EURO 2024 Copenhagen
Abstract Submission

EURO-Online login

3739. Incremental Accelerated Hyperbolic Smoothing Clustering Method: Computational Results

Invited abstract in session WC-27: Machine Learning and Ensemble Learning with optimization methods, stream Mathematical Optimization for XAI.

Wednesday, 12:30-14:00
Room: 047 (building: 208)

Authors (first author is the speaker)

1. Adilson Elias Xavier
Department System Eng and Computer Sciences, Federal University of Rio de Janeiro
2. Vinicius Layter Xavier
Instituto de Medicina Social Hesio Cordeiro (IMS); Programa de Pós-Graduação em Ciências Computacionais e Modelagem Matemática (PPG-CompMat), State Universit. of Rio de Janeiro

Abstract

This work considers the minimum sum-of-squares clustering (MSSC) problem, which has an intrinsic bi-level nature and the significant characteristic of being nondifferentiable.
To overcome these difficulties, the proposed method adopts a smoothing strategy, which engenders an unconstrained completely differentiable single-level alternative.
The proposed algorithm also applies a partition of the set of observations into two non-overlapping groups: ``data in frontier" and ``data in gravitational regions".
The article introduces a novel incremental procedure to produce starting points in an iterative way, which begins with only one centroid, and which adds one cluster centroid at a time.
To show the distinct performance of the new algorithm, we perform numerical experiments with a set of thirteen large test problems from the literature.
In short, except for a few solutions, numerical results show a high level of performance of the IncAHSCM algorithm according to different criteria of accuracy and speed, in compassion with the best-established clustering algorithms.
. The accuracy performance can be attributed to the complete differentiability offered by the hyperbolic smoothing approach, as well as, by the strategy to get good initial starting point.
The high speed of the algorithm can be attributed to the partition of the set of observations into two non-overlapping parts, which drastically simplify the computational tasks.

Keywords

Status: accepted

Back to the list of papers