Predictive Difference Based Approach

The most widely used technique for time series anomaly detection is the predictive difference based approach.

The logic of the approach is the following
Step 1: Fit the predictive model to the data
Step 2: Calculate the difference between the prediction and the true label, and in case the difference is too large mark the point as anomaly
The problem of this approach is that it is highly depedent on predictive accuracy of the model.

!wget https://raw.githubusercontent.com/jbrownlee/Datasets/master/monthly-sunspots.csv
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

from sklearn.preprocessing import MinMaxScaler

import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
scaler=MinMaxScaler()

df = pd.read_csv("monthly-sunspots.csv")
df["Month"] = pd.to_datetime(df["Month"]).astype(int)// 10**11 + 69740352
# df=df.drop("Month",axis=1)
df["Month"]=scaler.fit_transform(df["Month"].values.reshape(-1,1))

model = keras.Sequential()
model.add(layers.LSTM(128,input_shape=(1,2820),activation="relu"))
model.add(layers.Dense(1))
model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.001),loss=tf.keras.losses.MeanSquaredError())

model.fit(x_train,y_train,epochs=10)

y_pred=model.predict(x_train)

plt.plot(x_train.reshape(2820,),y_train.reshape(2820,))
plt.plot(x_train.reshape(2820,),y_pred.reshape(2820,))
plt.show()


before_anom=abs(y_train.reshape(2820,)-y_pred.reshape(2820,))
anom_pts=np.percentile(before_anom,95)
anoms=np.where(before_anom>anom_pts,1,0)

Another well known approach for time series anomaly detection is treating time-series as a collection of datapoints utilizing any anomaly detection algorithm to obtain the anomalies.</br>

!wget https://raw.githubusercontent.com/jbrownlee/Datasets/master/monthly-sunspots.csv
from sklearn.ensemble import IsolationForest
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

df = pd.read_csv("monthly-sunspots.csv")

anomaly=IsolationForest(n_estimators=100,contamination=0.05).fit_predict(df["Sunspots"].values.reshape(-1,1))

plt.plot(df.index,df.Sunspots)
for i,j in enumerate(anomaly):
  if j == -1:
    plt.plot(df.index.values[i],df.Sunspots.values[i],"g*")

plt.show()

Anomaly detection using the confidence intervals is another well known technique for obtaining the anomalies in time series data.

!wget https://raw.githubusercontent.com/jbrownlee/Datasets/master/monthly-sunspots.csv
from fbprophet import Prophet
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

df = pd.read_csv("monthly-sunspots.csv")
df=df.rename(columns={"Month":"ds","Sunspots":"y"})

prop = Prophet()
prop.fit(df)
pred=prop.predict(df)

anom_pred=np.where(df.y<=pred.yhat_upper,np.where(df.y>=pred.yhat_lower,1,-1),-1)

plt.plot(df.index,df.y)
for i,j in enumerate(anom_pred):
  if j == -1:
    plt.plot(df.index.values[i],df.y.values[i],"g*")

plt.show()

Lesser known technique for anomaly detection is to use connectivity based clustering algorithms for anomaly detection.

!wget https://raw.githubusercontent.com/jbrownlee/Datasets/master/monthly-sunspots.csv
from sklearn.cluster import DBSCAN
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

df=pd.read_csv("monthly-sunspots.csv")

dbscan=DBSCAN(eps=0.5,min_samples=10)
dbscan_out=dbscan.fit_predict(df.Sunspots.values.reshape(-1,1))

plt.plot(df.index,df.Sunspots)
for i,j in enumerate(dbscan_out):
  if j == -1:
    plt.plot(df.index.values[i],df.Sunspots.values[i],"g*")

plt.show()