Marcilio Carlos Pereira 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.

We present a data-driven analysis of MOCK, $\Delta$-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 $\Delta$-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.

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.