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 subdissimilarity 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.

On component-wise dissimilarity measures and metric properties in pattern recognition / De Santis, Enrico; Martino, Alessio; Rizzi, Antonello. - In: PEERJ. COMPUTER SCIENCE.. - ISSN 2376-5992. - 8:(2022), pp. 1-26. [10.7717/peerj-cs.1106]

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

Alessio Martino
;
2022

Abstract

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 subdissimilarity 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.
Metric learning, Pattern recognition, Dissimilarity space, Euclidean embedding, Kernel methods, Pseudo-Euclidean embedding
On component-wise dissimilarity measures and metric properties in pattern recognition / De Santis, Enrico; Martino, Alessio; Rizzi, Antonello. - In: PEERJ. COMPUTER SCIENCE.. - ISSN 2376-5992. - 8:(2022), pp. 1-26. [10.7717/peerj-cs.1106]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11385/221838
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