## 用 LSTM 做时间序列预测的一个小例子 ，问题：航班乘客预测

https://machinelearningmastery.com/time-series-prediction-lstm-recurrent-neural-networks-python-keras/

```import numpy
import matplotlib.pyplot as plt
import math
from keras.models import Sequential
from keras.layers import Dense
from keras.layers import LSTM
from sklearn.preprocessing import MinMaxScaler
from sklearn.metrics import mean_squared_error
%matplotlib inline```

```# load the dataset
dataframe = read_csv('international-airline-passengers.csv', usecols=[1], engine='python', skipfooter=3)
dataset = dataframe.values
# 将整型变为float
dataset = dataset.astype('float32')

plt.plot(dataset)
plt.show()```

timesteps 就是 LSTM 认为每个输入数据与前多少个陆续输入的数据有联系。例如具有这样用段序列数据 “…ABCDBCEDF…”，当 timesteps 为 3 时，在模型预测中如果输入数据为“D”，那么之前接收的数据如果为“B”和“C”则此时的预测输出为 B 的概率更大，之前接收的数据如果为“C”和“E”，则此时的预测输出为 F 的概率更大。

```# X is the number of passengers at a given time (t) and Y is the number of passengers at the next time (t + 1).

# convert an array of values into a dataset matrix
def create_dataset(dataset, look_back=1):
dataX, dataY = [], []
for i in range(len(dataset)-look_back-1):
a = dataset[i:(i+look_back), 0]
dataX.append(a)
dataY.append(dataset[i + look_back, 0])
return numpy.array(dataX), numpy.array(dataY)

# fix random seed for reproducibility
numpy.random.seed(7)```

```# normalize the dataset
scaler = MinMaxScaler(feature_range=(0, 1))
dataset = scaler.fit_transform(dataset)

# split into train and test sets
train_size = int(len(dataset) * 0.67)
test_size = len(dataset) - train_size
train, test = dataset[0:train_size,:], dataset[train_size:len(dataset),:]```

X=t and Y=t+1 时的数据，并且此时的维度为 [samples, features]

```# use this function to prepare the train and test datasets for modeling
look_back = 1
trainX, trainY = create_dataset(train, look_back)
testX, testY = create_dataset(test, look_back)```

```# reshape input to be [samples, time steps, features]
trainX = numpy.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))
testX = numpy.reshape(testX, (testX.shape[0], 1, testX.shape[1]))```

```# create and fit the LSTM network
model = Sequential()
model.fit(trainX, trainY, epochs=100, batch_size=1, verbose=2)```

Epoch 100/100 1s - loss: 0.0020

```# make predictions
trainPredict = model.predict(trainX)
testPredict = model.predict(testX)```

```# invert predictions
trainPredict = scaler.inverse_transform(trainPredict)
trainY = scaler.inverse_transform([trainY])
testPredict = scaler.inverse_transform(testPredict)
testY = scaler.inverse_transform([testY])```

```trainScore = math.sqrt(mean_squared_error(trainY[0], trainPredict[:,0]))
print('Train Score: %.2f RMSE' % (trainScore))
testScore = math.sqrt(mean_squared_error(testY[0], testPredict[:,0]))
print('Test Score: %.2f RMSE' % (testScore))```

Train Score: 22.92 RMSE Test Score: 47.53 RMSE

```# shift train predictions for plotting
trainPredictPlot = numpy.empty_like(dataset)
trainPredictPlot[:, :] = numpy.nan
trainPredictPlot[look_back:len(trainPredict)+look_back, :] = trainPredict

# shift test predictions for plotting
testPredictPlot = numpy.empty_like(dataset)
testPredictPlot[:, :] = numpy.nan
testPredictPlot[len(trainPredict)+(look_back*2)+1:len(dataset)-1, :] = testPredict

# plot baseline and predictions
plt.plot(scaler.inverse_transform(dataset))
plt.plot(trainPredictPlot)
plt.plot(testPredictPlot)
plt.show()```