TODO 28Jun2020

0. Dataset loading and getting all the data in an understandable format.
	Plotting it. - done 
1. Mutate time series - better outliers. - done 
2. Extracting Features from time series.
	Stationarity check
	Stationarity transformations - differencing and power transformations.
3. PCA on features - reduce dimensions to a subspace of n dimensions - get ones with largest variance
PCA - 
	Taking the whole dataset ignoring the class labels
	Compute the d-dimensional mean vector
	Computing the scatter matrix (alternatively, the covariance matrix)
	Computing eigenvectors and corresponding eigenvalues
	Ranking and choosing k eigenvectors
	Transforming the samples onto the new subspace
4. Try LDA if classes are known
5. STL decomposition of timeseries - 
	Analyse residuals.
	If > threshold then outlier
	Find a dynamic way to calculate threshold.
6. Model time series using AR
7. Model time series using MA
8. Model time series using ARMA and ARIMA and SARIMA, ARFIMA, Box-Jenkins
	
AR
MA
ARIMA
SARIMA
Forecast, calculate actual - pred then check against threshold

STL 
check residuals against threshold,

Threshold detection:
data point +- 3d from mean - z-score method
Median Absolute Deviation
Interquartile range

Scikit learn
OneClassSVM, Isolation forest and LOF


Other methods 
Clustering - DBSCAN
Trees - Isolation binary decision trees and random forests

Primary -
Z-value test for outlier analysis
z = xi - mu/ sigma
signifies the number of std devs a point is away from the mean
This provides a good proxy for the outlier score of that point.

An implicit assumption is that the data is modeled from a normal distribution, and therefore the
Z-value is a random variable drawn from a standard normal distribution with zero mean
and unit variance. 

In cases where the mean and standard deviation of the distribution
can be accurately estimated, a good “rule-of-thumb” is to use Zi ≥ 3 as a proxy for the
anomaly
3 sd