本文是對：

https://machinelearningmastery.com/multi-step-time-series-forecasting-long-short-term-memory-networks-python/

https://blog.csdn.net/iyangdi/article/details/77895186

博文的學習筆記，博主筆風都很浪，有些細節一筆帶過，本人以謙遜的態度進行了學習和整理，筆記內容都在程式碼的註釋中。有不清楚的可以去原博主文中檢視。

資料集下載：https://datamarket.com/data/set/22r0/sales-of-shampoo-over-a-three-year-period

後期我會補上我的github
 

本文其實是iyangdi博主最後一篇LSTM的文章，後續沒有繼續進行連載，不過後面的課程我會繼續通過對Jason Brownlee博士文章的學習上傳上來

本文在上文的基礎上，對真實資料進行了處理，進行了一次實戰的多步預測

上一章節可能有人疑惑為什麼資料預測出來都是橫線，是因為那些資料都是沒有意義的實驗資料

本節中的資料是真實資料

程式碼分析寫在了註釋裡

from pandas import DataFrame
from pandas import Series
from pandas import concat
from pandas import read_csv
from pandas import datetime
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import MinMaxScaler
from keras.models import Sequential
from keras.layers import Dense
from keras.layers import LSTM
from math import sqrt
from matplotlib import pyplot
from numpy import array


# 載入資料集
def parser(x):
    return datetime.strptime(x, '%Y/%m/%d')


# 將時間序列轉換為監督型別的資料序列
def series_to_supervised(data, n_in=1, n_out=1, dropnan=True):
    n_vars = 1 if type(data) is list else data.shape[1]
    df = DataFrame(data)
    cols, names = list(), list()
    # 這個for迴圈是用來輸入列標題的 var1(t-1)，var1(t)，var1(t+1)，var1(t+2)
    for i in range(n_in, 0, -1):
        cols.append(df.shift(i))
        names += [('var%d(t-%d)' % (j + 1, i)) for j in range(n_vars)]
    # 轉換為監督型資料的預測序列 每四個一組，對應 var1(t-1)，var1(t)，var1(t+1)，var1(t+2)
    for i in range(0, n_out):
        cols.append(df.shift(-i))
        if i == 0:
            names += [('var%d(t)' % (j + 1)) for j in range(n_vars)]
        else:
            names += [('var%d(t+%d)' % (j + 1, i)) for j in range(n_vars)]
    # 拼接資料
    agg = concat(cols, axis=1)
    agg.columns = names
    # 把null值轉換為0
    if dropnan:
        agg.dropna(inplace=True)
    print(agg)
    return agg


# 對傳入的數列做差分操作，相鄰兩值相減
def difference(dataset, interval=1):
    diff = list()
    for i in range(interval, len(dataset)):
        value = dataset[i] - dataset[i - interval]
        diff.append(value)
    return Series(diff)


# 將序列轉換為用於監督學習的訓練和測試集
def prepare_data(series, n_test, n_lag, n_seq):
    # 提取原始值
    raw_values = series.values
    # 將資料轉換為靜態的
    diff_series = difference(raw_values, 1)
    diff_values = diff_series.values
    diff_values = diff_values.reshape(len(diff_values), 1)
    # 重新調整資料為（-1,1）之間
    scaler = MinMaxScaler(feature_range=(-1, 1))
    scaled_values = scaler.fit_transform(diff_values)
    scaled_values = scaled_values.reshape(len(scaled_values), 1)
    # 轉化為有監督的資料X，y
    supervised = series_to_supervised(scaled_values, n_lag, n_seq)
    supervised_values = supervised.values
    # 分割為測試資料和訓練資料
    train, test = supervised_values[0:-n_test], supervised_values[-n_test:]
    return scaler, train, test


# 匹配LSTM網路訓練資料
def fit_lstm(train, n_lag, n_seq, n_batch, nb_epoch, n_neurons):
    # 重塑訓練資料格式 [samples, timesteps, features]
    X, y = train[:, 0:n_lag], train[:, n_lag:]
    X = X.reshape(X.shape[0], 1, X.shape[1])
    # 配置一個LSTM神經網路，新增網路引數
    model = Sequential()
    model.add(LSTM(n_neurons, batch_input_shape=(n_batch, X.shape[1], X.shape[2]), stateful=True))
    model.add(Dense(y.shape[1]))
    model.compile(loss='mean_squared_error', optimizer='adam')
    # 呼叫網路，迭代資料對神經網路進行訓練，最後輸出訓練好的網路模型
    for i in range(nb_epoch):
        model.fit(X, y, epochs=1, batch_size=n_batch, verbose=0, shuffle=False)
        model.reset_states()
    return model


# 用LSTM做預測
def forecast_lstm(model, X, n_batch):
    # 重構輸入引數 [samples, timesteps, features]
    X = X.reshape(1, 1, len(X))
    # 開始預測
    forecast = model.predict(X, batch_size=n_batch)
    # 結果轉換成陣列
    return [x for x in forecast[0, :]]


# 利用訓練好的網路模型，對測試資料進行預測
def make_forecasts(model, n_batch, train, test, n_lag, n_seq):
    forecasts = list()
    # 預測方式是用一個X值預測出後三步的Y值
    for i in range(len(test)):
        X, y = test[i, 0:n_lag], test[i, n_lag:]
        # 呼叫訓練好的模型預測未來資料
        forecast = forecast_lstm(model, X, n_batch)
        # 將預測的資料儲存
        forecasts.append(forecast)
    return forecasts


# 對預測後的縮放值（-1，1）進行逆變換
def inverse_difference(last_ob, forecast):
    # invert first forecast
    inverted = list()
    inverted.append(forecast[0] + last_ob)
    # propagate difference forecast using inverted first value
    for i in range(1, len(forecast)):
        inverted.append(forecast[i] + inverted[i - 1])
    return inverted


# 對預測完成的資料進行逆變換
def inverse_transform(series, forecasts, scaler, n_test):
    inverted = list()
    for i in range(len(forecasts)):
        # create array from forecast
        forecast = array(forecasts[i])
        forecast = forecast.reshape(1, len(forecast))
        # 將預測後的資料縮放逆轉換
        inv_scale = scaler.inverse_transform(forecast)
        inv_scale = inv_scale[0, :]
        # invert differencing
        index = len(series) - n_test + i - 1
        last_ob = series.values[index]
        # 將預測後的資料差值逆轉換
        inv_diff = inverse_difference(last_ob, inv_scale)
        # 儲存資料
        inverted.append(inv_diff)
    return inverted


# 評估每個預測時間步的RMSE
def evaluate_forecasts(test, forecasts, n_lag, n_seq):
    for i in range(n_seq):
        actual = [row[i] for row in test]
        predicted = [forecast[i] for forecast in forecasts]
        rmse = sqrt(mean_squared_error(actual, predicted))
        print('t+%d RMSE: %f' % ((i + 1), rmse))


# 在原始資料集的上下文中繪製預測圖
def plot_forecasts(series, forecasts, n_test):
    # plot the entire dataset in blue
    pyplot.plot(series.values)
    # plot the forecasts in red
    for i in range(len(forecasts)):
        off_s = len(series) - n_test + i - 1
        off_e = off_s + len(forecasts[i]) + 1
        xaxis = [x for x in range(off_s, off_e)]
        yaxis = [series.values[off_s]] + forecasts[i]
        pyplot.plot(xaxis, yaxis, color='red')
    # show the plot
    pyplot.show()


# 載入資料
series = read_csv('data_set/shampoo-sales.csv', header=0, parse_dates=[0], index_col=0, squeeze=True, date_parser=parser)
# 配置網路資訊
n_lag = 1
n_seq = 3
n_test = 10
n_epochs = 1500
n_batch = 1
n_neurons = 1
# 準備資料
scaler, train, test = prepare_data(series, n_test, n_lag, n_seq)
# 準備預測模型
model = fit_lstm(train, n_lag, n_seq, n_batch, n_epochs, n_neurons)
# 開始預測
forecasts = make_forecasts(model, n_batch, train, test, n_lag, n_seq)
# 逆轉換訓練資料和預測資料
forecasts = inverse_transform(series, forecasts, scaler, n_test + 2)
# 逆轉換測試資料
actual = [row[n_lag:] for row in test]
actual = inverse_transform(series, actual, scaler, n_test + 2)
# 比較預測資料和測試資料，計算兩者之間的損失值
evaluate_forecasts(actual, forecasts, n_lag, n_seq)
# 畫圖
plot_forecasts(series, forecasts, n_test + 2)