logistic Regression")看看精度：
LR_predictions = clf.predict(X.T)
print ('Accuracy of logistic regression: %d ' % float((np.dot(Y,LR_predictions) + np.dot(1-Y,1-LR_predictions))/float(Y.size)*100) +'% ' + "(percentage of correctly labelled datapoints)")
Ps：其中plot_decision_boundary的实现如下：
def plot_decision_boundary(model, X, y):# Set min and max values and give it some paddingx_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1h = 0.01# Generate a grid of points with distance h between themxx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))# Predict the function value for the whole gridZ = model(np.c_[xx.ravel(), yy.ravel()])Z = Z.reshape(xx.shape)# Plot the contour and training examples plt.figure()plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)plt.ylabel('x2')plt.xlabel('x1')plt.scatter(X[0, :], X[1, :], c=y[0,:], cmap=plt.cm.Spectral)
从分割图像和预测准确性上，我们可以看出，由于该数据不是线性可分的，因此，Logistic回归算法无法得到一个令人满意的结果。
4.使用神经网络模型：
步骤① 定义神经网络结构
def layer_sizes(X, Y):"""Arguments:X -- input dataset of shape (input size, number of examples)Y -- labels of shape (output size, number of examples)Returns:n_x -- the size of the input layern_h -- the size of the hidden layern_y -- the size of the output layer"""n_x = X.shape[0] # size of input layern_h = 4n_y = Y.shape[0] # size of output layerreturn (n_x, n_h, n_y)步骤②：初始化模型参数
按照之前理论课的内容，我们需要用一个较小的随机数来初始化W，用零向量初始化b。
def initialize_parameters(n_x, n_h, n_y):"""Argument:n_x -- size of the input layern_h -- size of the hidden layern_y -- size of the output layerReturns:params -- python dictionary containing your parameters:W1 -- weight matrix of shape (n_h, n_x)b1 -- bias vector of shape (n_h, 1)W2 -- weight matrix of shape (n_y, n_h)b2 -- bias vector of shape (n_y, 1)"""np.random.seed(2) W1 = np.random.randn(n_h, n_x) * 0.01 b1 = np.zeros((n_h, 1)) * 0.01 W2 = np.random.randn(n_y, n_h) * 0.01 b2 = np.zeros((n_y, 1)) * 0.01 assert (W1.shape == (n_h, n_x)) #python assert断言是声明其布尔值必须为真的判定，如果发生异常就说明表达示为假。可以理解assert断言语句为raise-if-not，用来测试表示式，其返回值为假，就会触发异常。assert (b1.shape == (n_h, 1))assert (W2.shape == (n_y, n_h))assert (b2.shape == (n_y, 1))parameters = {"W1": W1,"b1": b1,"W2": W2,"b2": b2}return parameters步骤③：循环
首先，我们从前向传播开始：
def forward_propagation(X, parameters):"""Argument:X -- input data of size (n_x, m)parameters -- python dictionary containing your parameters (output of initialization function)Returns:A2 -- The sigmoid output of the second activationcache -- a dictionary containing "Z1", "A1", "Z2" and "A2""""# Retrieve each parameter from the dictionary "parameters"W1 = parameters["W1"]b1 = parameters["b1"]W2 = parameters["W2"]b2 = parameters["b2"]# Implement Forward Propagation to calculate A2 (probabilities)Z1 = np.dot(W1, X) + b1A1 = np.tanh(Z1)Z2 = np.dot(W2, A1) + b2A2 = sigmoid(Z2)assert(A2.shape == (1, X.shape[1]))cache = {"Z1": Z1,"A1": A1,"Z2": Z2,"A2": A2}return A2, cache
def compute_cost(A2, Y, parameters):"""Computes the cross-entropy cost given in equation (13)Arguments:A2 -- The sigmoid output of the second activation, of shape (1, number of examples)Y -- "true" labels vector of shape (1, number of examples)parameters -- python dictionary containing your parameters W1, b1, W2 and b2Returns:cost -- cross-entropy cost given equation (13)"""m = Y.shape[1] # number of example# Compute the cross-entropy costlogprobs = np.multiply(np.log(A2),Y) + np.multiply(np.log(1 - A2), 1 - Y)cost = -np.sum(logprobs) / mcost = np.squeeze(cost) # makes sure cost is the dimension we expect. # E.g., turns [[17]] into 17 assert(isinstance(cost, float))return cost步骤④：反向传播
def backward_propagation(parameters, cache, X, Y):"""Implement the backward propagation using the instructions above.Arguments:parameters -- python dictionary containing our parameters cache -- a dictionary containing "Z1", "A1", "Z2" and "A2".X -- input data of shape (2, number of examples)Y -- "true" labels vector of shape (1, number of examples)Returns:grads -- python dictionary containing your gradients with respect to different parameters"""m = X.shape[1]# First, retrieve W1 and W2 from the dictionary "parameters".W1 = parameters["W1"]W2 = parameters["W2"]# Retrieve also A1 and A2 from dictionary "cache".A1 = cache["A1"]A2 = cache["A2"]# Backward propagation: calculate dW1, db1, dW2, db2. dZ2 = A2 - YdW2 = np.dot(dZ2, A1.T) / mdb2 = np.sum(dZ2, axis=1, keepdims=True) / mdZ1 = np.multiply(np.dot(W2.T, dZ2), (1 - np.power(A1, 2)))dW1 = np.dot(dZ1, X.T) / mdb1 = np.sum(dZ1, axis=1, keepdims=True) / mgrads = {"dW1": dW1,"db1": db1,"dW2": dW2,"db2": db2}return grads
此外，需要说明的是，学习速度选择的适当与否对最终的收敛结果有着很大的影响。
一个合适的学习速率可以使得函数快速且稳定的到达最优值附近。
而一个过大的学习速度会导致其无法正常收敛而出现大幅度的波动：
def update_parameters(parameters, grads, learning_rate = 1.2):"""Updates parameters using the gradient descent update rule given aboveArguments:parameters -- python dictionary containing your parameters grads -- python dictionary containing your gradients Returns:parameters -- python dictionary containing your updated parameters """# Retrieve each parameter from the dictionary "parameters"W1 = parameters["W1"]b1 = parameters["b1"]W2 = parameters["W2"]b2 = parameters["b2"]# Retrieve each gradient from the dictionary "grads"dW1 = grads["dW1"]db1 = grads["db1"]dW2 = grads["dW2"]db2 = grads["db2"]# Update rule for each parameterW1 = W1 - learning_rate * dW1b1 = b1 - learning_rate * db1W2 = W2 - learning_rate * dW2b2 = b2 - learning_rate * db2parameters = {"W1": W1,"b1": b1,"W2": W2,"b2": b2}return parameters接下来，我们希望将之前准备的几个函数整合到模型中，可以方便快速的直接使用：
def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):"""Arguments:X -- dataset of shape (2, number of examples)Y -- labels of shape (1, number of examples)n_h -- size of the hidden layernum_iterations -- Number of iterations in gradient descent loopprint_cost -- if True, print the cost every 1000 iterationsReturns:parameters -- parameters learnt by the model. They can then be used to predict."""np.random.seed(3)n_x = layer_sizes(X, Y)[0]n_y = layer_sizes(X, Y)[2]# Initialize parameters, then retrieve W1, b1, W2, b2. Inputs: "n_x, n_h, n_y". Outputs = "W1, b1, W2, b2, parameters".parameters = initialize_parameters(n_x, n_h, n_y)W1 = parameters["W1"]b1 = parameters["b1"]W2 = parameters["W2"]b2 = parameters["b2"]# Loop (gradient descent)for i in range(0, num_iterations):# Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache".A2, cache = forward_propagation(X, parameters)# Cost function. Inputs: "A2, Y, parameters". Outputs: "cost".cost = compute_cost(A2, Y, parameters)# Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads".grads = backward_propagation(parameters, cache, X, Y)# Gradient descent parameter update. Inputs: "parameters, grads". Outputs: "parameters".parameters = update_parameters(parameters, grads)# Print the cost every 1000 iterationsif print_cost and i % 1000 == 0:print ("Cost after iteration %i: %f" %(i, cost))return parameters注意：在整合模型的时候要把每个图像显示前面加上plt.figure，新建图像显示框，和MATLAB里面的figure一样，否则后面的图像会和前面的图像叠加显示。
步骤流程⑥：预测
def predict(parameters, X):"""Using the learned parameters, predicts a class for each example in XArguments:parameters -- python dictionary containing your parameters X -- input data of size (n_x, m)Returnspredictions -- vector of predictions of our model (red: 0 / blue: 1)"""A2, cache = forward_propagation(X, parameters)predictions = (A2 > 0.5)return predictions用我们的数据集来训练：
parameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True)# Plot the decision boundary
plt.figure()
plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
plt.title("Decision Boundary for hidden layer size " + str(4))
分类曲线如上图所示，接下来，我们使用预测函数计算一下我们模型的预测准确度：
# Print accuracy
predictions = predict(parameters, X)
print ('Accuracy: %d' % float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100) + '%')
# Accuracy: 90%步骤流程期⑦：调整隐藏层神经元数目对结果的影响
我们分别适用包含1,2,3,4,5,20,50个神经元的模型来进行训练：
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 ("Accuracy for {} hidden units: {} %".format(n_h, accuracy))在此学习一下 matplotlib的基本用法(一)——figure的使用
步骤流程期⑧：用其他数据集进行性能测试
noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure = load_extra_datasets()datasets = {"noisy_circles": noisy_circles,"noisy_moons": noisy_moons,"blobs": blobs,"gaussian_quantiles": gaussian_quantiles}### START CODE HERE ### (choose your dataset)
dataset = "noisy_moons"
### END CODE HERE ###X, Y = datasets[dataset]
X, Y = X.T, Y.reshape(1, Y.shape[0])# make blobs binary
if dataset == "blobs":Y = Y%2# Visualize the dataplt.figure()
plt.scatter(X[0, :], X[1, :], c=Y[0,:], s=40, cmap=plt.cm.Spectral);
其中，load_extra_datasets()函数的定义如下：
def load_extra_datasets(): N = 200noisy_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这篇关于deeplearning.ai 吴恩达网上课程学习（六）——浅层神经网络分类代码实战的文章就介绍到这儿，希望我们推荐的文章对编程师们有所帮助！
