Marcílio C. P. de Souto

Cristina Y. Morimoto, Aurora Pozo, Marcílio C. P. de Souto

A variety of clustering criteria has been applied as an objective function in Evolutionary Multi-Objective Clustering approaches (EMOCs). However, most EMOCs do not provide detailed analysis regarding the choice and usage of the objective functions. Aiming to support a better choice and definition of the objectives in the EMOCs, this paper proposes an analysis of the admissibility of the clustering criteria in evolutionary optimization by examining the search direction and its potential in finding optimal results. As a result, we demonstrate how the admissibility of the objective functions can influence the optimization. Furthermore, we provide insights regarding the combinations and usage of the clustering criteria in the EMOCs.

Cristina Y. Morimoto, Aurora Pozo, Marcílio C. P. de Souto

Evolutionary multi-objective clustering (EMOC), a modern clustering technique, has been widely applied to extract patterns, allowing us to analyze different aspects of complex data by considering multiple criteria. In this article, we present an analysis of the advances in EMOC studies and provide a profile of this study field by considering an extensive mapping of the literature to identify the main methods and concepts that have been adopted to design the EMOC approaches. This review provides a comprehensive view of the EMOC studies that supports newcomers or busy researchers in understanding the general features of the existing algorithms and guides the generation of new approaches. For that, we introduce a general architecture of EMOC to describe the main elements applied in designing EMOC algorithms and we correlate them with the main features found in the literature. Also, we categorized the EMOC algorithms based on shared characteristics that highlight the main features or application fields. The paper ends by addressing some potential subjects for future research.

Adriano Kultzak, Cristina Y. Morimoto, Aurora Pozo et al.

We present a data-driven analysis of MOCK, $Δ$-MOCK, and MOCLE. These are three closely related approaches that use multi-objective optimization for crisp clustering. More specifically, based on a collection of 12 datasets presenting different proprieties, we investigate the performance of MOCLE and MOCK compared to the recently proposed $Δ$-MOCK. Besides performing a quantitative analysis identifying which method presents a good/poor performance with respect to another, we also conduct a more detailed analysis on why such a behavior happened. Indeed, the results of our analysis provide useful insights into the strengths and weaknesses of the methods investigated.

Denis dos Reis, Marcílio de Souto, Elaine de Sousa et al.

Quantification is the research field that studies methods for counting the number of data points that belong to each class in an unlabeled sample. Traditionally, researchers in this field assume the availability of labelled observations for all classes to induce a quantification model. However, we often face situations where the number of classes is large or even unknown, or we have reliable data for a single class. When inducing a multi-class quantifier is infeasible, we are often concerned with estimates for a specific class of interest. In this context, we have proposed a novel setting known as One-class Quantification (OCQ). In contrast, Positive and Unlabeled Learning (PUL), another branch of Machine Learning, has offered solutions to OCQ, despite quantification not being the focal point of PUL. This article closes the gap between PUL and OCQ and brings both areas together under a unified view. We compare our method, Passive Aggressive Threshold (PAT), against PUL methods and show that PAT generally is the fastest and most accurate algorithm. PAT induces quantification models that can be reused to quantify different samples of data. We additionally introduce Exhaustive TIcE (ExTIcE), an improved version of the PUL algorithm Tree Induction for c Estimation (TIcE). We show that ExTIcE quantifies more accurately than PAT and the other assessed algorithms in scenarios where several negative observations are identical to the positive ones.

Ana C. Lorena, Luís P. F. Garcia, Jens Lehmann et al.

Characteristics extracted from the training datasets of classification problems have proven to be effective predictors in a number of meta-analyses. Among them, measures of classification complexity can be used to estimate the difficulty in separating the data points into their expected classes. Descriptors of the spatial distribution of the data and estimates of the shape and size of the decision boundary are among the known measures for this characterization. This information can support the formulation of new data-driven pre-processing and pattern recognition techniques, which can in turn be focused on challenges highlighted by such characteristics of the problems. This paper surveys and analyzes measures which can be extracted from the training datasets in order to characterize the complexity of the respective classification problems. Their use in recent literature is also reviewed and discussed, allowing to prospect opportunities for future work in the area. Finally, descriptions are given on an R package named Extended Complexity Library (ECoL) that implements a set of complexity measures and is made publicly available.