神经网络学习-python实现LSTM

对于风速这种时间序列的预测，常见的神经网络有：BP神经网络，径向基函数神经网络，Elman神经网络；另外还有一个自回归积分滑动平均模型ARIMA。以上两类做的人比较多，也比较成熟了，偶然了解到LSTM，决定那这个试一下，理由就是：没人做。

以下的代码为python实现lstm，另外KERAS里面有lstm的模型，如此一个深度学习的大坑，真是让人情不自禁的往里跳啊！

import copy, numpy as np
np.random.seed(0)
# compute sigmoid nonlinearity
def sigmoid(x):
output = 1 / (1 + np.exp(-x))
return output
# convert output of sigmoid function to its derivative
def sigmoid_output_to_derivative(output):
return output * (1 - output)
# training dataset generation
int2binary = {}
binary_dim = 8

largest_number = pow(2, binary_dim)
binary = np.unpackbits(
np.array([range(largest_number)], dtype=np.uint8).T, axis=1)
for i in range(largest_number):
int2binary[i] = binary[i]

# input variables
alpha = 0.1
input_dim = 2
hidden_dim = 16
output_dim = 1

# initialize neural network weights
synapse_0 = 2 * np.random.random((input_dim, hidden_dim)) - 1
synapse_1 = 2 * np.random.random((hidden_dim, output_dim)) - 1
synapse_h = 2 * np.random.random((hidden_dim, hidden_dim)) - 1

synapse_0_update = np.zeros_like(synapse_0)
synapse_1_update = np.zeros_like(synapse_1)
synapse_h_update = np.zeros_like(synapse_h)

# training logic
for j in range(10000):

# generate a simple addition problem (a + b = c)
a_int = np.random.randint(largest_number / 2)  # int version
a = int2binary[a_int]  # binary encoding

b_int = np.random.randint(largest_number / 2)  # int version
b = int2binary[b_int]  # binary encoding

# true answer
c_int = a_int + b_int
c = int2binary[c_int]

# where we'll store our best guess (binary encoded)
d = np.zeros_like(c)

overallError = 0

layer_2_deltas = list()
layer_1_values = list()
layer_1_values.append(np.zeros(hidden_dim))

# moving along the positions in the binary encoding
for position in range(binary_dim):
# generate input and output
X = np.array([[a[binary_dim - position - 1], b[binary_dim - position - 1]]])
y = np.array([[c[binary_dim - position - 1]]]).T

# hidden layer (input ~+ prev_hidden)
layer_1 = sigmoid(np.dot(X, synapse_0) + np.dot(layer_1_values[-1], synapse_h))

# output layer (new binary representation)
layer_2 = sigmoid(np.dot(layer_1, synapse_1))

# did we miss?... if so, by how much?
layer_2_error = y - layer_2
layer_2_deltas.append((layer_2_error) * sigmoid_output_to_derivative(layer_2))
overallError += np.abs(layer_2_error[0])

# decode estimate so we can print it out
d[binary_dim - position - 1] = np.round(layer_2[0][0])

# store hidden layer so we can use it in the next timestep
layer_1_values.append(copy.deepcopy(layer_1))

future_layer_1_delta = np.zeros(hidden_dim)

for position in range(binary_dim):
X = np.array([[a[position], b[position]]])
layer_1 = layer_1_values[-position - 1]
prev_layer_1 = layer_1_values[-position - 2]

# error at output layer
layer_2_delta = layer_2_deltas[-position - 1]
# error at hidden layer
layer_1_delta = (future_layer_1_delta.dot(synapse_h.T) + layer_2_delta.dot(
synapse_1.T)) * sigmoid_output_to_derivative(layer_1)

# let's update all our weights so we can try again
synapse_1_update += np.atleast_2d(layer_1).T.dot(layer_2_delta)
synapse_h_update += np.atleast_2d(prev_layer_1).T.dot(layer_1_delta)
synapse_0_update += X.T.dot(layer_1_delta)

future_layer_1_delta = layer_1_delta

synapse_0 += synapse_0_update * alpha
synapse_1 += synapse_1_update * alpha
synapse_h += synapse_h_update * alpha

synapse_0_update *= 0
synapse_1_update *= 0
synapse_h_update *= 0

# print out progress
if (j % 1000 == 0):
print( "Error:" + str(overallError))
print("Pred:" + str(d))
print("True:" + str(c))
out = 0
for index, x in enumerate(reversed(d)):
out += x * pow(2, index)
print(str(a_int) + " + " + str(b_int) + " = " + str(out))
print("------------")