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On component-wise dissimilarity measures and metric properties in pattern recognition

In many real-world applications concerning pattern recognition techniques, it is of utmost importance the automatic learning of the most appropriate dissimilarity measure to be used in object comparison. Real-world objects are often complex entities and need a specific representation grounded on a c...

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Autores principales: De Santis, Enrico, Martino, Alessio, Rizzi, Antonello
Formato: Online Artículo Texto
Lenguaje:English
Publicado: PeerJ Inc. 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9575871/
https://www.ncbi.nlm.nih.gov/pubmed/36262128
http://dx.doi.org/10.7717/peerj-cs.1106
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author De Santis, Enrico
Martino, Alessio
Rizzi, Antonello
author_facet De Santis, Enrico
Martino, Alessio
Rizzi, Antonello
author_sort De Santis, Enrico
collection PubMed
description In many real-world applications concerning pattern recognition techniques, it is of utmost importance the automatic learning of the most appropriate dissimilarity measure to be used in object comparison. Real-world objects are often complex entities and need a specific representation grounded on a composition of different heterogeneous features, leading to a non-metric starting space where Machine Learning algorithms operate. However, in the so-called unconventional spaces a family of dissimilarity measures can be still exploited, that is, the set of component-wise dissimilarity measures, in which each component is treated with a specific sub-dissimilarity that depends on the nature of the data at hand. These dissimilarities are likely to be non-Euclidean, hence the underlying dissimilarity matrix is not isometrically embeddable in a standard Euclidean space because it may not be structurally rich enough. On the other hand, in many metric learning problems, a component-wise dissimilarity measure can be defined as a weighted linear convex combination and weights can be suitably learned. This article, after introducing some hints on the relation between distances and the metric learning paradigm, provides a discussion along with some experiments on how weights, intended as mathematical operators, interact with the Euclidean behavior of dissimilarity matrices.
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spelling pubmed-95758712022-10-18 On component-wise dissimilarity measures and metric properties in pattern recognition De Santis, Enrico Martino, Alessio Rizzi, Antonello PeerJ Comput Sci Algorithms and Analysis of Algorithms In many real-world applications concerning pattern recognition techniques, it is of utmost importance the automatic learning of the most appropriate dissimilarity measure to be used in object comparison. Real-world objects are often complex entities and need a specific representation grounded on a composition of different heterogeneous features, leading to a non-metric starting space where Machine Learning algorithms operate. However, in the so-called unconventional spaces a family of dissimilarity measures can be still exploited, that is, the set of component-wise dissimilarity measures, in which each component is treated with a specific sub-dissimilarity that depends on the nature of the data at hand. These dissimilarities are likely to be non-Euclidean, hence the underlying dissimilarity matrix is not isometrically embeddable in a standard Euclidean space because it may not be structurally rich enough. On the other hand, in many metric learning problems, a component-wise dissimilarity measure can be defined as a weighted linear convex combination and weights can be suitably learned. This article, after introducing some hints on the relation between distances and the metric learning paradigm, provides a discussion along with some experiments on how weights, intended as mathematical operators, interact with the Euclidean behavior of dissimilarity matrices. PeerJ Inc. 2022-10-10 /pmc/articles/PMC9575871/ /pubmed/36262128 http://dx.doi.org/10.7717/peerj-cs.1106 Text en © 2022 De Santis et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Computer Science) and either DOI or URL of the article must be cited.
spellingShingle Algorithms and Analysis of Algorithms
De Santis, Enrico
Martino, Alessio
Rizzi, Antonello
On component-wise dissimilarity measures and metric properties in pattern recognition
title On component-wise dissimilarity measures and metric properties in pattern recognition
title_full On component-wise dissimilarity measures and metric properties in pattern recognition
title_fullStr On component-wise dissimilarity measures and metric properties in pattern recognition
title_full_unstemmed On component-wise dissimilarity measures and metric properties in pattern recognition
title_short On component-wise dissimilarity measures and metric properties in pattern recognition
title_sort on component-wise dissimilarity measures and metric properties in pattern recognition
topic Algorithms and Analysis of Algorithms
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9575871/
https://www.ncbi.nlm.nih.gov/pubmed/36262128
http://dx.doi.org/10.7717/peerj-cs.1106
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