{"title":"Beyond the orthogonal group: a discussion on robust ICA and sphering transformations","authors":"Marc Vidal","doi":"10.1007/s11634-026-00699-0","DOIUrl":"10.1007/s11634-026-00699-0","url":null,"abstract":"<div><p>We discuss the robust independent component analysis (ICA) method of Leyder et al. (2026), called PICARD, with particular emphasis on the role of whitening and sphering transformations. We show that robust sphering alters the geometry of the ICA problem, so that the classical reduction to an orthogonal mixing model does not apply in general. Nevertheless, PICARD appears empirically stable despite deviations from exact decorrelation and unit variance, suggesting that these conditions may not be strictly necessary in practice. We further characterize the induced perturbation asymptotically and discuss alternative formulations that incorporate the resulting geometry into the estimation procedure.</p></div>","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 3","pages":"821 - 833"},"PeriodicalIF":2.1,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discussion of “Independent component analysis by robust distance correlation”: a note on the geometry of the bowl transform and on the reach of the consistency for robust ICA","authors":"Pietro Coretto","doi":"10.1007/s11634-026-00696-3","DOIUrl":"10.1007/s11634-026-00696-3","url":null,"abstract":"<div><p>This is a discussion of PICARD, the robust independent component analysis (ICA) estimator built on a transformed distance correlation and on the bowl transform. I develop two threads. The first reads the bowl transform as a multivariate redescending <span>(psi)</span>-function, makes its exponential decay explicit, and describes how the transformed norm concentrates as the dimension grows. The second examines the reach of the strong-consistency result, relating its population target to classical ICA identifiability and to the behavior of robust whitening under non-elliptical sources.</p></div>","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 3","pages":"767 - 773"},"PeriodicalIF":2.1,"publicationDate":"2026-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11634-026-00696-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discussion of “independent component analysis by robust distance correlation”: on robustness in dependence-based ICA","authors":"Yuchen Xu, David S. Matteson, Ruey Tsay","doi":"10.1007/s11634-026-00695-4","DOIUrl":"10.1007/s11634-026-00695-4","url":null,"abstract":"<div><p>PICARD combines MCD whitening, a bowl transform, and distance-correlation minimization for robust independent component analysis (ICA). This discussion uses PICARD as a point of departure for reviewing several meanings of robustness in ICA, including resistance to high-leverage observations, robust preprocessing, bounded and slow-growing contrasts, divergence-based weighting, marginal transformations, missingness, and model misspecification. Within this broader landscape, PICARD is best understood as a geometric robustification of dependence-based ICA: it changes the Euclidean geometry in which empirical dependence is computed, thereby reducing the leverage of atypical observations that would otherwise dominate whitening or pairwise distances. Among all the benchmarks in the literature, probability integral transform (PIT) and copula-based mechanisms represent a different yet comparable branch, aimed more directly at marginal scale, distributional shape, and monotone invariance. We further discuss how PICARD’s geometric viewpoint relates to alternative distance-dependence criteria, temporal structure, group ICA, and non-Gaussian component analysis.</p></div>","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 3","pages":"835 - 846"},"PeriodicalIF":2.1,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the ADAC issue 2 of volume 20 (2026)","authors":"Maurizio Vichi, Andrea Cerioli, Hans A. Kestler","doi":"10.1007/s11634-026-00691-8","DOIUrl":"10.1007/s11634-026-00691-8","url":null,"abstract":"","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 2","pages":"315 - 322"},"PeriodicalIF":2.1,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148314722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Variable selection via knockoffs for clustered data","authors":"Silvia Bacci, Leonardo Grilli, Ersilia Lucenteforte, Carla Rampichini","doi":"10.1007/s11634-026-00682-9","DOIUrl":"10.1007/s11634-026-00682-9","url":null,"abstract":"<div><p>We extend the knockoffs method for selecting predictors to clustered data (cross-sectional or repeated measures). In this setting, variable selection is complex because some predictors are measured at the observation level (level 1), whereas others are measured at the cluster level (level 2), so their values are constant within clusters. Moreover, level 1 predictors are correlated within clusters. The solution we propose is to conduct variable selection separately at the two levels. To this end, we suggest a two-step approach: (i) decompose each level 1 predictor into level 2 and level 1 components by replacing it with the cluster mean and the deviation from the cluster mean; (ii) perform variable selection separately at the two levels, where the level 1 data matrix includes the deviations from the cluster means and the level 2 data matrix includes the level 2 predictors and the cluster means of level 1 predictors. To evaluate the performance of the proposed approach, we conduct a simulation study comparing the sequential knockoff, the derandomised knockoff, and the Lasso. The study shows satisfactory results for false discovery rate and power. All methods fail when applied to the complete data matrix, including both level 1 and level 2 predictors. In contrast, all methods perform better when applied to the level 1 and level 2 data matrices separately. Moreover, the sequential knockoffs method performs substantially better than the Lasso and the derandomised knockoffs. Our proposal to implement the knockoffs method in a clustered data framework is feasible, flexible, and effective.</p></div>","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 3","pages":"903 - 921"},"PeriodicalIF":2.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11634-026-00682-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Model-based clustering of functional data via random projection ensembles","authors":"Matteo Mori, Laura Anderlucci","doi":"10.1007/s11634-026-00684-7","DOIUrl":"10.1007/s11634-026-00684-7","url":null,"abstract":"<div><p>Clustering functional data is a challenging task due to intrinsic infinite-dimensionality and the need for stable, data-adaptive partitioning. In this work, we propose a clustering framework based on Random Projections, which simultaneously performs dimensionality reduction and generates multiple stochastic representations of the original functions. Each projection is clustered independently, and the resulting partitions are then aggregated through an ensemble consensus procedure, enhancing robustness and mitigating the influence of any single projection. To focus on the most informative representations, projections are ranked according to clustering quality criteria, and only a selected subset is retained. In particular, we adopt Gaussian Mixture Models as base clusterers and employ a measure based on the Kullback–Leibler divergence to order the random projections; these choices enable fast computation and eliminate the need to specify the number of clusters a priori. The performance of the proposed methodology is assessed through an extensive simulation study and real-data applications; the obtained results suggest that the proposal represents an effective tool for the clustering of functional data.</p></div>","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 3","pages":"877 - 901"},"PeriodicalIF":2.1,"publicationDate":"2026-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11634-026-00684-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sarah Leyder, Jakob Raymaekers, Peter J. Rousseeuw, Tom Van Deuren, Tim Verdonck
{"title":"Independent component analysis by robust distance correlation","authors":"Sarah Leyder, Jakob Raymaekers, Peter J. Rousseeuw, Tom Van Deuren, Tim Verdonck","doi":"10.1007/s11634-026-00674-9","DOIUrl":"10.1007/s11634-026-00674-9","url":null,"abstract":"<div>\u0000 \u0000 <p>Independent component analysis (ICA) is a powerful tool that attempts to decompose a multivariate signal or distribution into fully independent sources, not just uncorrelated ones like PCA does. ICA is harder to do, but it has many important applications. Unfortunately, most approaches to ICA are not robust against outliers. Here we propose a robust ICA method called PICARD, which estimates the components by minimizing a robust measure of dependence between multivariate random variables. The dependence measure used is the distance correlation (dCor). In order to make it more robust we first apply a new transformation called the bowl transform, which is bounded, continuous, injective, and maps far outliers to points close to the origin. This preserves the crucial property that a zero dCor implies independence. PICARD estimates the independent sources sequentially, by looking for the component that has the smallest dCor with the remainder. We prove that PICARD is strongly consistent. Its robustness is investigated by a simulation study, in which it generally outperforms its competitors. The method is illustrated on three applications, including the well-known cocktail party problem.</p>\u0000 </div>","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 3","pages":"727 - 765"},"PeriodicalIF":2.1,"publicationDate":"2026-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11634-026-00674-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Randomized smart subset selection for high-dimensional generalized linear models with false positive control","authors":"Nicholas Rios, Zhaoxue Tong","doi":"10.1007/s11634-026-00675-8","DOIUrl":"10.1007/s11634-026-00675-8","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce a novel variable selection method for high-dimensional generalized linear models, called Randomized Smart Subset Selection (RS3). RS3 combines randomized block-wise model fitting with importance-weighted stochastic subset sampling to efficiently identify active predictors. Two extensions are proposed: (i) RS3+SCAD, which applies penalized regression with the SCAD penalty to a reduced set of candidate variables, improving computational efficiency while adaptively determining model size; and (ii) RS3+FPCS, a subsampling-based procedure for false positive control based on coefficient sign stability. Simulation studies demonstrate that RS3 and its variants achieve high true positive rates with low false discovery, even under moderate predictor correlation. Applications to gene expression data show that RS3+SCAD consistently identifies sparse, biologically interpretable gene sets, outperforming existing methods in terms of prediction accuracy and stability.</p>\u0000 <p>MSC Codes: 62F40, 62J12, 62H30</p>\u0000 </div>","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 3","pages":"857 - 875"},"PeriodicalIF":2.1,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11634-026-00675-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial for ADAC issue 1 of volume 20 (2026)","authors":"Berthold Lausen, Maurizio Vichi","doi":"10.1007/s11634-026-00676-7","DOIUrl":"10.1007/s11634-026-00676-7","url":null,"abstract":"","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"20 :","pages":"1 - 9"},"PeriodicalIF":1.3,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11634-026-00676-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial for ADAC issue 4 of volume 19 (2025)","authors":"Maurizio Vichi, Andrea Cerioli, Hans A. Kestler","doi":"10.1007/s11634-025-00660-7","DOIUrl":"10.1007/s11634-025-00660-7","url":null,"abstract":"","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"19 4","pages":"855 - 859"},"PeriodicalIF":1.3,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}