De Santis E, Martino A, Rizzi A. On component-wise dissimilarity measures and metric properties in pattern recognition.
PeerJ Comput Sci 2022;
8:e1106. [PMID:
36262128 PMCID:
PMC9575871 DOI:
10.7717/peerj-cs.1106]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Accepted: 08/26/2022] [Indexed: 06/16/2023]
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 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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