I couldn't find suitable framework that deals with MTS-CPCA so I'll build the algorithm from scratch
What's MTS?
Time series data can be seen everywhere including stock exchange, financial market, medicine and engineering, which is one kind of the important data needed to be mined for the valuable information and knowledge. It has two categories according to various number of the variables, they are univariate time series (UTS) and multivariate time series(MTS).
MTS (Multivariate time series) is an important type of data that is indispensable in a variety of domains as medicine domain which is the evolution of a group of synchronous variables over a duration of time as shown in the figure and there is a lot of effort given due to the expensive of gathering these labeled data to be able to offer a method gives a reliable accuracy by only using a limited amount of these data.
What's PCA?
This is a linear unsupervised algorithm to find orthogonal transformation axes that diagonalize the covariance matrix the goal is to eliminate low variance and highly correlated features.
Why PCA?
Due to the high dimensionality of MTS, the dimensionality reduction is proposed to validly integrate into the clustering,classification and regression process and a good MTS accuracy can be obtained in lower dimensions
Suppose there was a dataset X having N multivariate time series Σ_i=cov(x_i) , x_i ∈ R^(n_i * m) where n_i is the length of MTS sample and m is the number of the variables Σ = 1/N ∑Σ_i