arXiv subjects

Renato Cordeiro de Amorim

Publications and source records attributed to Renato Cordeiro de Amorim.

17 recordsLinked to original sources

arXiv2026

An interpretable Good--Turing restart criterion for k-means++

The k-means++ algorithm is commonly restarted multiple times to avoid poor local optima, yet the number of restarts is almost always chosen arbitrarily and applied uniformly regardless of data set difficulty. This undermines any comparison relying on such a choice and wastes computation on easy data sets while potentially under-serving hard ones. Here, we introduce the Good-Turing Restart Criterion (GTRC). This combines a Good-Turing estimate, a proven unconditional bound, and a confidence-based bound on the probability that a further restart would improve on the current result, stopping once this probability falls below a user-specified tolerance. Our experiments on 34 real-world data sets show that GTRC identifies the point beyond which further k-means++ restarts yield only negligible improvement, achieving a more favourable balance between the number of restarts used and clustering quality than three existing stopping rules for multistart local search and popular fixed restart counts. Software: https://github.com/RCdeAmorim/Good-Turing-Restart-Criterion.

cs.LG↗

arXiv2026

Counterfactuals for Feature-Weighted Clustering

Counterfactual explanations provide local, interpretable insight by identifying changes to an input that would alter its assigned outcome. Although well established in supervised learning, their extension to clustering is less direct, since cluster assignments are unlabeled and governed by the geometry of the partition. This paper introduces VoICE, a Voronoi-Induced Counterfactual Explainability framework for feature-weighted $k$-means clustering. Rather than treating cluster change as a crossing of a single pairwise centroid boundary, VoICE formulates counterfactual generation as projection onto the full weighted Voronoi region of a target cluster, incorporating feature weights directly into both the clustering geometry and the counterfactual objective to yield least-cost and parsimonious explanations under actionability constraints. Target regions are further intersected with data-derived bounds and homothetically contracted towards their centroids, limiting extrapolation and boundary sensitivity. VoICE consistently produces valid target-cluster membership, across several benchmark datasets, where the leading pairwise baseline does not.

cs.LG↗

arXiv2026

Shapley-Inspired Feature Weighting in $k$-means with No Additional Hyperparameters

Clustering algorithms often assume all features contribute equally to the data structure, an assumption that usually fails in high-dimensional or noisy settings. Feature weighting methods can address this, but most require additional parameter tuning. We propose SHARK (Shapley Reweighted $k$-means), a feature-weighted clustering algorithm motivated by the use of Shapley values from cooperative game theory to quantify feature relevance, which requires no additional parameters beyond those in $k$-means. We prove that the $k$-means objective can be decomposed into a sum of per-feature Shapley values, providing an axiomatic foundation for unsupervised feature relevance and reducing Shapley computation from exponential to polynomial time. SHARK iteratively re-weights features by the inverse of their Shapley contribution, emphasising informative dimensions and down-weighting irrelevant ones, and is equivalent to replacing the arithmetic mean of feature dispersions with their harmonic mean. Experiments on synthetic and real-world data sets show that SHARK consistently matches or outperforms existing methods, achieving superior robustness and accuracy, particularly in scenarios where noise may be present. Software: https://github.com/rickfawley/SHARK.

cs.LG↗

arXiv2026

Scalable unsupervised feature selection via weight stability

Unsupervised feature selection is critical for improving clustering performance in high-dimensional data, where irrelevant features can obscure meaningful structure. In this work, we propose the Minkowski weighted $k$-means++, a novel initialisation strategy for the Minkowski Weighted $k$-means. Our initialisation selects centroids probabilistically using feature relevance estimates derived from the data itself. Building on this, we propose two new feature selection algorithms, FS-MWK++, which aggregates feature weights across a range of Minkowski exponents identifying stable and informative features, and SFS-MWK++, a scalable variant based on subsampling. We support our approach with a theoretical analysis, demonstrating that, under explicit assumptions on noise features and cluster structure, relevant features are assigned consistently higher weights than noise features across a range of Minkowski exponents. Our software can be found at https://github.com/xzhang4-ops1/FSMWK.

cs.LG↗

arXiv2026

ClustRecNet: A Novel End-to-End Deep Learning Framework for Clustering Algorithm Recommendation

Identifying an effective clustering algorithm for a given dataset remains a fundamental unsupervised learning issue. We introduce ClustRecNet, a novel end-to-end deep learning framework that recommends suitable clustering algorithm(s) by directly learning high-order representations of raw tabular data. To facilitate robust meta-learning, we first construct a comprehensive repository of 34,000 synthetic datasets encompassing a large variety of clustering scenarios, run 10 popular clustering algorithms, and use Adjusted Rand Index (ARI) to establish ground-truth labels. ClustRecNet's architecture incorporates a convolution block, two residual blocks, and an attention block to capture local and global structural patterns, effectively bypassing the knowledge bottleneck associated with manual feature engineering. Extensive evaluation on both synthetic and real-world benchmarks demonstrates that ClustRecNet consistently outperforms traditional internal cluster validity indices such as Silhouette, Calinski-Harabasz, Davies-Bouldin, and Dunn as well as state-of-the-art Automated Machine Learning (AutoML) approaches such as ML2DAC, AutoCluster, and AutoML4Clust. For example, our framework achieves an average 0.497 ARI gain over the Calinski-Harabasz cluster validity index on synthetic data and an average 44.16% ARI improvement over the leading AutoML approach (ML2DAC) on real-world benchmarks. Code and data are available at: https://github.com/mrbakhtyari/ClustRecNet

cs.LG↗

arXiv2026

Cluster-Adaptive Feature Extraction and its Theoretical Foundation with Minkowski Weighted k-Means

The Minkowski weighted $k$-means ($mwk$-means) algorithm extends classical $k$-means by incorporating feature weights and a Minkowski distance. We first show that the $mwk$-means objective can be expressed as a power-mean aggregation of within-cluster dispersions, with the order determined by the Minkowski exponent $p$. This formulation reveals how $p$ controls the transition between selective and uniform use of features. Using this representation, we derive bounds for the objective function and characterise the structure of the feature weights, showing that they depend only on relative dispersion and follow a power-law relationship with dispersion ratios. This leads to explicit guarantees on the suppression of high-dispersion features, and we establish convergence of the algorithm. Building on these theoretical results, we introduce Cluster-Adaptive Feature Extraction (CAFE), a method that uses the $mwk$-means feature weights to rescale the data prior to unsupervised feature extraction. We prove that this rescaling reverses the within-cluster dispersion ordering, suppressing noisy features and amplifying informative ones. Numerous experiments conducted under controlled within-cluster noise show that CAFE consistently improves the results of traditional feature extraction methods.

cs.LG↗

arXiv2026

Improving clustering quality evaluation in noisy Gaussian mixtures

Clustering is a well-established technique in machine learning and data analysis, widely used across various domains. Cluster validity indices, such as the Average Silhouette Width, Calinski-Harabasz, and Davies-Bouldin indices, play a crucial role in assessing clustering quality when external ground truth labels are unavailable. However, these measures can be affected by different degrees of feature relevance, potentially leading to unreliable evaluations in high-dimensional or noisy data sets. We introduce a theoretically grounded Feature Importance Rescaling (FIR) method that enhances the quality of clustering validation by adjusting feature contributions based on their dispersion. It attenuates noise features, clarifies clustering compactness and separation, and thereby aligns clustering validation more closely with the ground truth. Through extensive experiments on synthetic data sets under different configurations and a case study on real-world data, we demonstrate that FIR consistently improves the correlation between the values of cluster validity indices and the ground truth, particularly in settings with noisy or irrelevant features. The results show that FIR increases the robustness of clustering evaluation, reduces variability in performance across different data sets, and remains effective even when clusters exhibit significant overlap. These findings highlight the potential of FIR as a valuable enhancement of clustering validation, making it a practical tool for unsupervised learning tasks where labelled data is unavailable.

cs.LG↗

arXiv2025

Hybrid Interval Type-2 Mamdani-TSK Fuzzy System for Regression Analysis

Regression analysis is employed to examine and quantify the relationships between input variables and a dependent and continuous output variable. It is widely used for predictive modelling in fields such as finance, healthcare, and engineering. However, traditional methods often struggle with real-world data complexities, including uncertainty and ambiguity. While deep learning approaches excel at capturing complex non-linear relationships, they lack interpretability and risk over-fitting on small datasets. Fuzzy systems provide an alternative framework for handling uncertainty and imprecision, with Mamdani and Takagi-Sugeno-Kang (TSK) systems offering complementary strengths: interpretability versus accuracy. This paper presents a novel fuzzy regression method that combines the interpretability of Mamdani systems with the precision of TSK models. The proposed approach introduces a hybrid rule structure with fuzzy and crisp components and dual dominance types, enhancing both accuracy and explainability. Evaluations on benchmark datasets demonstrate state-of-the-art performance in several cases, with rules maintaining a component similar to traditional Mamdani systems while improving precision through improved rule outputs. This hybrid methodology offers a balanced and versatile tool for predictive modelling, addressing the trade-off between interpretability and accuracy inherent in fuzzy systems. In the 6 datasets tested, the proposed approach gave the best fuzzy methodology score in 4 datasets, out-performed the opaque models in 2 datasets and produced the best overall score in 1 dataset with the improvements in RMSE ranging from 0.4% to 19%.

cs.LG↗

arXiv2024

A Deep Learning Approach to Language-independent Gender Prediction on Twitter

This work presents a set of experiments conducted to predict the gender of Twitter users based on language-independent features extracted from the text of the users' tweets. The experiments were performed on a version of TwiSty dataset including tweets written by the users of six different languages: Portuguese, French, Dutch, English, German, and Italian. Logistic regression (LR), and feed-forward neural networks (FFNN) with back-propagation were used to build models in two different settings: Inter-Lingual (IL) and Cross-Lingual (CL). In the IL setting, the training and testing were performed on the same language whereas in the CL, Italian and German datasets were set aside and only used as test sets and the rest were combined to compose training and development sets. In the IL, the highest accuracy score belongs to LR whereas in the CL, FFNN with three hidden layers yields the highest score. The results show that neural network based models underperform traditional models when the size of the training set is small; however, they beat traditional models by a non-trivial margin, when they are fed with large enough data. Finally, the feature analysis confirms that men and women have different writing styles independent of their language.

cs.CL↗

arXiv2023

On large sum-free sets: revised bounds and patterns

In this paper we rectify two previous results found in the literature. Our work leads to a new upper bound for the largest sum-free subset of $[1,n]$ with lowest value in $\left [\frac{n}{3},\frac{n}{2}\right ]$, and the identification of all patterns that can be used to form sum-free sets of maximum cardinality.

math.CO↗

arXiv2023

On sum-free subsets of abelian groups

In this paper we discuss some of the key properties of sum-free subsets of abelian groups. Our discussion has been designed with a broader readership in mind, and is hence not overly technical. We consider answers to questions like: how many sum-free subsets are there in a given abelian group $G$? what are its sum-free subsets of maximum cardinality? what is the maximum cardinality of these sum-free subsets? what does a typical sum-free subset of $G$ looks like? among others.

math.CO↗

arXiv2020

Improving cluster recovery with feature rescaling factors

The data preprocessing stage is crucial in clustering. Features may describe entities using different scales. To rectify this, one usually applies feature normalisation aiming at rescaling features so that none of them overpowers the others in the objective function of the selected clustering algorithm. In this paper, we argue that the rescaling procedure should not treat all features identically. Instead, it should favour the features that are more meaningful for clustering. With this in mind, we introduce a feature rescaling method that takes into account the within-cluster degree of relevance of each feature. Our comprehensive simulation study, carried out on real and synthetic data, with and without noise features, clearly demonstrates that clustering methods that use the proposed data normalization strategy clearly outperform those that use traditional data normalization.

cs.LG↗

arXiv2020

Identifying meaningful clusters in malware data

Finding meaningful clusters in drive-by-download malware data is a particularly difficult task. Malware data tends to contain overlapping clusters with wide variations of cardinality. This happens because there can be considerable similarity between malware samples (some are even said to belong to the same family), and these tend to appear in bursts. Clustering algorithms are usually applied to normalised data sets. However, the process of normalisation aims at setting features with different range values to have a similar contribution to the clustering. It does not favour more meaningful features over those that are less meaningful, an effect one should perhaps expect of the data pre-processing stage. In this paper we introduce a method to deal precisely with the problem above. This is an iterative data pre-processing method capable of aiding to increase the separation between clusters. It does so by calculating the within-cluster degree of relevance of each feature, and then it uses these as a data rescaling factor. By repeating this until convergence our malware data was separated in clear clusters, leading to a higher average silhouette width.

cs.CR↗

arXiv2018

An efficient density-based clustering algorithm using reverse nearest neighbour

Density-based clustering is the task of discovering high-density regions of entities (clusters) that are separated from each other by contiguous regions of low-density. DBSCAN is, arguably, the most popular density-based clustering algorithm. However, its cluster recovery capabilities depend on the combination of the two parameters. In this paper we present a new density-based clustering algorithm which uses reverse nearest neighbour (RNN) and has a single parameter. We also show that it is possible to estimate a good value for this parameter using a clustering validity index. The RNN queries enable our algorithm to estimate densities taking more than a single entity into account, and to recover clusters that are not well-separated or have different densities. Our experiments on synthetic and real-world data sets show our proposed algorithm outperforms DBSCAN and its recent variant ISDBSCAN.

cs.LG↗

arXiv2016

A-Ward_p\b{eta}: Effective hierarchical clustering using the Minkowski metric and a fast k -means initialisation

In this paper we make two novel contributions to hierarchical clustering. First, we introduce an anomalous pattern initialisation method for hierarchical clustering algorithms, called A-Ward, capable of substantially reducing the time they take to converge. This method generates an initial partition with a sufficiently large number of clusters. This allows the cluster merging process to start from this partition rather than from a trivial partition composed solely of singletons. Our second contribution is an extension of the Ward and Ward p algorithms to the situation where the feature weight exponent can differ from the exponent of the Minkowski distance. This new method, called A-Ward p\b{eta} , is able to generate a much wider variety of clustering solutions. We also demonstrate that its parameters can be estimated reasonably well by using a cluster validity index. We perform numerous experiments using data sets with two types of noise, insertion of noise features and blurring within-cluster values of some features. These experiments allow us to conclude: (i) our anomalous pattern initialisation method does indeed reduce the time a hierarchical clustering algorithm takes to complete, without negatively impacting its cluster recovery ability; (ii) A-Ward p\b{eta} provides better cluster recovery than both Ward and Ward p.

cs.LG↗

arXiv2016

Recovering the number of clusters in data sets with noise features using feature rescaling factors

In this paper we introduce three methods for re-scaling data sets aiming at improving the likelihood of clustering validity indexes to return the true number of spherical Gaussian clusters with additional noise features. Our method obtains feature re-scaling factors taking into account the structure of a given data set and the intuitive idea that different features may have different degrees of relevance at different clusters. We experiment with the Silhouette (using squared Euclidean, Manhattan, and the p$^{th}$ power of the Minkowski distance), Dunn's, Calinski-Harabasz and Hartigan indexes on data sets with spherical Gaussian clusters with and without noise features. We conclude that our methods indeed increase the chances of estimating the true number of clusters in a data set.

stat.ML↗

arXiv2015

A survey on feature weighting based K-Means algorithms

In a real-world data set there is always the possibility, rather high in our opinion, that different features may have different degrees of relevance. Most machine learning algorithms deal with this fact by either selecting or deselecting features in the data preprocessing phase. However, we maintain that even among relevant features there may be different degrees of relevance, and this should be taken into account during the clustering process. With over 50 years of history, K-Means is arguably the most popular partitional clustering algorithm there is. The first K-Means based clustering algorithm to compute feature weights was designed just over 30 years ago. Various such algorithms have been designed since but there has not been, to our knowledge, a survey integrating empirical evidence of cluster recovery ability, common flaws, and possible directions for future research. This paper elaborates on the concept of feature weighting and addresses these issues by critically analysing some of the most popular, or innovative, feature weighting mechanisms based in K-Means.

cs.LG↗