神经网络对比

 

1. 只能分两类

层数固定不变

层数可以变化

''' 11行神经网络① 固定三层，两类 ''' # 只适合 0, 1 两类。若不是，要先转化 import numpy as np X = np.array([[0,0,1],[0,1,1],[1,0,1],[1,1,1]]) y = np.array([0,1,1,0]).reshape(-1,1) # 此处reshape是为了便于算法简洁实现 wi = 2*np.random.randn(3,5) - 1 wh = 2*np.random.randn(5,1) - 1 for j in range(10000): li = X lh = 1/(1+np.exp(-(np.dot(li,wi)))) lo = 1/(1+np.exp(-(np.dot(lh,wh)))) lo_delta = (y - lo)*(lo*(1-lo)) lh_delta = np.dot(lo_delta, wh.T) * (lh * (1-lh)) wh += np.dot(lh.T, lo_delta) wi += np.dot(li.T, lh_delta) print('训练结果：', lo)

''' 11行神经网络① 层数可变，两类 ''' # 只适合 0, 1 两类。若不是，要先转化 import numpy as np X = np.array([[0,0,1],[0,1,1],[1,0,1],[1,1,1]]) y = np.array([0,1,1,0]).reshape(-1,1) # 此处reshape是为了便于算法简洁实现 neurals = [3,15,1] w = [np.random.randn(i,j) for i,j in zip(neurals[:-1], neurals[1:])] + [None] l = [None] * len(neurals) l_delta = [None] * len(neurals) for j in range(1000): l[0] = X for i in range(1, len(neurals)): l[i] = 1 / (1 + np.exp(-(np.dot(l[i-1], w[i-1])))) l_delta[-1] = (y - l[-1]) * (l[-1] * (1 - l[-1])) for i in range(len(neurals)-2, 0, -1): l_delta[i] = np.dot(l_delta[i+1], w[i].T) * (l[i] * (1 - l[i])) for i in range(len(neurals)-2, -1, -1): w[i] += np.dot(l[i].T, l_delta[i+1]) print('训练结果：', l[-1])

 

2.可以分多类

层数固定不变

层数可以变化

''' 11行神经网络① 固定三层，多类 ''' import numpy as np X = np.array([[0,0,1],[0,1,1],[1,0,1],[1,1,1]]) #y = np.array([0,1,1,0]) # 可以两类 y = np.array([0,1,2,3]) # 可以多类 wi = np.random.randn(3,5) wh = np.random.randn(5,4) # 改 bh = np.random.randn(1,5) bo = np.random.randn(1,4) # 改 epsilon = 0.01 # 学习速率 lamda = 0.01 # 正则化强度 for j in range(1000): li = X lh = np.tanh(np.dot(li, wi) + bh) # tanh 函数 lo = np.exp(np.dot(lh, wh) + bo) probs = lo / np.sum(lo, axis=1, keepdims=True) # 后向传播 lo_delta = np.copy(probs) lo_delta[range(X.shape[0]), y] -= 1 lh_delta = np.dot(lo_delta, wh.T) * (1 - np.power(lh, 2)) # 更新权值、偏置 wh -= epsilon * (np.dot(lh.T, lo_delta) + lamda * wh) wi -= epsilon * (np.dot(li.T, lh_delta) + lamda * wi) bo -= epsilon * np.sum(lo_delta, axis=0, keepdims=True) bh -= epsilon * np.sum(lh_delta, axis=0) print('训练结果：', np.argmax(probs, axis=1))

''' 11行神经网络① 层数可变，多类 ''' import numpy as np X = np.array([[0,0,1],[0,1,1],[1,0,1],[1,1,1]]) #y = np.array([0,1,1,0]) # 可以两类 y = np.array([0,1,2,3]) # 可以多类 neurals = [3, 10, 8, 4] w = [np.random.randn(i,j) for i,j in zip(neurals[:-1], neurals[1:])] + [None] b = [None] + [np.random.randn(1,j) for j in neurals[1:]] l = [None] * len(neurals) l_delta = [None] * len(neurals) epsilon = 0.01 # 学习速率 lamda = 0.01 # 正则化强度 for j in range(1000): # 前向传播 l[0] = X for i in range(1, len(neurals)-1): l[i] = np.tanh(np.dot(l[i-1], w[i-1]) + b[i]) # tanh 函数 l[-1] = np.exp(np.dot(l[-2], w[-2]) + b[-1]) probs = l[-1] / np.sum(l[-1], axis=1, keepdims=True) # 后向传播 l_delta[-1] = np.copy(probs) l_delta[-1][range(X.shape[0]), y] -= 1 for i in range(len(neurals)-2, 0, -1): l_delta[i] = np.dot(l_delta[i+1], w[i].T) * (1 - np.power(l[i], 2)) # tanh 函数的导数 # 更新权值、偏置 b[-1] -= epsilon * np.sum(l_delta[-1], axis=0, keepdims=True) for i in range(len(neurals)-2, -1, -1): w[i] -= epsilon * (np.dot(l[i].T, l_delta[i+1]) + lamda * w[i]) if i == 0: break b[i] -= epsilon * np.sum(l_delta[i], axis=0) # 打印损失 if j % 100 == 0: loss = np.sum(-np.log(probs[range(X.shape[0]), y])) loss += lamda/2 * np.sum([np.sum(np.square(wi)) for wi in w[:-1]]) # 可选 loss *= 1/X.shape[0] # 可选 print('loss:', loss) print('训练结果：', np.argmax(probs, axis=1))