Nonlinear process monitoring using a mixture of probabilistic PCA with clusterings

TL;DR: Light is shed on the versatility and capability of PCA in processing high-dimensional data in general and specifically on its potential in forensic studies to help other research communities interested in unravelling latent structure from high- dimensional data.

TL;DR: Wang et al. as mentioned in this paper take advantage of position encoding, residual connection, and multi-head attention mechanism embedded in the Transformer structure to establish an effective and efficient wastewater treatment process fault detection model, where offline modeling and online monitoring are performed successively to achieve accurate detection of the faults.

TL;DR: In this paper , an improved approach using a mixture of probabilistic principal component analysis (MPPCA) for the anomaly detection of structures under multiple operational conditions with missing measurement data was presented.

TL;DR: In this paper , a neural network (NN) is used to model a mixture of probabilistic principal component analyzers (MPPCA) framework which parameters are updated via back-propagation.

TL;DR: In this paper, the authors proposed a method called the "gap statistic" for estimating the number of clusters (groups) in a set of data, which uses the output of any clustering algorithm (e.g. K-means or hierarchical), comparing the change in within-cluster dispersion with that expected under an appropriate reference null distribution.

TL;DR: In this paper, the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis.

TL;DR: The gap statistic is proposed for estimating the number of clusters (groups) in a set of data by comparing the change in within‐cluster dispersion with that expected under an appropriate reference null distribution.

TL;DR: PCA is formulated within a maximum likelihood framework, based on a specific form of gaussian latent variable model, which leads to a well-defined mixture model for probabilistic principal component analyzers, whose parameters can be determined using an expectation-maximization algorithm.