使用自動編碼器進行時間序列異常偵測
作者： pavithrasv
建立日期 2020/05/31
上次修改日期 2020/05/31
說明： 使用自動編碼器偵測時間序列中的異常。
簡介
此腳本示範如何使用重建卷積自動編碼器模型來偵測時間序列資料中的異常。
設定
import numpy as np
import pandas as pd
import keras
from keras import layers
from matplotlib import pyplot as plt
載入資料
我們將使用 Numenta 異常基準 (NAB) 資料集。它提供包含標記異常行為期間的人工時間序列資料。資料是有序的、帶有時間戳記的、單值的指標。
我們將使用 art_daily_small_noise.csv 檔案進行訓練，並使用 art_daily_jumpsup.csv 檔案進行測試。此資料集的簡單性讓我們能夠有效地示範異常偵測。
master_url_root = "https://raw.githubusercontent.com/numenta/NAB/master/data/"
df_small_noise_url_suffix = "artificialNoAnomaly/art_daily_small_noise.csv"
df_small_noise_url = master_url_root + df_small_noise_url_suffix
df_small_noise = pd.read_csv(
df_small_noise_url, parse_dates=True, index_col="timestamp"
)
df_daily_jumpsup_url_suffix = "artificialWithAnomaly/art_daily_jumpsup.csv"
df_daily_jumpsup_url = master_url_root + df_daily_jumpsup_url_suffix
df_daily_jumpsup = pd.read_csv(
df_daily_jumpsup_url, parse_dates=True, index_col="timestamp"
)
資料快速瀏覽
print(df_small_noise.head())
print(df_daily_jumpsup.head())
value
timestamp
2014-04-01 00:00:00 18.324919
2014-04-01 00:05:00 21.970327
2014-04-01 00:10:00 18.624806
2014-04-01 00:15:00 21.953684
2014-04-01 00:20:00 21.909120
value
timestamp
2014-04-01 00:00:00 19.761252
2014-04-01 00:05:00 20.500833
2014-04-01 00:10:00 19.961641
2014-04-01 00:15:00 21.490266
2014-04-01 00:20:00 20.187739
視覺化資料
沒有異常的時間序列資料
我們將使用以下資料進行訓練。
fig, ax = plt.subplots()
df_small_noise.plot(legend=False, ax=ax)
plt.show()
具有異常的時間序列資料
我們將使用以下資料進行測試，並查看資料中的突然跳升是否被偵測為異常。
fig, ax = plt.subplots()
df_daily_jumpsup.plot(legend=False, ax=ax)
plt.show()
準備訓練資料
從訓練時間序列資料檔案取得資料值，並正規化 value 資料。我們每 5 分鐘會有一個 value，持續 14 天。
- 24 * 60 / 5 = 每天 288 個時間步長
- 288 * 14 = 總共 4032 個資料點
# Normalize and save the mean and std we get,
# for normalizing test data.
training_mean = df_small_noise.mean()
training_std = df_small_noise.std()
df_training_value = (df_small_noise - training_mean) / training_std
print("Number of training samples:", len(df_training_value))
Number of training samples: 4032
建立序列
從訓練資料中建立結合 TIME_STEPS 連續資料值的序列。
TIME_STEPS = 288
# Generated training sequences for use in the model.
def create_sequences(values, time_steps=TIME_STEPS):
output = []
for i in range(len(values) - time_steps + 1):
output.append(values[i : (i + time_steps)])
return np.stack(output)
x_train = create_sequences(df_training_value.values)
print("Training input shape: ", x_train.shape)
Training input shape: (3745, 288, 1)
建立模型
我們將建立卷積重建自動編碼器模型。該模型將接收形狀為 (batch_size, sequence_length, num_features) 的輸入，並傳回相同形狀的輸出。在此案例中，sequence_length 為 288，而 num_features 為 1。
model = keras.Sequential(
[
layers.Input(shape=(x_train.shape[1], x_train.shape[2])),
layers.Conv1D(
filters=32,
kernel_size=7,
padding="same",
strides=2,
activation="relu",
),
layers.Dropout(rate=0.2),
layers.Conv1D(
filters=16,
kernel_size=7,
padding="same",
strides=2,
activation="relu",
),
layers.Conv1DTranspose(
filters=16,
kernel_size=7,
padding="same",
strides=2,
activation="relu",
),
layers.Dropout(rate=0.2),
layers.Conv1DTranspose(
filters=32,
kernel_size=7,
padding="same",
strides=2,
activation="relu",
),
layers.Conv1DTranspose(filters=1, kernel_size=7, padding="same"),
]
)
model.compile(optimizer=keras.optimizers.Adam(learning_rate=0.001), loss="mse")
model.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━┩ │ conv1d (Conv1D) │ (None, 144, 32) │ 256 │ ├─────────────────────────────────┼───────────────────────────┼────────────┤ │ dropout (Dropout) │ (None, 144, 32) │ 0 │ ├─────────────────────────────────┼───────────────────────────┼────────────┤ │ conv1d_1 (Conv1D) │ (None, 72, 16) │ 3,600 │ ├─────────────────────────────────┼───────────────────────────┼────────────┤ │ conv1d_transpose │ (None, 144, 16) │ 1,808 │ │ (Conv1DTranspose) │ │ │ ├─────────────────────────────────┼───────────────────────────┼────────────┤ │ dropout_1 (Dropout) │ (None, 144, 16) │ 0 │ ├─────────────────────────────────┼───────────────────────────┼────────────┤ │ conv1d_transpose_1 │ (None, 288, 32) │ 3,616 │ │ (Conv1DTranspose) │ │ │ ├─────────────────────────────────┼───────────────────────────┼────────────┤ │ conv1d_transpose_2 │ (None, 288, 1) │ 225 │ │ (Conv1DTranspose) │ │ │ └─────────────────────────────────┴───────────────────────────┴────────────┘
Total params: 9,505 (37.13 KB)
Trainable params: 9,505 (37.13 KB)
Non-trainable params: 0 (0.00 B)
訓練模型
請注意，由於這是重建模型，因此我們將 x_train 同時用作輸入和目標。
history = model.fit(
x_train,
x_train,
epochs=50,
batch_size=128,
validation_split=0.1,
callbacks=[
keras.callbacks.EarlyStopping(monitor="val_loss", patience=5, mode="min")
],
)
Epoch 1/50
26/27 ━━━━━━━━━━━━━━━━━━━[37m━ 0s 4ms/step - loss: 0.8419
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1700346169.474466 1961179 device_compiler.h:187] Compiled cluster using XLA! This line is logged at most once for the lifetime of the process.
27/27 ━━━━━━━━━━━━━━━━━━━━ 10s 187ms/step - loss: 0.8262 - val_loss: 0.2280
Epoch 2/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.1485 - val_loss: 0.0513
Epoch 3/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0659 - val_loss: 0.0389
Epoch 4/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0563 - val_loss: 0.0341
Epoch 5/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0489 - val_loss: 0.0298
Epoch 6/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0434 - val_loss: 0.0272
Epoch 7/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0386 - val_loss: 0.0258
Epoch 8/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0349 - val_loss: 0.0241
Epoch 9/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0319 - val_loss: 0.0230
Epoch 10/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0297 - val_loss: 0.0236
Epoch 11/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0279 - val_loss: 0.0233
Epoch 12/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0264 - val_loss: 0.0225
Epoch 13/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0255 - val_loss: 0.0228
Epoch 14/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0245 - val_loss: 0.0223
Epoch 15/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0236 - val_loss: 0.0234
Epoch 16/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0227 - val_loss: 0.0256
Epoch 17/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0219 - val_loss: 0.0240
Epoch 18/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0214 - val_loss: 0.0245
Epoch 19/50
27/27 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0207 - val_loss: 0.0250
讓我們繪製訓練和驗證損失，以查看訓練的進展情況。
plt.plot(history.history["loss"], label="Training Loss")
plt.plot(history.history["val_loss"], label="Validation Loss")
plt.legend()
plt.show()
偵測異常
我們將透過判斷模型重建輸入資料的能力來偵測異常。
- 找出訓練樣本的 MAE 損失。
- 找出最大 MAE 損失值。這是我們的模型嘗試重建樣本時表現最差的情況。我們將以此作為異常偵測的
threshold（閾值）。 - 如果樣本的重建損失大於此
threshold值，那麼我們可以推斷模型正在看到它不熟悉的模式。我們將此樣本標記為anomaly（異常）。
# Get train MAE loss.
x_train_pred = model.predict(x_train)
train_mae_loss = np.mean(np.abs(x_train_pred - x_train), axis=1)
plt.hist(train_mae_loss, bins=50)
plt.xlabel("Train MAE loss")
plt.ylabel("No of samples")
plt.show()
# Get reconstruction loss threshold.
threshold = np.max(train_mae_loss)
print("Reconstruction error threshold: ", threshold)
118/118 ━━━━━━━━━━━━━━━━━━━━ 1s 6ms/step
Reconstruction error threshold: 0.1232659916089631
比較重建
為了好玩，讓我們看看我們的模型如何重建第一個樣本。這是我們訓練資料集第 1 天的 288 個時間步長。
# Checking how the first sequence is learnt
plt.plot(x_train[0])
plt.plot(x_train_pred[0])
plt.show()
準備測試資料
df_test_value = (df_daily_jumpsup - training_mean) / training_std
fig, ax = plt.subplots()
df_test_value.plot(legend=False, ax=ax)
plt.show()
# Create sequences from test values.
x_test = create_sequences(df_test_value.values)
print("Test input shape: ", x_test.shape)
# Get test MAE loss.
x_test_pred = model.predict(x_test)
test_mae_loss = np.mean(np.abs(x_test_pred - x_test), axis=1)
test_mae_loss = test_mae_loss.reshape((-1))
plt.hist(test_mae_loss, bins=50)
plt.xlabel("test MAE loss")
plt.ylabel("No of samples")
plt.show()
# Detect all the samples which are anomalies.
anomalies = test_mae_loss > threshold
print("Number of anomaly samples: ", np.sum(anomalies))
print("Indices of anomaly samples: ", np.where(anomalies))
Test input shape: (3745, 288, 1)
118/118 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step
Number of anomaly samples: 394
Indices of anomaly samples: (array([1654, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 2710, 2711,
2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 2720, 2721, 2722,
2723, 2724, 2725, 2726, 2727, 2728, 2729, 2730, 2731, 2732, 2733,
2734, 2735, 2736, 2737, 2738, 2739, 2740, 2741, 2742, 2743, 2744,
2745, 2746, 2747, 2748, 2749, 2750, 2751, 2752, 2753, 2754, 2755,
2756, 2757, 2758, 2759, 2760, 2761, 2762, 2763, 2764, 2765, 2766,
2767, 2768, 2769, 2770, 2771, 2772, 2773, 2774, 2775, 2776, 2777,
2778, 2779, 2780, 2781, 2782, 2783, 2784, 2785, 2786, 2787, 2788,
2789, 2790, 2791, 2792, 2793, 2794, 2795, 2796, 2797, 2798, 2799,
2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2808, 2809, 2810,
2811, 2812, 2813, 2814, 2815, 2816, 2817, 2818, 2819, 2820, 2821,
2822, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 2830, 2831, 2832,
2833, 2834, 2835, 2836, 2837, 2838, 2839, 2840, 2841, 2842, 2843,
2844, 2845, 2846, 2847, 2848, 2849, 2850, 2851, 2852, 2853, 2854,
2855, 2856, 2857, 2858, 2859, 2860, 2861, 2862, 2863, 2864, 2865,
2866, 2867, 2868, 2869, 2870, 2871, 2872, 2873, 2874, 2875, 2876,
2877, 2878, 2879, 2880, 2881, 2882, 2883, 2884, 2885, 2886, 2887,
2888, 2889, 2890, 2891, 2892, 2893, 2894, 2895, 2896, 2897, 2898,
2899, 2900, 2901, 2902, 2903, 2904, 2905, 2906, 2907, 2908, 2909,
2910, 2911, 2912, 2913, 2914, 2915, 2916, 2917, 2918, 2919, 2920,
2921, 2922, 2923, 2924, 2925, 2926, 2927, 2928, 2929, 2930, 2931,
2932, 2933, 2934, 2935, 2936, 2937, 2938, 2939, 2940, 2941, 2942,
2943, 2944, 2945, 2946, 2947, 2948, 2949, 2950, 2951, 2952, 2953,
2954, 2955, 2956, 2957, 2958, 2959, 2960, 2961, 2962, 2963, 2964,
2965, 2966, 2967, 2968, 2969, 2970, 2971, 2972, 2973, 2974, 2975,
2976, 2977, 2978, 2979, 2980, 2981, 2982, 2983, 2984, 2985, 2986,
2987, 2988, 2989, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997,
2998, 2999, 3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008,
3009, 3010, 3011, 3012, 3013, 3014, 3015, 3016, 3017, 3018, 3019,
3020, 3021, 3022, 3023, 3024, 3025, 3026, 3027, 3028, 3029, 3030,
3031, 3032, 3033, 3034, 3035, 3036, 3037, 3038, 3039, 3040, 3041,
3042, 3043, 3044, 3045, 3046, 3047, 3048, 3049, 3050, 3051, 3052,
3053, 3054, 3055, 3056, 3057, 3058, 3059, 3060, 3061, 3062, 3063,
3064, 3065, 3066, 3067, 3068, 3069, 3070, 3071, 3072, 3073, 3074,
3075, 3076, 3077, 3078, 3079, 3080, 3081, 3082, 3083, 3084, 3085,
3086, 3087, 3088, 3089, 3090, 3091, 3092, 3093, 3094]),)
繪製異常
我們現在知道哪些資料樣本是異常。有了這個，我們將從原始測試資料中找到對應的 timestamps（時間戳記）。我們將使用以下方法來做到這一點
假設 time_steps = 3，我們有 10 個訓練值。我們的 x_train 將如下所示
- 0, 1, 2
- 1, 2, 3
- 2, 3, 4
- 3, 4, 5
- 4, 5, 6
- 5, 6, 7
- 6, 7, 8
- 7, 8, 9
除了初始和最終的 time_steps-1 資料值之外，所有資料值都會在 time_steps 個樣本中出現。因此，如果我們知道樣本 [(3, 4, 5), (4, 5, 6), (5, 6, 7)] 是異常，我們可以說資料點 5 是異常。
# data i is an anomaly if samples [(i - timesteps + 1) to (i)] are anomalies
anomalous_data_indices = []
for data_idx in range(TIME_STEPS - 1, len(df_test_value) - TIME_STEPS + 1):
if np.all(anomalies[data_idx - TIME_STEPS + 1 : data_idx]):
anomalous_data_indices.append(data_idx)
讓我們將異常覆蓋在原始測試資料圖上。
df_subset = df_daily_jumpsup.iloc[anomalous_data_indices]
fig, ax = plt.subplots()
df_daily_jumpsup.plot(legend=False, ax=ax)
df_subset.plot(legend=False, ax=ax, color="r")
plt.show()
