Keras【极简】LSTM【时序预测】

1、序言

样本介绍

现有一样本，含3个时序【y、y1、y2】，其中【y】受【y1、y2】影响

目标

对【时序y】进行预测

import numpy as np, matplotlib.pyplot as mp
x_len = 1075
x = np.linspace(0, np.pi * 10.75, x_len, endpoint=False)
y = np.cos(x) + np.sin(x * 5) * .2  # y是由y1和y2组成
y1 = np.sin(x) + 2.6
y2 = np.cos(x * 5) * .2 + 1.4
mp.plot(x, y1, 'y', label='y1')
mp.plot(x, y2, label='y2')
mp.plot(x, y, 'g', label='y', linewidth=2)
mp.legend()
mp.show()

2、仅用时序y进行预测

import numpy as np, matplotlib.pyplot as mp
from keras.models import Sequential
from keras.layers import Dense, LSTM

"""创建样本"""
x_len = 1075
x = np.linspace(0, np.pi * 10.75, x_len, endpoint=False)
# y1 = np.sin(x) - 2
# y2 = np.cos(x * 5) * .2
y = np.cos(x) + np.sin(x * 5) * .2  # y受由y1和y2影响
y = (y - min(y)) / (max(y) - min(y))  # 标准化
window = 75  # 时序滑窗大小
X = np.reshape([y[i: i + window] for i in range(x_len - window)],
               (-1, window, 1))  # shape (1000, 75, 1)
Y = y[window:].reshape(-1, 1)  # shape (1000, 1)

"""建模"""
model = Sequential()
model.add(LSTM(50, input_shape=(window, 1), return_sequences=True))
model.add(LSTM(100))
model.add(Dense(1))
model.compile('adam', 'mse')
model.fit(X, Y, batch_size=100, epochs=20, verbose=2)

"""预测"""
pred_len = 200  # 预测序列长度
for start in (0, 333, 666, 999):
    x_pred = np.linspace(np.pi * (window + start) / 100,
                         np.pi * (window + start + pred_len) / 100,
                         pred_len, endpoint=False)
    y_pred = []  # 存放预测序列
    X_pred = X[start]
    for i in range(pred_len):
        Y_pred = model.predict(X_pred.reshape(-1, window, 1))  # 预测
        y_pred.append(Y_pred[0])
        X_pred = np.concatenate((X_pred, Y_pred))[1:]  # 窗口滑动
    mp.scatter(x_pred[0], y_pred[0], c='r', s=9)  # 预测起始点
    mp.plot(x_pred, y_pred, 'r')  # 预测序列
mp.plot(x, y, 'y', linewidth=5, alpha=0.3)  # 原序列
mp.show()

3、使用全部时序进行预测

import numpy as np, matplotlib.pyplot as mp
from keras.models import Sequential
from keras.layers import Dense, LSTM
from sklearn.preprocessing import MinMaxScaler

"""创建样本"""
x_len = 1075
x = np.linspace(0, np.pi * 10.75, x_len, endpoint=False)
y = np.array([[np.sin(x[i] * 5) * .2 + np.cos(x[i]),
               np.cos(x[i] * 5) * .2,
               np.sin(x[i])] for i in range(x_len)])  # shape(1075, 3)
y = MinMaxScaler().fit_transform(y)  # 标准化
d = y.shape[1]  # 维度（dimension）
window = 75  # 时序滑窗大小
X = np.array([[[y[j, k] for k in range(d)] for j in range(i, i + window)]
              for i in range(x_len - window)])  # shape(1000, 75, 3)
Y = np.array([[y[i, k] for k in range(d)]
              for i in range(window, x_len)])  # shape(1000, 3)

"""建模"""
model = Sequential()
model.add(LSTM(50, input_shape=(window, d), return_sequences=True))
model.add(LSTM(100))
model.add(Dense(d))
model.compile('adam', 'mse')
model.fit(X, Y, batch_size=100, epochs=10, verbose=2)

"""预测"""
pred_len = 200  # 预测序列长度
for start in (0, 333, 666, 999):
    x_pred = np.linspace(np.pi * (window + start) / 100,
                         np.pi * (window + start + pred_len) / 100,
                         pred_len, endpoint=False)
    y_pred = []  # 存放预测序列
    X_pred = X[start]
    for i in range(pred_len):
        Y_pred = model.predict(X_pred.reshape(1, window, d))  # shape(1, 3)
        y_pred.append(Y_pred[0][0])
        X_pred = np.concatenate((X_pred, Y_pred))[1:]  # 窗口滑动
    mp.scatter(x_pred[0], y_pred[0], c='r', s=9)  # 预测起始点
    mp.plot(x_pred, y_pred, 'r')  # 预测序列
mp.plot(x, y[:, 0], 'y', linewidth=4, alpha=.3)  # 原序列
mp.show()