Factor Uniqueness of the Structural Parafac Model.

Factor analysis is a well-known method for describing the covariance structure among a set of manifest variables through a limited number of unobserved factors. When the observed variables are collected at various occasions on the same statistical units, the data have a three-way structure and standard factor analysis may fail. To overcome these limitations, three-way models, such as the Parafac model, can be adopted.

A Model-Based Approach to Simultaneous Clustering and Dimensional Reduction of Ordinal Data.

The literature on clustering for continuous data is rich and wide; differently, that one developed for categorical data is still limited. In some cases, the clustering problem is made more difficult by the presence of noise variables/dimensions that do not contain information about the clustering structure and could mask it. The aim of this paper is to propose a model for simultaneous clustering and dimensionality reduction of ordered categorical data able to detect the discriminative dimensions discarding the noise ones.

Constrained Candecomp/Parafac via the Lasso.

The Candecomp/Parafac (CP) model is a well-known tool for summarizing a three-way array by extracting a limited number of components. Unfortunately, in some cases, the model suffers from the so-called degeneracy, that is a solution with diverging and uninterpretable components. To avoid degeneracy, orthogonality constraints are usually applied to one of the component matrices.

A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption.

Hidden Markov models (HMMs) are frequently used to analyse longitudinal data, where the same set of subjects is repeatedly observed over time. In this context, several sources of heterogeneity may arise at individual and/or time level, which affect the hidden process, that is, the transition probabilities between the hidden states. In this paper, we propose the use of a finite mixture of non-homogeneous HMMs (NH-HMMs) to face the heterogeneity problem.