2. Stacked LSTM

from math import sin
from math import pi
from math import exp
from random import random
from random import randint
from random import uniform
from numpy import array
from matplotlib import pyplot
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

length = 100
freq = 5
sequence = [sin(2 * pi * freq * (i/length)) for i in range(length)]

pyplot.plot(sequence)
pyplot.show()

length = 100
period = 10
decay = 0.05
sequence = [0.5 + 0.5 * sin(2 * pi * i / period) \
            * exp(-decay * i) for i in range(length)]

pyplot.plot(sequence)
pyplot.show()

def generate_sequence(length, period, decay):
    return [0.5 + 0.5 * sin(2 * pi * i / period) *\
           exp(-decay * i) for i in range(length)]

def generate_examples(length, n_patterns, output):
  X, y = list(), list()
  for _ in range(n_patterns):
    p = randint(10, 20)
    d = uniform(0.01, 0.1)
    sequence = generate_sequence(length + output, p, d)
    X.append(sequence[:-output])
    y.append(sequence[-output:])
  X = array(X).reshape(n_patterns, length, 1)
  y = array(y).reshape(n_patterns, output)
  return X, y

plt.figure(figsize =(12,12))
X, y = generate_examples(100, 20, 5)
for i in range(len(X)):
    pyplot.plot([x for x in X[i, :, 0]] + [x for x in y[i]], '-o') 
pyplot.show()   

# Example of one output for whole sequence
from keras.models import Sequential
from keras.layers import LSTM,Dense

# configure problem
length = 50
output = 5


# define model
model = Sequential()
model.add(LSTM(20, return_sequences=True, input_shape=(length, 1))) 
model.add(LSTM(20, return_sequences=True))
model.add(LSTM(20, return_sequences=True))
model.add(LSTM(20))
model.add(Dense(output))


# compile
model.compile(loss='mae',
              optimizer='adam')


print(model.summary())

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
lstm_13 (LSTM)               (None, 50, 20)            1760      
_________________________________________________________________
lstm_14 (LSTM)               (None, 50, 20)            3280      
_________________________________________________________________
lstm_15 (LSTM)               (None, 50, 20)            3280      
_________________________________________________________________
lstm_16 (LSTM)               (None, 20)                3280      
_________________________________________________________________
dense_4 (Dense)              (None, 5)                 105       
=================================================================
Total params: 11,705
Trainable params: 11,705
Non-trainable params: 0
_________________________________________________________________
None

X, y = generate_examples(length, 500, output)
model.fit(X, y, batch_size=10, epochs=5, verbose = 2)

Epoch 1/5
20s - loss: 0.0586
Epoch 2/5
20s - loss: 0.0413
Epoch 3/5
21s - loss: 0.0403
Epoch 4/5
20s - loss: 0.0400
Epoch 5/5
20s - loss: 0.0419





<keras.callbacks.History at 0x12cabab70>

# evaluate model
X, y = generate_examples(length, 100, output) 
loss = model.evaluate(X, y, verbose=0) 
print('MAE: %f' % loss)

MAE: 0.050917

# prediction on new data
X, y = generate_examples(length, 20, output) 
yhat = model.predict(X, verbose=0) 
pyplot.plot(y[0], label='y') 
pyplot.plot(yhat[0], label='yhat') 
pyplot.legend()
pyplot.show()