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Dirección de Estudios de Posgrado

Seminario programado

A Novel Dimensionality Reduction Technique for Euclidean and (some) non-Euclidean spaces

A Novel Dimensionality Reduction Technique for Euclidean and (some) non-Euclidean spaces

This work derives from the domain of similarity search: the apparently simple task of finding objects, from some large collection, which are similar to another object presented as a query. Everyday examples exist, such as Shazam and Google Image Search. The general problem is not solved however, as even a relatively modest collection of eg 1M images may take ten days to query unless either huge parallel compute power, or clever methods, are applied. For clever methods, the step to the analysis of high-dimensional distance geometry is a clear requirement!
This talk describes the nSimplex method, where n objects in a search space are used to construct a geometric model in (n-1)-dimensional Euclidean space. This model gives strong upper- and lower-bound properties with respect to the original space. In conjunction with a further study of the distribution of angles in high-dimensional spaces, we then use the nSimplex method to produce a distance estimator in a Euclidean space of much lower dimension than the original.
We consider this estimation function used as a general dimensionality reduction mechanism, and compare it with the mainstream techniques of Principle Component Analysis, Multidimensional Scaling, and Random Projection. It performs better than these techniques in almost all circumstances and, unlike these methods, can also be applied to some useful non-Euclidean spaces.

Prof. Richard Connor graduated with BSc and PhD from the University of St Andrews during the 1980s, and has recently returned there after 25 years. His early research interests in database programming languages migrated first to semistructured data analysis and from there to similarity search. He is also interested in computer science education at all levels, and is an author of the current Scottish school curriculum for computing education.

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Lugar: Auditorio Depto. Ciencias de la Computación y en línea https://bluejeans.com/227475033/4428

Fecha: 02-12-2022

Hora: 12:00 pm