Abstract In clustering, selecting the most appropriate partitioning of a dataset is often guided by clustering validity indexes. However, with numerous competing indexes each with its own strengths and weaknesses, choosing the right one can be challenging and may significantly affect clustering outcomes. Despite their widespread use, limited research has explored how index performance varies across problem types, with traditional benchmarks focusing on ground-truth properties that cannot be known prior to clustering. Instance Space Analysis (ISA) is a visual meta-learning methodology that provides tools to examine the relationship between problem features and algorithmic performance. This study presents the first application of ISA to clustering validity indexes, analysing the behaviour of nine indexes across a diverse set of 18,351 synthetic benchmark datasets and eight clustering algorithms. The results uncover distinct performance patterns and offer data-driven guidance for selecting appropriate indexes based on measurable problem characteristics, providing insights into the relative strengths and weaknesses of commonly used indexes.

The quest for greater insights into algorithm strengths and weaknesses, as revealed when studying algorithm performance on large collections of test problems, is supported by interactive visual analytics tools. A recent advance is Instance Space Analysis, which presents a visualization of the space occupied by the test datasets, and the performance of algorithms across the instance space. The strengths and weaknesses of algorithms can be visually assessed, and the adequacy of the test datasets can be scrutinized through visual analytics. This article presents the first Instance Space Analysis of regression problems in Machine Learning, considering the performance of 14 popular algorithms on 4,855 test datasets from a variety of sources. The two-dimensional instance space is defined by measurable characteristics of regression problems, selected from over 26 candidate features. It enables the similarities and differences between test instances to be visualized, along with the predictive performance of regression algorithms across the entire instance space. The purpose of creating this framework for visual analysis of an instance space is twofold: one may assess the capability and suitability of various regression techniques; meanwhile the bias, diversity, and level of difficulty of the regression problems popularly used by the community can be visually revealed. This article shows the applicability of the created regression instance space to provide insights into the strengths and weaknesses of regression algorithms, and the opportunities to diversify the benchmark test instances to support greater insights.

This paper presents an artificial beehive algorithm for optimization in continuous search spaces based on a model aimed at individual bee behavior. The algorithm defines a set of behavioral rules for each agent to determine what kind of actions must be carried out. Also, the algorithm proposed includes some adaptations not considered in the biological model to increase the performance in the search for better solutions. To compare the performance of the algorithm with other swarm-based Techniques, we conducted statistical analyses by using the so-called t test. This comparison is done with several common benchmark functions. © 2009 Wiley Periodicals, Inc.