arXiv subjects

Ricardo J. G. B. Campello

Publications and source records attributed to Ricardo J. G. B. Campello.

10 recordsLinked to original sources

arXiv2026

CROCS: A Two-Stage Clustering Framework for Behaviour-Centric Consumer Segmentation with Smart Meter Data

With grid operators confronting rising uncertainty from renewable integration and a broader push toward electrification, Demand-Side Management (DSM) -- particularly Demand Response (DR) -- has attracted significant attention as a cost-effective mechanism for balancing modern electricity systems. Unprecedented volumes of consumption data from a continuing global deployment of smart meters enable consumer segmentation based on real usage behaviours, promising to inform the design of more effective DSM and DR programs. However, existing clustering-based segmentation methods insufficiently reflect the behavioural diversity of consumers, often relying on rigid temporal alignment, and faltering in the presence of anomalies, missing data, or large-scale deployments. To address these challenges, we propose a novel two-stage clustering framework -- Clustered Representations Optimising Consumer Segmentation (CROCS). In the first stage, each consumer's daily load profiles are clustered independently to form a Representative Load Set (RLS), providing a compact summary of their typical diurnal consumption behaviours. In the second stage, consumers are clustered using the Weighted Sum of Minimum Distances (WSMD), a novel set-to-set measure that compares RLSs by accounting for both the prevalence and similarity of those behaviours. Finally, community detection on the WSMD-induced graph reveals higher-order prototypes that embody the shared diurnal behaviours defining consumer groups, enhancing the interpretability of the resulting clusters. Extensive experiments on both synthetic and real Australian smart meter datasets demonstrate that CROCS captures intra-consumer variability, uncovers both synchronous and asynchronous behavioural similarities, and remains robust to anomalies and missing data, while scaling efficiently through natural parallelisation. These results...

stat.ML↗

arXiv2026

FOSC-X: An Extended Framework for Optimal Local Cuts and Non-Horizontal Cluster Selection from Clustering Hierarchies

Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem. Existing approaches focus on finding a single optimal solution. We introduce FOSC-X, a framework for extracting the top-M globally optimal flat clusterings from local, non-horizontal cuts of a hierarchical cluster tree, while optionally enforcing constraints on the number of clusters. This enables automatic identification of multiple high-quality alternative clusterings that capture different aspects of the hierarchical structure. Without constraints, the top-M problem can be solved in polynomial time using dynamic programming, exploiting the property that locally optimal partial candidates within subtrees can be combined to form globally optimal solutions while automatically determining the number of clusters. However, this can lead to solutions with numbers of clusters that are ultimately undesirable -- e.g., too large to be meaningful or practically analysed within a particular application domain. Imposing cluster-count constraints breaks the optimality property underlying the unconstrained dynamic programming approach, since locally optimal partial candidates may no longer combine into feasible globally optimal solutions. FOSC-X addresses this challenge through a dynamic programming strategy that maintains compact sets of feasible candidates using lower and upper feasibility bounds while pruning infeasible or dominated combinations. The resulting method guarantees optimal rankings of the top-M solutions with linear-time complexity in the number of cluster nodes and dataset size, both with and without cluster-count constraints. Experiments show that FOSC-X efficiently reveals alternative clustering structures overlooked by single-solution extraction methods.

stat.ML↗

arXiv2026

On the Use of Bagging for Local Intrinsic Dimensionality Estimation

The theory of Local Intrinsic Dimensionality (LID) has become a valuable tool for characterizing local complexity within and across data manifolds, supporting a range of data mining and machine learning tasks. Accurate LID estimation requires samples drawn from small neighborhoods around each query to avoid biases from nonlocal effects and potential manifold mixing, yet limited data within such neighborhoods tends to cause high estimation variance. As a variance reduction strategy, we propose an ensemble approach that uses subbagging to preserve the local distribution of nearest neighbor (NN) distances. The main challenge is that the uniform reduction in total sample size within each subsample increases the proximity threshold for finding a fixed number k of NNs around the query. As a result, in the specific context of LID estimation, the sampling rate has an additional, complex interplay with the neighborhood size, where both combined determine the sample size as well as the locality and resolution considered for estimation. We analyze both theoretically and experimentally how the choice of the sampling rate and the k-NN size used for LID estimation, alongside the ensemble size, affects performance, enabling informed prior selection of these hyper-parameters depending on application-based preferences. Our results indicate that within broad and well-characterized regions of the hyper-parameters space, using a bagged estimator will most often significantly reduce variance as well as the mean squared error when compared to the corresponding non-bagged baseline, with controllable impact on bias. We additionally propose and evaluate different ways of combining bagging with neighborhood smoothing for substantial further improvements on LID estimation performance.

cs.LG↗

arXiv2025

Benchmarking of Clustering Validity Measures Revisited

Validation plays a crucial role in the clustering process. Many different internal validity indexes exist for the purpose of determining the best clustering solution(s) from a given collection of candidates, e.g., as produced by different algorithms or different algorithm hyper-parameters. In this study, we present a comprehensive benchmark study of 26 internal validity indexes, which includes highly popular classic indexes as well as more recently developed ones. We adopted an enhanced revision of the methodology presented in Vendramin et al. (2010), developed here to address several shortcomings of this previous work. This overall new approach consists of three complementary custom-tailored evaluation sub-methodologies, each of which has been designed to assess specific aspects of an index's behaviour while preventing potential biases of the other sub-methodologies. Each sub-methodology features two complementary measures of performance, alongside mechanisms that allow for an in-depth investigation of more complex behaviours of the internal validity indexes under study. Additionally, a new collection of 16177 datasets has been produced, paired with eight widely-used clustering algorithms, for a wider applicability scope and representation of more diverse clustering scenarios.

stat.ML↗

arXiv2025

Comparing Clustering Approaches for Smart Meter Time Series: Investigating the Influence of Dataset Properties on Performance

The widespread adoption of smart meters for monitoring energy consumption has generated vast quantities of high-resolution time series data which remains underutilised. While clustering has emerged as a fundamental tool for mining smart meter time series (SMTS) data, selecting appropriate clustering methods remains challenging despite numerous comparative studies. These studies often rely on problematic methodologies and consider a limited scope of methods, frequently overlooking compelling methods from the broader time series clustering literature. Consequently, they struggle to provide dependable guidance for practitioners designing their own clustering approaches. This paper presents a comprehensive comparative framework for SMTS clustering methods using expert-informed synthetic datasets that emphasise peak consumption behaviours as fundamental cluster concepts. Using a phased methodology, we first evaluated 31 distance measures and 8 representation methods using leave-one-out classification, then examined the better-suited methods in combination with 11 clustering algorithms. We further assessed the robustness of these combinations to systematic changes in key dataset properties that affect clustering performance on real-world datasets, including cluster balance, noise, and the presence of outliers. Our results revealed that methods accommodating local temporal shifts while maintaining amplitude sensitivity, particularly Dynamic Time Warping and $k$-sliding distance, consistently outperformed traditional approaches. Among other key findings, we identified that when combined with $k$-medoids or hierarchical clustering using Ward's linkage, these methods exhibited consistent robustness across varying dataset characteristics without...

stat.AP↗

arXiv2024

On the Use of Relative Validity Indices for Comparing Clustering Approaches

Relative Validity Indices (RVIs) such as the Silhouette Width Criterion and Davies Bouldin indices are the most widely used tools for evaluating and optimising clustering outcomes. Traditionally, their ability to rank collections of candidate dataset partitions has been used to guide the selection of the number of clusters, and to compare partitions from different clustering algorithms. However, there is a growing trend in the literature to use RVIs when selecting a Similarity Paradigm (SP) for clustering - the combination of normalisation procedure, representation method, and distance measure which affects the computation of object dissimilarities used in clustering. Despite the growing prevalence of this practice, there has been no empirical or theoretical investigation into the suitability of RVIs for this purpose. Moreover, since RVIs are computed using object dissimilarities, it remains unclear how they would need to be implemented for fair comparisons of different SPs. This study presents the first comprehensive investigation into the reliability of RVIs for SP selection. We conducted extensive experiments with seven popular RVIs on over 2.7 million clustering partitions of synthetic and real-world datasets, encompassing feature-vector and time-series data. We identified fundamental conceptual limitations undermining the use of RVIs for SP selection, and our empirical findings confirmed this predicted unsuitability. Among our recommendations, we suggest instead that practitioners select SPs by using external validation on high quality labelled datasets or carefully designed outcome-oriented objective criteria, both of which should be informed by careful consideration of dataset characteristics, and domain requirements. Our findings have important implications for clustering methodology and evaluation, suggesting the need for more rigorous approaches to SP selection.

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arXiv2024

Robust Statistical Scaling of Outlier Scores: Improving the Quality of Outlier Probabilities for Outliers (Extended Version)

Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be difficult for humans to interpret. Statistical scaling addresses this problem by transforming outlier scores into outlier probabilities without using ground-truth labels, thereby improving interpretability and comparability across algorithms. However, the quality of this transformation can be different for outliers and inliers. Missing outliers in scenarios where they are of particular interest - such as healthcare, finance, or engineering - can be costly or dangerous. Thus, ensuring good probabilities for outliers is essential. This paper argues that statistical scaling, as commonly used in the literature, does not produce equally good probabilities for outliers as for inliers. Therefore, we propose robust statistical scaling, which uses robust estimators to improve the probabilities for outliers. We evaluate several variants of our method against other outlier score transformations for real-world datasets and outlier detection algorithms, where it can improve the probabilities for outliers.

cs.LG↗

arXiv2024

Dimensionality-Aware Outlier Detection: Theoretical and Experimental Analysis

We present a nonparametric method for outlier detection that takes full account of local variations in intrinsic dimensionality within the dataset. Using the theory of Local Intrinsic Dimensionality (LID), our 'dimensionality-aware' outlier detection method, DAO, is derived as an estimator of an asymptotic local expected density ratio involving the query point and a close neighbor drawn at random. The dimensionality-aware behavior of DAO is due to its use of local estimation of LID values in a theoretically-justified way. Through comprehensive experimentation on more than 800 synthetic and real datasets, we show that DAO significantly outperforms three popular and important benchmark outlier detection methods: Local Outlier Factor (LOF), Simplified LOF, and kNN.

cs.LG↗

arXiv2024

LDReg: Local Dimensionality Regularized Self-Supervised Learning

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called $\textit{local dimensionality regularization (LDReg)}$. Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

cs.LG↗

arXiv2018

Efficient Computation of Multiple Density-Based Clustering Hierarchies

HDBSCAN*, a state-of-the-art density-based hierarchical clustering method, produces a hierarchical organization of clusters in a dataset w.r.t. a parameter mpts. While the performance of HDBSCAN* is robust w.r.t. mpts in the sense that a small change in mpts typically leads to only a small or no change in the clustering structure, choosing a "good" mpts value can be challenging: depending on the data distribution, a high or low value for mpts may be more appropriate, and certain data clusters may reveal themselves at different values of mpts. To explore results for a range of mpts values, however, one has to run HDBSCAN* for each value in the range independently, which is computationally inefficient. In this paper, we propose an efficient approach to compute all HDBSCAN* hierarchies for a range of mpts values by replacing the graph used by HDBSCAN* with a much smaller graph that is guaranteed to contain the required information. An extensive experimental evaluation shows that with our approach one can obtain over one hundred hierarchies for the computational cost equivalent to running HDBSCAN* about 2 times.

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