» 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 datetime import datetime
from matplotlib import pyplot as plt
from matplotlib import dates as md

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)

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)

Quick look at the data

print(df_small_noise.head())

print(df_daily_jumpsup.head())
             timestamp      value
0  2014-04-01 00:00:00  18.324919
1  2014-04-01 00:05:00  21.970327
2  2014-04-01 00:10:00  18.624806
3  2014-04-01 00:15:00  21.953684
4  2014-04-01 00:20:00  21.909120
             timestamp      value
0  2014-04-01 00:00:00  19.761252
1  2014-04-01 00:05:00  20.500833
2  2014-04-01 00:10:00  19.961641
3  2014-04-01 00:15:00  21.490266
4  2014-04-01 00:20:00  20.187739

Visualize the data

def plot_dates_values(data):
    dates = data["timestamp"].to_list()
    values = data["value"].to_list()
    dates = [datetime.strptime(x, "%Y-%m-%d %H:%M:%S") for x in dates]
    plt.subplots_adjust(bottom=0.2)
    plt.xticks(rotation=25)
    ax = plt.gca()
    xfmt = md.DateFormatter("%Y-%m-%d %H:%M:%S")
    ax.xaxis.set_major_formatter(xfmt)
    plt.plot(dates, values)
    plt.show()

Timeseries data without anomalies

We will use the following data for training.

plot_dates_values(df_small_noise)
/usr/local/lib/python3.7/site-packages/pandas/plotting/_converter.py:129: FutureWarning: Using an implicitly registered datetime converter for a matplotlib plotting method. The converter was registered by pandas on import. Future versions of pandas will require you to explicitly register matplotlib converters.
To register the converters:
    >>> from pandas.plotting import register_matplotlib_converters
    >>> register_matplotlib_converters()
  warnings.warn(msg, FutureWarning)

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.

plot_dates_values(df_daily_jumpsup)

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
def get_value_from_df(df):
    return df.value.to_list()


def normalize(values):
    mean = np.mean(values)
    values -= mean
    std = np.std(values)
    values /= std
    return values, mean, std


# Get the `value` column from the training dataframe.
training_value = get_value_from_df(df_small_noise)

# Normalize `value` and save the mean and std we get,
# for normalizing test data.
training_value, training_mean, training_std = normalize(training_value)
len(training_value)
4032

Create sequences

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

TIME_STEPS = 288


def create_sequences(values, time_steps=TIME_STEPS):
    output = []
    for i in range(len(values) - time_steps):
        output.append(values[i : (i + time_steps)])
    # Convert 2D sequences into 3D as we will be feeding this into
    # a convolutional layer.
    return np.expand_dims(output, axis=2)


x_train = create_sequences(training_value)
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 [==============================] - 1s 39ms/step - loss: 0.5689 - val_loss: 0.1147
Epoch 2/50
27/27 [==============================] - 1s 31ms/step - loss: 0.0853 - val_loss: 0.0430
Epoch 3/50
27/27 [==============================] - 1s 35ms/step - loss: 0.0594 - val_loss: 0.0371
Epoch 4/50
27/27 [==============================] - 1s 33ms/step - loss: 0.0498 - val_loss: 0.0327
Epoch 5/50
27/27 [==============================] - 1s 35ms/step - loss: 0.0420 - val_loss: 0.0297
Epoch 6/50
27/27 [==============================] - 1s 37ms/step - loss: 0.0367 - val_loss: 0.0272
Epoch 7/50
27/27 [==============================] - 1s 37ms/step - loss: 0.0331 - val_loss: 0.0256
Epoch 8/50
27/27 [==============================] - 1s 36ms/step - loss: 0.0302 - val_loss: 0.0246
Epoch 9/50
27/27 [==============================] - 1s 36ms/step - loss: 0.0282 - val_loss: 0.0237
Epoch 10/50
27/27 [==============================] - 1s 37ms/step - loss: 0.0266 - val_loss: 0.0235
Epoch 11/50
27/27 [==============================] - 1s 37ms/step - loss: 0.0254 - val_loss: 0.0230
Epoch 12/50
27/27 [==============================] - 1s 38ms/step - loss: 0.0243 - val_loss: 0.0237
Epoch 13/50
27/27 [==============================] - 1s 39ms/step - loss: 0.0232 - val_loss: 0.0247
Epoch 14/50
27/27 [==============================] - 1s 39ms/step - loss: 0.0224 - val_loss: 0.0236
Epoch 15/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0215 - val_loss: 0.0242
Epoch 16/50
27/27 [==============================] - 1s 41ms/step - loss: 0.0207 - val_loss: 0.0226
Epoch 17/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0199 - val_loss: 0.0235
Epoch 18/50
27/27 [==============================] - 1s 39ms/step - loss: 0.0191 - val_loss: 0.0229
Epoch 19/50
27/27 [==============================] - 1s 41ms/step - loss: 0.0184 - val_loss: 0.0225
Epoch 20/50
27/27 [==============================] - 1s 41ms/step - loss: 0.0177 - val_loss: 0.0219
Epoch 21/50
27/27 [==============================] - 1s 44ms/step - loss: 0.0170 - val_loss: 0.0205
Epoch 22/50
27/27 [==============================] - 1s 43ms/step - loss: 0.0164 - val_loss: 0.0194
Epoch 23/50
27/27 [==============================] - 1s 41ms/step - loss: 0.0158 - val_loss: 0.0204
Epoch 24/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0154 - val_loss: 0.0199
Epoch 25/50
27/27 [==============================] - 1s 44ms/step - loss: 0.0149 - val_loss: 0.0190
Epoch 26/50
27/27 [==============================] - 1s 43ms/step - loss: 0.0144 - val_loss: 0.0187
Epoch 27/50
27/27 [==============================] - 1s 45ms/step - loss: 0.0141 - val_loss: 0.0183
Epoch 28/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0137 - val_loss: 0.0185
Epoch 29/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0132 - val_loss: 0.0175
Epoch 30/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0128 - val_loss: 0.0177
Epoch 31/50
27/27 [==============================] - 1s 43ms/step - loss: 0.0124 - val_loss: 0.0163
Epoch 32/50
27/27 [==============================] - 1s 44ms/step - loss: 0.0120 - val_loss: 0.0170
Epoch 33/50
27/27 [==============================] - 1s 43ms/step - loss: 0.0116 - val_loss: 0.0154
Epoch 34/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0112 - val_loss: 0.0150
Epoch 35/50
27/27 [==============================] - 1s 42ms/step - loss: 0.0109 - val_loss: 0.0142
Epoch 36/50
27/27 [==============================] - 1s 44ms/step - loss: 0.0105 - val_loss: 0.0145
Epoch 37/50
27/27 [==============================] - 1s 44ms/step - loss: 0.0101 - val_loss: 0.0132
Epoch 38/50
27/27 [==============================] - 1s 46ms/step - loss: 0.0098 - val_loss: 0.0130
Epoch 39/50
27/27 [==============================] - 1s 47ms/step - loss: 0.0095 - val_loss: 0.0118
Epoch 40/50
27/27 [==============================] - 1s 44ms/step - loss: 0.0092 - val_loss: 0.0120
Epoch 41/50
27/27 [==============================] - 1s 46ms/step - loss: 0.0089 - val_loss: 0.0111
Epoch 42/50
27/27 [==============================] - 1s 47ms/step - loss: 0.0087 - val_loss: 0.0109
Epoch 43/50
27/27 [==============================] - 1s 49ms/step - loss: 0.0085 - val_loss: 0.0102
Epoch 44/50
27/27 [==============================] - 1s 54ms/step - loss: 0.0082 - val_loss: 0.0103
Epoch 45/50
27/27 [==============================] - 1s 47ms/step - loss: 0.0080 - val_loss: 0.0094
Epoch 46/50
27/27 [==============================] - 1s 50ms/step - loss: 0.0078 - val_loss: 0.0096
Epoch 47/50
27/27 [==============================] - 1s 48ms/step - loss: 0.0077 - val_loss: 0.0093
Epoch 48/50
27/27 [==============================] - 1s 51ms/step - loss: 0.0075 - val_loss: 0.0093
Epoch 49/50
27/27 [==============================] - 2s 57ms/step - loss: 0.0074 - val_loss: 0.0093
Epoch 50/50
27/27 [==============================] - 1s 48ms/step - loss: 0.0072 - val_loss: 0.0095

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()
<matplotlib.legend.Legend at 0x159955f50>

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:  0.08677480230901682

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.show()
plt.plot(x_train_pred[0])
plt.show()

png

png

Prepare test data

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


test_value = get_value_from_df(df_daily_jumpsup)
test_value = normalize_test(test_value, training_mean, training_std)
plt.plot(test_value.tolist())
plt.show()

# Create sequences from test values.
x_test = create_sequences(test_value)
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).tolist()
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:  418
Indices of anomaly samples:  (array([ 769,  773,  774,  775,  777,  778,  781,  790,  791,  792,  793,
        794,  795,  796,  799,  970,  973,  974, 1942, 1945, 1946, 2521,
       2698, 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]),)

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(test_value) - TIME_STEPS + 1):
    time_series = range(data_idx - TIME_STEPS + 1, data_idx)
    if all([anomalies[j] for j in time_series]):
        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, :]
plt.subplots_adjust(bottom=0.2)
plt.xticks(rotation=25)
ax = plt.gca()
xfmt = md.DateFormatter("%Y-%m-%d %H:%M:%S")
ax.xaxis.set_major_formatter(xfmt)

dates = df_daily_jumpsup["timestamp"].to_list()
dates = [datetime.strptime(x, "%Y-%m-%d %H:%M:%S") for x in dates]
values = df_daily_jumpsup["value"].to_list()
plt.plot(dates, values, label="test data")

dates = df_subset["timestamp"].to_list()
dates = [datetime.strptime(x, "%Y-%m-%d %H:%M:%S") for x in dates]
values = df_subset["value"].to_list()
plt.plot(dates, values, label="anomalies", color="r")

plt.legend()
plt.show()

png