任务：将400个两种颜色的点用背景色分为两类。
前面的还是建议重点学神经网络知识，至于数据集怎么做的后面在深究，首先先看看数据集，代码如下：
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
打印看看返回的X,Y
由于X太多不方便粘贴，只打印了shape,可看出X是2行400列的矩阵（2，400），Y是1行400列矩阵（1，400）。
然后用X的数据作为二维的坐标点，Y的0，1作为分类点，比如0代表红色点，1代表蓝色点，这样400个两种颜色的点就可以显示出来，代码如下：
""" 测试函数：实现数据集的显示 """ def test(): X,Y=planar_utils.load_planar_dataset() plt.scatter(X[0,:],X[1,:],c=np.squeeze(Y),s = 80,cmap=plt.cm.Spectral) plt.show()
显示结果如下：
利用两层神经网络，一层隐藏层，一层输出层，400个点，所以有400个样本，两种特征（两种颜色），所以输入层节点是2个，隐藏层定义4个节点，输出层1个节点，脑海里就有神经网络的结构图了,故W1(4,2),b1(4,1),W2(1,4),b2(1,1)简单的演示一遍。Z1=W1*X=(4,400),Z2=W2*Z1=(1,400),就对应Y的维度了。中间加激活函数和b值不影响维度
具体公式推导如下，右上角是神经网络：
下面看代码：
def sigmoid(z): s=1.0/(1+np.exp(-z)) return s """ 返回输入层节点和输出层节点 """ def lay_sizer(X,Y): n_x = X.shape[0] n_y = Y.shape[0] return n_x,n_y """ 初始化W和b,n_h就是隐藏层节点 """ def initialize_parameters(n_x,n_h,n_y): W1 = np.random.randn(n_h,n_x)*0.01 b1=np.zeros((n_h,1)) W2 = np.random.randn(n_y, n_h) * 0.01 b2 = np.zeros((n_y, 1)) parameters={'W1':W1, 'b1':b1, 'W2':W2, 'b2':b2} return parameters """ 前向传播，返回中间量Z1 A1 Z2 A2 最后一层加sigmoid因为要实现二分类 """ def forward_propagation(X,parameters): W1 = parameters['W1'] W2 = parameters['W2'] b1 = parameters['b1'] b2 = parameters['b2'] Z1 = np.dot(W1, X) + b1 A1 = np.tanh(Z1)#Relu(Z1) Z2 = np.dot(W2, A1) + b2 A2 = sigmoid(Z2) cache={'Z1':Z1, 'Z2':Z2, 'A1':A1, 'A2':A2} return cache,A2 """ 利用交叉熵函数计算损失值 """ def compute_cost(A2,Y): m=Y.shape[1] cost=-1 / m *(np.dot(Y,np.log(A2).T)+np.dot((1-Y),np.log(1-A2).T)) cost=np.squeeze(cost) return cost """ 后向传播：注意维度 """ def back_propagation(parameters,cache,X,Y): m = Y.shape[1] A2 = cache['A2'] A1 = cache['A1'] W2 = parameters['W2'] dZ2 = A2-Y dW2 = 1/m*(np.dot(dZ2,A1.T)) db2 = 1/m*(np.sum(dZ2,axis=1,keepdims=True)) #db2(n_y,1) 按行相加 保持二维性 # [[1,2],[3,4]] [[3],[7]] dA1 = np.dot(W2.T,dZ2) dZ1 = dA1*(1-np.power(A1,2)) dW1 = 1/m*np.dot(dZ1,X.T) db1 = 1/m*(np.sum(dZ1,axis=1,keepdims=True)) #db1(n_h,1) 按行相加 保持二维性 grads={'dW2':dW2, 'dW1':dW1, 'db2':db2, 'db1':db1} return grads """ 更新参数 W和b """ def update_parameters(grads,parameters,learning_rate): dW2=grads['dW2'] dW1=grads['dW1'] db2=grads['db2'] db1=grads['db1'] W2=parameters['W2'] W1= parameters['W1'] b2 = parameters['b2'] b1 = parameters['b1'] W2 = W2 - learning_rate*dW2 W1 = W1 - learning_rate * dW1 b2 = b2 - learning_rate * db2 b1 = b1 - learning_rate * db1 parameters = {'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2} return parameters """ 构建模型 """ def nn_model(X,Y,num_iterations,learning_rate,print_cost,n_h): n_x,n_y = lay_sizer(X, Y) parameters = initialize_parameters(n_x, n_h, n_y) #costs=[] for i in range(num_iterations): cache, A2 = forward_propagation(X, parameters) cost = compute_cost(A2, Y) #costs.append(cost) grads = back_propagation(parameters, cache, X,Y) parameters = update_parameters(grads, parameters, learning_rate) if print_cost and i%100==0: print('Cost after iterations {}:{}'.format(i,cost)) return parameters #,costs """ 用更新好的参数预测Y值 """ def prediction(X,parameters): cache,A2=forward_propagation(X,parameters) predictions=np.around(A2) return predictions def train_accuracy(): X, Y = planar_utils.load_planar_dataset() parameters = nn_model(X, Y, num_iterations=10000, learning_rate=1.2, print_cost=True,n_h=8) # print('parameters W1', parameters['W1']) # print('parameters W2', parameters['W2']) # print('parameters b1', parameters['b1']) # print('parameters b2', parameters['b2']) predictions = prediction(X, parameters) print(predictions) planar_utils.plot_decision_boundary(lambda x: prediction(x.T, parameters), X, np.squeeze(Y)) plt.show() ###########二分类精度求解 result = np.dot(np.squeeze(Y), np.squeeze(predictions.T)) + np.dot(np.squeeze(1 - Y), np.squeeze(1 - predictions.T)) print('The accuracy is {}%'.format((result) / Y.size * 100)) if __name__=='__main__': #test() train_accuracy()
结果：
更改隐藏层个数：
def Different_Hidden_Size(): X, Y = planar_utils.load_planar_dataset() hidden_layer_sizes=[1,2,3,4,5,10,20] plt.figure(figsize=(16,16)) for i,n_h in enumerate(hidden_layer_sizes): print('n_h=',n_h) plt.subplot(3,3,i+1) plt.title('hidden_layer_sizes{}'.format(n_h)) parameters = nn_model(X, Y, num_iterations=2000, learning_rate=1.2, print_cost=False,n_h=n_h) planar_utils.plot_decision_boundary(lambda x: prediction(x.T, parameters), X, np.squeeze(Y)) predictions = prediction(X, parameters) ###########二分类精度求解 result = np.dot(np.squeeze(Y), np.squeeze(predictions.T)) + np.dot(np.squeeze(1 - Y), np.squeeze(1 - predictions.T)) print('The accuracy hidden_layer_sizes{} is {}%'.format(n_h,(result) / Y.size * 100)) plt.savefig('1.png') plt.show()
if __name__=='__main__': #test() #train_accuracy() Different_Hidden_Size()
结果：
