Minimal Learning Machine: Theoretical Results and Clustering-Based Reference Point Selection

Autor:	Hämäläinen, Joonas, Alencar, Alisson S. C., Kärkkäinen, Tommi, Mattos, César L. C., Souza Júnior, Amauri H., Gomes, João P. P.
Rok vydání:	2019
Předmět:	FOS: Computer and information sciences Computer Science - Machine Learning Minimal Learning Machine koneoppiminen Statistics - Machine Learning universal approximation Machine Learning (stat.ML) interpolointi approksimointi reference point selection clustering Machine Learning (cs.LG)
DOI:	10.48550/arxiv.1909.09978
Popis:	The Minimal Learning Machine (MLM) is a nonlinear supervised approach based on learning a linear mapping between distance matrices computed in the input and output data spaces, where distances are calculated using a subset of points called reference points. Its simple formulation has attracted several recent works on extensions and applications. In this paper, we aim to address some open questions related to the MLM. First, we detail theoretical aspects that assure the interpolation and universal approximation capabilities of the MLM, which were previously only empirically verified. Second, we identify the task of selecting reference points as having major importance for the MLM's generalization capability. Several clustering-based methods for reference point selection in regression scenarios are then proposed and analyzed. Based on an extensive empirical evaluation, we conclude that the evaluated methods are both scalable and useful. Specifically, for a small number of reference points, the clustering-based methods outperformed the standard random selection of the original MLM formulation. Comment: 29 pages, Accepted to JMLR
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f0e6fc8e38f484dc70ab664fc8bb58fc Zobrazit plný text záznamu