import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = 'SimHei' # 設置中文顯示
plt.rcParams['axes.unicode_minus'] = False

df_train = pd.read_excel('訓練集.xlsx', index_col=0, parse_dates=['date'])
df_test = pd.read_csv('測試集.csv', index_col=0, parse_dates=['date'])
df_train

其中df_train和df_test分別為模型的訓練集和測試集，數據不存在缺失值、異常值。

2.2 時序圖

2.2.1 訓練集時序圖

plt.figure(figsize=(15, 10))

plt.subplot(3, 1, 1)

plt.plot(df_train['meantemp'], color='y',  alpha=0.3)

plt.title('meantemp時序圖')

plt.grid(True)

plt.subplot(3, 1, 2)

plt.plot(df_train['humidity'], color='y',  alpha=0.3)

plt.title('humidity時序圖')

plt.grid(True)

plt.subplot(3, 1, 3)

plt.plot(df_train['meanpressure'], color='y',  alpha=0.3)

plt.title('meanpressure時序圖')

plt.grid(True)

plt.show()

2.2.2?測試集時序圖

plt.figure(figsize=(15, 10))

plt.subplot(3, 1, 1)

plt.plot(df_test['meantemp'], color='g',  alpha=0.3)

plt.title('meantemp時序圖')

plt.grid(True)

plt.subplot(3, 1, 2)

plt.plot(df_test['humidity'], color='g',  alpha=0.3)

plt.title('humidity時序圖')

plt.grid(True)

plt.subplot(3, 1, 3)

plt.plot(df_test['meanpressure'], color='g',  alpha=0.3)

plt.title('meanpressure時序圖')

plt.grid(True)

plt.show()

2.3?數據0-1標準化

from sklearn.preprocessing import MinMaxScaler



def normalize_dataframe(train_df, test_df):

    scaler = MinMaxScaler()

    scaler.fit(train_df)  # 在訓練集上擬合歸一化模型

    train_data = pd.DataFrame(scaler.transform(train_df), columns=train_df.columns, index = df_train.index)

    test_data = pd.DataFrame(scaler.transform(test_df), columns=test_df.columns, index = df_test.index)

    return train_data, test_data



data_train, data_test = normalize_dataframe(df_train, df_test)

data_train

歸一化時只使用訓練集的統計量，并將歸一化后的轉換應用于訓練集和測試集，避免直接對所有數據集進行歸一化處理從而產生信息泄露。

2.4?滑動窗口劃分數據

def prepare_data(data, win_size, target_feature_idxs):

    num_features = data.shape[1]

    X = []  

    y = []  

    for i in range(len(data) - win_size):

        temp_x = data[i:i + win_size, :]  

        temp_y = [data[i + win_size, idx] for idx in target_feature_idxs]  

        X.append(temp_x)

        y.append(temp_y)

    X = np.asarray(X)

    y = np.asarray(y)



    return X, y



win_size = 12 # 時間窗口

target_feature_idxs = [0, 1, 2] # 指定待預測特征列索引

train_x, train_y = prepare_data(data_train.values, win_size, target_feature_idxs)

test_x, test_y = prepare_data(data_test.values, win_size, target_feature_idxs)

print("訓練集形狀:", train_x.shape, train_y.shape)

print("測試集形狀:", test_x.shape, test_y.shape)

訓練集形狀 (1449, 12, 3) 表示：

1449：樣本數，即訓練集中有1449個樣本。

12：時間窗口大小，每個樣本有12個時間步長的數據，用于預測下一個時間步的數據。

3：特征數，每個時間步長有3個特征（meantemp、humidity 和 meanpressure）。

測試集形狀 (102, 12, 3) 表示：

102：樣本數，即測試集中有102個樣本。

12：時間窗口大小，每個樣本有12個時間步長的數據，用于預測下一個時間步的數據。

3：特征數，每個時間步長有3個特征（meantemp、humidity 和 meanpressure）。

2.5?模型建立

from keras.layers import LSTM, Dense

from keras.models import Model

from keras.layers import Input



# 輸入維度

input_shape = Input(shape=(train_x.shape[1], train_x.shape[2]))



# LSTM層

lstm_layer = LSTM(128, activation='relu')(input_shape)



# 全連接層

dense_1 = Dense(64, activation='relu')(lstm_layer)

dense_2 = Dense(32, activation='relu')(dense_1)



# 輸出層

output_1 = Dense(1, name='meantemp')(dense_2)

output_2 = Dense(1, name='humidity')(dense_2)

output_3 = Dense(1, name='meanpressure')(dense_2)



model = Model(inputs = input_shape, outputs = [output_1, output_2, output_3])

model.compile(loss='mse', optimizer='adam')

# 模型擬合

history = model.fit(train_x, [train_y[:,i] for i in range(train_y.shape[1])], epochs=100, batch_size=32, validation_data=(test_x, [test_y[:,i] for i in range(test_y.shape[1])]))



plt.figure()

plt.plot(history.history['loss'], c='b', label='loss')

plt.plot(history.history['val_loss'], c='g', label='val_loss')

plt.legend()

plt.show()
model.summary()

這是一個多輸入多輸出的 LSTM 模型，接受包含12個時間步長和3個特征的輸入序列，在經過一層128個神經元的 LSTM 層和兩個全連接層后，輸出三個單獨的預測結果，分別是 meantemp、humidity 和 meanpressure。

2.6?模型評價

from sklearn import metrics

y_pred = model.predict(test_x)

# 計算均方誤差（MSE）

mse_meantemp = metrics.mean_squared_error(test_y[:,0], np.array([i for arr in y_pred[0] for i in arr]))

# 計算均方根誤差（RMSE）

rmse_meantemp = np.sqrt(mse_meantemp)

# 計算平均絕對誤差（MAE）

mae_meantemp = metrics.mean_absolute_error(test_y[:,0], np.array([i for arr in y_pred[0] for i in arr]))

from sklearn.metrics import r2_score # 擬合優度

r2_meantemp = r2_score(test_y[:,0], np.array([i for arr in y_pred[0] for i in arr]))

print("meantemp均方誤差 (MSE):", mse_meantemp)

print("meantemp均方根誤差 (RMSE):", rmse_meantemp)

print("meantemp平均絕對誤差 (MAE):", mae_meantemp)

print("meantemp擬合優度:", r2_meantemp)
mse_humidity = metrics.mean_squared_error(test_y[:,1], np.array([i for arr in y_pred[1] for i in arr]))

rmse_humidity = np.sqrt(mse_humidity)

mae_humidity = metrics.mean_absolute_error(test_y[:,1], np.array([i for arr in y_pred[1] for i in arr]))

r2_humidity = r2_score(test_y[:,1], np.array([i for arr in y_pred[1] for i in arr]))

print("humidity均方誤差 (MSE):", mse_humidity)

print("humidity均方根誤差 (RMSE):", rmse_humidity)

print("humidity平均絕對誤差 (MAE):", mae_humidity)

print("humidity擬合優度:", r2_humidity)
mse_meanpressure = metrics.mean_squared_error(test_y[:,2], np.array([i for arr in y_pred[2] for i in arr]))

rmse_meanpressure = np.sqrt(mse_meanpressure)

mae_meanpressure= metrics.mean_absolute_error(test_y[:,2], np.array([i for arr in y_pred[2] for i in arr]))

r2_meanpressure = r2_score(test_y[:,2], np.array([i for arr in y_pred[2] for i in arr]))

print("meanpressure均方誤差 (MSE):", mse_meanpressure)

print("meanpressure均方根誤差 (RMSE):", rmse_meanpressure)

print("meanpressure平均絕對誤差 (MAE):", mae_meanpressure)

print("meanpressure擬合優度:", r2_meanpressure)

2.7?模型向后預測

def predict_next_11_days(model, input_data):

    input_sequence = input_data.copy()



    # 預測未來 11 天的數據

    future_predictions = []

    for _ in range(11):

        predictions = model.predict(np.expand_dims(input_sequence[-1], axis=0))

        next_data = np.append(input_sequence[-1, 1:], np.array(predictions).reshape(1,3), axis=0)

        input_sequence = np.append(input_sequence, [next_data], axis=0)

        future_predictions.append(predictions)

    future_predictions = np.array(future_predictions).reshape(11, 3)



    return future_predictions



future_predictions = predict_next_11_days(model, test_x[-1:])

future_predictions

2.8?預測可視化

# 反歸一化

train_max_meantemp = np.max(df_train['meantemp'])

train_min_meantemp = np.min(df_train['meantemp'])

train_max_humidity = np.max(df_train['humidity'])

train_min_humidity = np.min(df_train['humidity'])

train_max_meanpressure = np.max(df_train['meanpressure'])

train_min_meanpressure = np.min(df_train['meanpressure'])



series_meantemp = np.array(future_predictions[:, 0])*(train_max_meantemp - train_min_meantemp)+train_min_meantemp

series_humidity = np.array(future_predictions[:, 1])*(train_max_humidity - train_min_humidity)+train_min_humidity

series_meanpressure = np.array(future_predictions[:, 2])*(train_max_meanpressure - train_min_meanpressure)+train_min_meanpressure



plt.figure(figsize=(20, 15), dpi =300)

plt.subplot(3,2,1)

plt.plot(pd.date_range(start='2013-01-13', end='2016-12-31', freq='D'), df_train.iloc[12::]['meantemp'],

         label='訓練集', color='blue', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-01', end='2017-04-24', freq='D'), df_test['meantemp'],

         label='測試集', color='gold', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-13', end='2017-04-24', freq='D'),

         y_pred[0]*(train_max_meantemp-train_min_meantemp)+train_min_meantemp,

         label='測試集預測', color='navy', alpha=0.8)

plt.plot(pd.date_range(start='2017-04-24', end='2017-05-04', freq='D'),

         series_meantemp, label='向后預測10天', color='limegreen', alpha=0.8)

plt.legend()

plt.title('meantemp')

plt.grid(True)

plt.xlabel('time')

plt.ylabel('°C')

plt.subplot(3,2, 2)

plt.plot(pd.date_range(start='2017-01-01', end='2017-04-24', freq='D'), df_test['meantemp'],

         label='測試集', color='gold', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-13', end='2017-04-24', freq='D'),

         y_pred[0]*(train_max_meantemp-train_min_meantemp)+train_min_meantemp,

         label='測試集預測', color='navy', alpha=0.8)

plt.plot(pd.date_range(start='2017-04-24', end='2017-05-04', freq='D'),

         series_meantemp, label='向后預測10天', color='limegreen', alpha=0.8)

plt.legend()

plt.title('meantemp')

plt.grid(True)

plt.xlabel('time')

plt.ylabel('°C')



plt.subplot(3,2,3)

plt.plot(pd.date_range(start='2013-01-13', end='2016-12-31', freq='D'), df_train.iloc[12::]['humidity'],

         label='訓練集', color='blue', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-01', end='2017-04-24', freq='D'), df_test['humidity'],

         label='測試集', color='gold', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-13', end='2017-04-24', freq='D'),

         y_pred[1]*(train_max_humidity-train_min_humidity)+train_min_humidity,

         label='測試集預測', color='navy', alpha=0.8)

plt.plot(pd.date_range(start='2017-04-24', end='2017-05-04', freq='D'),

         series_humidity, label='向后預測10天', color='limegreen', alpha=0.8)

plt.legend()

plt.title('humidity')

plt.grid(True)

plt.xlabel('time')

plt.ylabel('°C')

plt.subplot(3,2,4)

plt.plot(pd.date_range(start='2017-01-01', end='2017-04-24', freq='D'), df_test['humidity'],

         label='測試集', color='gold', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-13', end='2017-04-24', freq='D'),

         y_pred[1]*(train_max_humidity-train_min_humidity)+train_min_humidity,

         label='測試集預測', color='navy', alpha=0.8)

plt.plot(pd.date_range(start='2017-04-24', end='2017-05-04', freq='D'),

         series_humidity, label='向后預測10天', color='limegreen', alpha=0.8)

plt.legend()

plt.title('humidity')

plt.grid(True)

plt.xlabel('time')

plt.ylabel('°C')



plt.subplot(3,2,5)

plt.plot(pd.date_range(start='2013-01-13', end='2016-12-31', freq='D'), df_train.iloc[12::]['meanpressure'],

         label='訓練集', color='blue', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-01', end='2017-04-24', freq='D'), df_test['meanpressure'],

         label='測試集', color='gold', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-13', end='2017-04-24', freq='D'),

         y_pred[2]*(train_max_meanpressure-train_min_meanpressure)+train_min_meanpressure,

         label='測試集預測', color='navy', alpha=0.8)

plt.plot(pd.date_range(start='2017-04-24', end='2017-05-04', freq='D'),

         series_meanpressure, label='向后預測10天', color='limegreen', alpha=0.8)

plt.legend()

plt.title('meanpressure')

plt.grid(True)

plt.xlabel('pa')

plt.ylabel('°C')

plt.subplot(3,2,6)

plt.plot(pd.date_range(start='2017-01-01', end='2017-04-24', freq='D'), df_test['meanpressure'],

         label='測試集', color='gold', alpha=0.8)

plt.plot(pd.date_range(start='2017-01-13', end='2017-04-24', freq='D'),

         y_pred[2]*(train_max_meanpressure-train_min_meanpressure)+train_min_meanpressure,

         label='測試集預測', color='navy', alpha=0.8)

plt.plot(pd.date_range(start='2017-04-24', end='2017-05-04', freq='D'),

         series_meanpressure, label='向后預測10天', color='limegreen', alpha=0.8)

plt.legend()

plt.title('meanpressure')

plt.grid(True)

plt.xlabel('time')

plt.ylabel('pa')

plt.show()

文章轉自微信公眾號@Python機器學習AI

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時間窗口劃分：時序預測模型的多種形式解析

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