1.LSTM 网络
可以理解为RNN的升级。
Long Short Term Memory networks（以下简称LSTMs），一种特殊的RNN网络，该网络设计出来是为了解决长依赖问题。该网络由 Hochreiter & Schmidhuber (1997)引入，并有许多人对其进行了改进和普及。他们的工作被用来解决了各种各样的问题，直到目前还被广泛应用。
所有循环神经网络都具有神经网络的重复模块链的形式。 在标准的RNN中，该重复模块将具有非常简单的结构，例如单个tanh层。标准的RNN网络如下图所示
LSTMs也具有这种链式结构，但是它的重复单元不同于标准RNN网络里的单元只有一个网络层，它的内部有四个网络层。LSTMs的结构如下图所示。
在解释LSTMs的详细结构时先定义一下图中各个符号的含义，符号包括下面几种
图中黄色类似于CNN里的激活函数操作，粉色圆圈表示点操作，单箭头表示数据流向，箭头合并表示向量的合并（concat）操作，箭头分叉表示向量的拷贝操作。
# please note, all tutorial code are running under python3.5.
# If you use the version like python2.7, please modify the code accordingly
# 8 - RNN LSTM Regressor example
# to try tensorflow, un-comment following two lines
# import os
# os.environ['KERAS_BACKEND']='tensorflow'
import numpy as np
np.random.seed(1337) # for reproducibility
import matplotlib.pyplot as plt
from keras.models import Sequential
from keras.layers import LSTM, TimeDistributed, Dense
from keras.optimizers import Adam
BATCH_START = 0
TIME_STEPS = 20
BATCH_SIZE = 50
INPUT_SIZE = 1
OUTPUT_SIZE = 1
CELL_SIZE = 20
LR = 0.006
def get_batch():
global BATCH_START, TIME_STEPS
# xs shape (50batch, 20steps)
xs = np.arange(BATCH_START, BATCH_START+TIME_STEPS*BATCH_SIZE).reshape((BATCH_SIZE, TIME_STEPS)) / (10*np.pi)
seq = np.sin(xs)
res = np.cos(xs)
BATCH_START += TIME_STEPS
# plt.plot(xs[0, :], res[0, :], 'r', xs[0, :], seq[0, :], 'b--')
# plt.show()
return [seq[:, :, np.newaxis], res[:, :, np.newaxis], xs]
model = Sequential()
# build a LSTM RNN
model.add(LSTM(
batch_input_shape=(BATCH_SIZE, TIME_STEPS, INPUT_SIZE), # Or: input_dim=INPUT_SIZE, input_length=TIME_STEPS,
output_dim=CELL_SIZE,
return_sequences=True, # True: output at all steps. False: output as last step.
stateful=True, # True: the final state of batch1 is feed into the initial state of batch2
))
# add output layer
model.add(TimeDistributed(Dense(OUTPUT_SIZE)))
adam = Adam(LR)
model.compile(optimizer=adam,
loss='mse',)
print('Training ------------')
for step in range(501):
# data shape = (batch_num, steps, inputs/outputs)
X_batch, Y_batch, xs = get_batch()
cost = model.train_on_batch(X_batch, Y_batch)
pred = model.predict(X_batch, BATCH_SIZE)
plt.plot(xs[0, :], Y_batch[0].flatten(), 'r', xs[0, :], pred.flatten()[:TIME_STEPS], 'b--')
plt.ylim((-1.2, 1.2))
plt.draw()
plt.pause(0.1)
if step % 10 == 0:
print('train cost: ', cost)
