» Code examples / Timeseries / Timeseries anomaly detection using an Autoencoder

Timeseries anomaly detection using an Autoencoder

Author: pavithrasv
Date created: 2020/05/31
Last modified: 2020/05/31
Description: Detect anomalies in a timeseries using an Autoencoder.

View in Colab GitHub source


Introduction

This script demonstrates how you can use a reconstruction convolutional autoencoder model to detect anomalies in timeseries data.


Setup

import numpy as np
import pandas as pd
from tensorflow import keras
from tensorflow.keras import layers
from matplotlib import pyplot as plt

Load the data

We will use the Numenta Anomaly Benchmark(NAB) dataset. It provides artifical timeseries data containing labeled anomalous periods of behavior. Data are ordered, timestamped, single-valued metrics.

We will use the art_daily_small_noise.csv file for training and the art_daily_jumpsup.csv file for testing. The simplicity of this dataset allows us to demonstrate anomaly detection effectively.

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"
)

Quick look at the data

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

Visualize the data

Timeseries data without anomalies

We will use the following data for training.

fig, ax = plt.subplots()
df_small_noise.plot(legend=False, ax=ax)
plt.show()

png

Timeseries data with anomalies

We will use the following data for testing and see if the sudden jump up in the data is detected as an anomaly.

fig, ax = plt.subplots()
df_daily_jumpsup.plot(legend=False, ax=ax)
plt.show()

png


Prepare training data

Get data values from the training timeseries data file and normalize the value data. We have a value for every 5 mins for 14 days.

  • 24 * 60 / 5 = 288 timesteps per day
  • 288 * 14 = 4032 data points in total
# 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

Create sequences

Create sequences combining TIME_STEPS contiguous data values from the training data.

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):
        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:  (3744, 288, 1)

Build a model

We will build a convolutional reconstruction autoencoder model. The model will take input of shape (batch_size, sequence_length, num_features) and return output of the same shape. In this case, sequence_length is 288 and num_features is 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)            3600      
_________________________________________________________________
conv1d_transpose (Conv1DTran (None, 144, 16)           1808      
_________________________________________________________________
dropout_1 (Dropout)          (None, 144, 16)           0         
_________________________________________________________________
conv1d_transpose_1 (Conv1DTr (None, 288, 32)           3616      
_________________________________________________________________
conv1d_transpose_2 (Conv1DTr (None, 288, 1)            225       
=================================================================
Total params: 9,505
Trainable params: 9,505
Non-trainable params: 0
_________________________________________________________________

Train the model

Please note that we are using x_train as both the input and the target since this is a reconstruction model.

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
27/27 [==============================] - 2s 35ms/step - loss: 0.6599 - val_loss: 0.0711
Epoch 2/50
27/27 [==============================] - 1s 27ms/step - loss: 0.0772 - val_loss: 0.0397
Epoch 3/50
27/27 [==============================] - 1s 28ms/step - loss: 0.0591 - val_loss: 0.0376
Epoch 4/50
27/27 [==============================] - 1s 29ms/step - loss: 0.0518 - val_loss: 0.0332
Epoch 5/50
27/27 [==============================] - 1s 29ms/step - loss: 0.0461 - val_loss: 0.0299
Epoch 6/50
27/27 [==============================] - 1s 28ms/step - loss: 0.0411 - val_loss: 0.0268
Epoch 7/50
27/27 [==============================] - 1s 28ms/step - loss: 0.0370 - val_loss: 0.0249
Epoch 8/50
27/27 [==============================] - 1s 29ms/step - loss: 0.0338 - val_loss: 0.0234
Epoch 9/50
27/27 [==============================] - 1s 30ms/step - loss: 0.0314 - val_loss: 0.0225
Epoch 10/50
27/27 [==============================] - 1s 29ms/step - loss: 0.0293 - val_loss: 0.0220
Epoch 11/50
27/27 [==============================] - 1s 28ms/step - loss: 0.0275 - val_loss: 0.0209
Epoch 12/50
27/27 [==============================] - 1s 30ms/step - loss: 0.0258 - val_loss: 0.0204
Epoch 13/50
27/27 [==============================] - 1s 31ms/step - loss: 0.0243 - val_loss: 0.0203
Epoch 14/50
27/27 [==============================] - 1s 30ms/step - loss: 0.0229 - val_loss: 0.0198
Epoch 15/50
27/27 [==============================] - 1s 31ms/step - loss: 0.0218 - val_loss: 0.0192
Epoch 16/50
27/27 [==============================] - 1s 31ms/step - loss: 0.0208 - val_loss: 0.0175
Epoch 17/50
27/27 [==============================] - 1s 32ms/step - loss: 0.0197 - val_loss: 0.0174
Epoch 18/50
27/27 [==============================] - 1s 31ms/step - loss: 0.0189 - val_loss: 0.0158
Epoch 19/50
27/27 [==============================] - 1s 35ms/step - loss: 0.0181 - val_loss: 0.0148
Epoch 20/50
27/27 [==============================] - 1s 33ms/step - loss: 0.0174 - val_loss: 0.0144
Epoch 21/50
27/27 [==============================] - 1s 35ms/step - loss: 0.0167 - val_loss: 0.0148
Epoch 22/50
27/27 [==============================] - 1s 35ms/step - loss: 0.0161 - val_loss: 0.0137
Epoch 23/50
27/27 [==============================] - 1s 34ms/step - loss: 0.0155 - val_loss: 0.0135
Epoch 24/50
27/27 [==============================] - 1s 34ms/step - loss: 0.0150 - val_loss: 0.0128
Epoch 25/50
27/27 [==============================] - 1s 33ms/step - loss: 0.0146 - val_loss: 0.0130
Epoch 26/50
27/27 [==============================] - 1s 32ms/step - loss: 0.0141 - val_loss: 0.0118
Epoch 27/50
27/27 [==============================] - 1s 33ms/step - loss: 0.0137 - val_loss: 0.0113
Epoch 28/50
27/27 [==============================] - 1s 31ms/step - loss: 0.0133 - val_loss: 0.0111
Epoch 29/50
27/27 [==============================] - 1s 32ms/step - loss: 0.0128 - val_loss: 0.0113
Epoch 30/50
27/27 [==============================] - 1s 33ms/step - loss: 0.0124 - val_loss: 0.0104
Epoch 31/50
27/27 [==============================] - 1s 33ms/step - loss: 0.0121 - val_loss: 0.0091
Epoch 32/50
27/27 [==============================] - 1s 33ms/step - loss: 0.0117 - val_loss: 0.0092
Epoch 33/50
27/27 [==============================] - 1s 34ms/step - loss: 0.0112 - val_loss: 0.0091
Epoch 34/50
27/27 [==============================] - 1s 37ms/step - loss: 0.0109 - val_loss: 0.0085
Epoch 35/50
27/27 [==============================] - 1s 37ms/step - loss: 0.0105 - val_loss: 0.0081
Epoch 36/50
27/27 [==============================] - 1s 37ms/step - loss: 0.0101 - val_loss: 0.0074
Epoch 37/50
27/27 [==============================] - 1s 36ms/step - loss: 0.0098 - val_loss: 0.0076
Epoch 38/50
27/27 [==============================] - 1s 38ms/step - loss: 0.0095 - val_loss: 0.0074
Epoch 39/50
27/27 [==============================] - 1s 39ms/step - loss: 0.0092 - val_loss: 0.0070
Epoch 40/50
27/27 [==============================] - 1s 40ms/step - loss: 0.0089 - val_loss: 0.0069
Epoch 41/50
27/27 [==============================] - 1s 38ms/step - loss: 0.0086 - val_loss: 0.0068
Epoch 42/50
27/27 [==============================] - 1s 39ms/step - loss: 0.0084 - val_loss: 0.0063
Epoch 43/50
27/27 [==============================] - 1s 38ms/step - loss: 0.0082 - val_loss: 0.0061
Epoch 44/50
27/27 [==============================] - 1s 41ms/step - loss: 0.0079 - val_loss: 0.0057
Epoch 45/50
27/27 [==============================] - 1s 40ms/step - loss: 0.0077 - val_loss: 0.0055
Epoch 46/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0075 - val_loss: 0.0055
Epoch 47/50
27/27 [==============================] - 1s 39ms/step - loss: 0.0074 - val_loss: 0.0051
Epoch 48/50
27/27 [==============================] - 1s 36ms/step - loss: 0.0072 - val_loss: 0.0054
Epoch 49/50
27/27 [==============================] - 1s 40ms/step - loss: 0.0071 - val_loss: 0.0053
Epoch 50/50
27/27 [==============================] - 1s 41ms/step - loss: 0.0070 - val_loss: 0.0052

Let's plot training and validation loss to see how the training went.

plt.plot(history.history["loss"], label="Training Loss")
plt.plot(history.history["val_loss"], label="Validation Loss")
plt.legend()
plt.show()

png


Detecting anomalies

We will detect anomalies by determining how well our model can reconstruct the input data.

  1. Find MAE loss on training samples.
  2. Find max MAE loss value. This is the worst our model has performed trying to reconstruct a sample. We will make this the threshold for anomaly detection.
  3. If the reconstruction loss for a sample is greater than this threshold value then we can infer that the model is seeing a pattern that it isn't familiar with. We will label this sample as an anomaly.
# 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)

png

Reconstruction error threshold:  0.06655808810755175

Compare recontruction

Just for fun, let's see how our model has recontructed the first sample. This is the 288 timesteps from day 1 of our training dataset.

# Checking how the first sequence is learnt
plt.plot(x_train[0])
plt.plot(x_train_pred[0])
plt.show()

png

Prepare test data

def normalize_test(values, mean, std):
    values -= mean
    values /= std
    return values


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))

png

Test input shape:  (3744, 288, 1)

png

Number of anomaly samples:  411
Indices of anomaly samples:  (array([ 217,  774,  790,  793,  794, 1654, 1942, 1943, 1944, 1945, 1948,
       2140, 2519, 2521, 2699, 2701, 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, 3095, 3097]),)

Plot anomalies

We now know the samples of the data which are anomalies. With this, we will find the corresponding timestamps from the original test data. We will be using the following method to do that:

Let's say time_steps = 3 and we have 10 training values. Our x_train will look like this:

  • 0, 1, 2
  • 1, 2, 3
  • 2, 3, 4
  • 3, 4, 5
  • 4, 5, 6
  • 5, 6, 7
  • 6, 7, 8
  • 7, 8, 9

All except the initial and the final time_steps-1 data values, will appear in time_steps number of samples. So, if we know that the samples [(3, 4, 5), (4, 5, 6), (5, 6, 7)] are anomalies, we can say that the data point 5 is an anomaly.

# 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)

Let's overlay the anomalies on the original test data plot.

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()

png