In-profile monitoring for cluster-correlated data based on regularized state space model

Cluster-correlated data: profiles within a cluster have similar patterns and are correlated, while profiles from different clusters have quite different features and are almost uncorrelated.
In-profile monitoring: we aim to model the dynamic evolution mechanism behind the system rather than the static features of the curve. As such, profiles of different samples can vary in time length, and features can be unsynchronized with time variations. More importantly, it gives the feasibility of detecting anomalies inside the profile. We highlight this idea as in-profile monitoring (INPOM).
Regularized state space model: to account for the clusterwise correlation among different profiles, the traditional state space model (SSM) is extended to a regularized SSM (RSSM) by imposing a graph Laplacian regularization on the observation matrix of SSM. An L1 regularization is also imposed on the transition matrix of SSM to avoid overfitting. by treating the above regularizations as prior information, the model parameters can be efficiently learned via Bayesian inference, where expectation maximization (EM) algorithm is incorporated for posterior maximization. Built upon this, a T2 monitoring statistic based on one-step-ahead prediction error is constructed for INPOM.