今天，接着跟大家分享一波ReLU函数。这个函数也是激活函数。表达式如下：
y = {
x，x>0
0，x<=0
}
代码实现如下：
def ReLU(inx): return np.maximum(0,inx)
绘图：
Inx = np.arange(-5,5,0.5) y = ReLU(Inx) plt.plot(Inx,y) plt.ylim(-0.5,5) plt.show()
可以从图像看出ReLU函数是非线性函数，相比阶跃函数，它的输出结果有0和自身的输入。阶跃函数的输出结果只有0和1。
多维数组运算：
def Matrix_calc(): Matrix1 = np.array([[1,2],[3,4],[5,6]]) dimension = Matrix1.ndim print('{}的维度:'.format(Matrix1),dimension) shape = Matrix1.shape print('{}的形状:'.format(Matrix1),shape) Matrix2 = np.array([[7,8],[9,0]]) dimension2 = Matrix2.ndim print('{}的维度:'.format(Matrix2),dimension2) shape2 = Matrix2.shape print('{}的形状:'.format(Matrix2),shape2) Matrix3 = np.dot(Matrix2,Matrix2)#矩阵的点积 print(Matrix3) print("{}的形状:".format(Matrix3),Matrix3.shape) dimension3 = Matrix3.ndim print("{}的维度:".format(Matrix3),dimension3)
运行结果：
构建三层网络：
def network_build(inx,weights,theta): b = -theta#偏置等于阈值的负值 y = np.dot(inx,weights) + b#输入与权重的点积加上偏置 #等同于 y = inx * weights + b return y
#第一层网络 inx = np.array([0.5,1])#传入的数据 #print(inx.shape) weights = np.array([[0.3,0.5,0.7],[0.4,0.6,0.8]])#第一层网络的权重 # print(weights.shape) # result = np.dot(inx,weights) # print(result) theta = np.array([0.1,0.3,0.5])#第一层网络的阈值 # for n in range(5): # theta = np.array([0.1, 0.3, 0.5]) # weights = np.array([[0.3, 0.5, 0.7], [0.4, 0.6, 0.8]]) # 权重 result = network_build(inx,weights,theta) output = sigmoid(result)#调用sigmoid函数优化 print(output)#第一层网络的输出结果 print() print() #第二层网络 inx2 = output#下层网络的输入数据等于上层网络输出的结果 weights2 = np.array([[0.1,0.3],[0.5,0.7],[0.2,0.4]])#第二层网络的权重 theta2 = np.array([0.1,0.2])#第二层网络的阈值 result2 = network_build(inx2,weights2,theta2) output2 = sigmoid(result2) print(output2) #第三层网络 print() print() inx3 = output2 weights3 = np.array([[0.1,0.3,0.5],[0.2,0.4,0.6]]) theta3 = np.array([0.1,0.2,0.3]) y = network_build(inx3,weights3,theta3) print(y) output3 = identity_func(y)#调用恒等函数作为激活函数 print(output3)
运行结果：
恒等函数构建：
def identity_func(inx):#恒等函数，输入等于输出，激活函数 return inx
我们结合上面构建三层网络的例子，再做一下调整，也能得到三层网络：
def init_network():#初始化网络#这个网络中有我们每一层需要的权重以及theta阈值。 network = {} network['W1'] = np.array([[0.1,0.2,0.3],[0.4,0.5,0.6]]) network['W2'] = np.array([[0.2,0.4],[0.1,0.3],[0.5,0.7]]) network['W3'] = np.array([[0.1,0.3],[0.2,0.4]]) network['theta1'] = np.array([0.1,0.2,0.3]) network['theta2'] = np.array([0.1,0.3]) network['theta3'] = np.array([0.2,0.4]) return networkdef forward(network,inx): b1 = -network['theta1']#偏置1 b2 = -network['theta2']#偏置2 b3 = -network['theta3']#偏置3 result1 = np.dot(inx,network['W1'])+b1 output1 = sigmoid(result1)#调用sigmoid激活函数 print('Sigmoid激活函数输出结果：',output1) result2 = np.dot(output1,network['W2'])+b2 output2 = ReLU(result2)#调用ReLU激活函数 print('ReLU激活函数输出结果：',output2) result3 = np.dot(output2, network['W3']) + b3 output3 = identity_func(result3)#调用恒等激活函数 print('identity_func恒等激活函数输出结果：',output3)
运行代码：
network = init_network() x = [0.1,0.6]#输入的数据 forward(network,x)
运行结果：
最后，感谢大家前来观看鄙人的文章，文中或有诸多不妥之处，还望指出和海涵。