Real-time monitoring of high-dimensional autocorrelated categorical data: a dynamic probabilistic tensor decomposition approach

In modern scientific and engineering domains, high-dimensional (HD) categorical data are prevalent, characterised by many categorical variables each evaluated by attribute levels rather than continuous values. The advancement of sensing technologies, on the other hand, facilitates high-speed data collection, making HD categorical data also exhibit temporal correlation. Monitoring HD autocorrelated categorical data for process fault detection is challenging due to the complicated cross-correlation and autocorrelation thereof. To solve this, we propose using a high-way conditional probability tensor to represent the conditional distribution of HD categorical variables observed at each time point given their past observations. By developing a dynamic probabilistic tensor decomposition (DPTD) approach, we efficiently decompose the tensor of big size into a few latent classes, greatly reducing model parameters, and meanwhile make the decomposition rely on the categorical data at the previous time points. The cross-correlation between different categorical variables is efficiently captured by the mixture of latent classes and the autocorrelation over time is also explicitly incorporated by the time-varying decomposition. The DPTD model is learned by an efficient expectation-maximisation algorithm, followed by an online monitoring scheme for fault detection. Extensive numerical simulations and real case studies validate the superior modelling and monitoring capabilities of our proposed method.