EURO 2024 Copenhagen
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4030. Classification in a vector space with the infinity norm

Invited abstract in session WD-6: Advancements of OR-analytics in statistics, machine learning and data science 19, stream Advancements of OR-analytics in statistics, machine learning and data science.

Wednesday, 14:30-16:00
Room: 1013 (building: 202)

Authors (first author is the speaker)

1. Milena Venkova
School of Mathematical Sciences, Technological University Dublin
2. Seán McGarraghy
Management Information Systems, University College Dublin

Abstract

Zhou and Schoelkopf (2005) note that "Many real-world machine learning problems are situated on finite discrete sets. Typically we may assume that there exist pairwise relationships among data."
In this talk we consider the general setting of classification on data sets in finite metric spaces: these include a broad range of cases, including pairwise relationships satisfying the triangle inequality.
Instead of embedding the data in an Euclidian space and using kernel techniques, we embed it in a real vector space endowed with the infinity norm. This embedding is necessarily isometric which means that the data in the normed space can be studied without introducing any distortion to the original metric space setting. While the target feature space is no longer an inner product space, and so the idea of kernel does not carry forward, there is still potential for a linear class boundary using the Hahn-Banach Theorem.
We discuss the advantages and disadvantages of such an embedding in the context of classifiers such as support vector machines.
In particular, we are interested in the problem of adjusting an already-trained binary classifier in response to new data. New training set data may become available after training a support vector machine: will the same trained machine still work or does it need to be adjusted; and if so, how?

Keywords

Status: accepted


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