C7. Innovations in cluster and latent class models

17:20 - 18:30, Aula 12

Chair: Gianluca Sottile

Biclustering of discrete data by extended finite mixtures of latent trait models

Dalila Failli, Maria Francesca Marino and Francesca Martella

Abstract: We aim at performing a joint clustering of units and variables in a binary data matrix in a biclustering perspective. In this framework, units are partitioned into clusters (components) via a finite mixture approach; in each component, variables are partitioned into clusters (segments) by adopting a flexible specification of the linear predictor. Dependence between variables is modeled via a multidimensional, continuous, latent trait. The proposed model is applied to the Regensburg Pediatric Appendicitis data set, with the aim of identifying homogeneous groups of pediatric patients with respect to subsets of clinical features.

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Inferring the dynamics of quasi-reaction systems via non-linear local mean-field approximations

Matteo Framba, Veronica Vinciotti and Ernst C. Wit

Abstract: In modelling stochastic phenomena, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive mea- surements is large. Local linear approximation (LLA) approaches account for the stochasticity in the system but fail to capture the non-linear nature of the underlying process. At the mean level, the dynamics of the system can be described by a system of ordinary differential equations (ODEs), which have an explicit solution only for simple unitary systems. Making use of this, we propose an approximate solution for generic quasi-reaction systems. The explicit ODEs solutions obtained for each time point are used in a non-linear regression framework for conducting inference and prediction for the next time point. The performance of our algorithm is compared to the LLA approach using a simulation study. We show that there is an improvement in the kinetic rate estimation, particularly for data observed at large time intervals.

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Seismic events classification through latent class regression models for point processes

Giada Lo Galbo, Giada Adelfio and Marcello Chiodi

Abstract: We are trying to identify sub-processes of seismic events from the point processes’ point of view and according to the latent class regression approach. Each seismic event is classified as membership of one of the 4 identified sub-classes of seismic sequences, each defined by particular and well-defined characteristics. So far, seismic sub-sequences have been identified and described according to several declustering methods. In this application, we show how sub-processes can be identified starting from the definition of a spatio-temporal intensity function for point processes, assuming independence of the past.

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Determining the optimal number of clusters through Symmetric Non-Negative Matrix Factorization

Agostino Stavolo, Maria Gabriella Grassia, Marina Marino and Rocco Mazza, Simone Paesano, Dario Sacco

Abstract: Cluster analysis, as a form of unsupervised learning, has been developed to group observations by leveraging application-specific similarity measures. This study investigates matrix factorization techniques, with a specific focus on analyzing lexical tables within the framework of term-document matrices. Symmetric Non-Negative Matrix Factorization (SNMF) takes center stage as an effective tool for clustering operations. The primary challenge addressed is the automated determination of the optimal number of clusters.

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