Gaussian Mixtures (GMs) are a powerful tool for approximating probability distributions across a variety of fields. In some applications the number of GM components rapidly grows with time, so that reduction algorithms are necessary. Given a GM with a large number of components, the problem of Gaussian Mixture Reduction (GMR) consists in finding a GM with considerably less components that is not too dissimilar from the original one. There are many issues that make non trivial this problem. First of all, many dissimilarity measures exist for GMs, although most of them lack closed forms, and their numerical computation is a demanding task, especially for distributions in high dimensions. Moreover, some basic reduction actions can be simple or complex tasks depending on which dissimilarity measure is chosen. It follows that most reduction procedures proposed in the literature are made of steps that are aimed at maintaining low dissimilarity according to different measures, thus leading to a pipeline of actions that are not mutually consistent. In this paper Composite Transportation Dissimilarities are discussed and exploited to formulate a GMR framework that preserves consistency with a unique dissimilarity measure, and provides a generalization of the celebrated Runnalls’ GMR approach.

Composite Transportation Dissimilarity in Consistent Gaussian Mixture Reduction

Manes Costanzo;D'Ortenzio Alessandro
2021

Abstract

Gaussian Mixtures (GMs) are a powerful tool for approximating probability distributions across a variety of fields. In some applications the number of GM components rapidly grows with time, so that reduction algorithms are necessary. Given a GM with a large number of components, the problem of Gaussian Mixture Reduction (GMR) consists in finding a GM with considerably less components that is not too dissimilar from the original one. There are many issues that make non trivial this problem. First of all, many dissimilarity measures exist for GMs, although most of them lack closed forms, and their numerical computation is a demanding task, especially for distributions in high dimensions. Moreover, some basic reduction actions can be simple or complex tasks depending on which dissimilarity measure is chosen. It follows that most reduction procedures proposed in the literature are made of steps that are aimed at maintaining low dissimilarity according to different measures, thus leading to a pipeline of actions that are not mutually consistent. In this paper Composite Transportation Dissimilarities are discussed and exploited to formulate a GMR framework that preserves consistency with a unique dissimilarity measure, and provides a generalization of the celebrated Runnalls’ GMR approach.
File in questo prodotto:
File Dimensione Formato  
C097_Composite Transportation Dissimilarity in Consistent Gaussian Mixture Reduction_DOM_ICIF21b.pdf

non disponibili

Descrizione: Articolo pubblicato
Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 366.34 kB
Formato Adobe PDF
366.34 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/178074
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? ND
social impact