2026-10-13T16:42:19Z https://api.figshare.com/v2/oai

oai:figshare.com:article/30663476 2026-09-28T07:01:16Z category_7 category_13 category_19 category_21 category_24 category_39 category_811 category_132 category_133 portal_87 item_type_3 month_year_09_2026

Fuzzy clustering and dimensionality reduction of a three-way data matrix Ilaria Bombelli (22651421) Mariaelena Bottazzi Schenone (22651424) Maurizio Vichi (11678124) Medicine Genetics Pharmacology Biotechnology Evolutionary Biology Ecology Mathematical Sciences not elsewhere classified Infectious Diseases Plant Biology Three-way data three-modes data dimensionality reduction techniques fuzzy cluster analysis disjoint factor analysis 62-08 62H12 62H25 62H30 62H86 <p>A three-way three-mode data array X, where modes are units, variables, and occasions, is the data structure that can comprehensively and statistically analyze a collective phenomenon. When X has a large dimension, it is important to synthesize its information by identifying classes of similar occasions where units are described by a reduced set of LVs. In this paper, a simultaneous reduction of the occasions and variables of X is proposed. A fuzzy clustering of the occasions allows the identification of <i>K</i> clusters of multivariate data matrices that are within-cluster perceived similar. For each cluster, a consensus matrix with respect to the units is identified. Variables in the cluster are correlated and maintain their covariance structure that can be synthesized for each consensus matrix by applying a Second-Order Disjoint Factor Analysis. The proposal allows therefore to softly cluster occasions into <i>K</i> clusters and, for each consensus matrix, firstly identify a set of <i>Q</i> first-order factors and secondly identify a unique general factor, which can be considered as the most synthetic indicator summarizing the original <i>J</i> variables. The performance of the methodology is tested through a detailed simulation study. Finally, it is also applied to a real dataset, where its strength and usefulness are revealed.</p> 2025-11-20T05:20:42Z Dataset Dataset 10.6084/m9.figshare.30663476.v2 https://figshare.com/articles/dataset/Fuzzy_clustering_and_dimensionality_reduction_of_a_three-way_data_matrix/30663476 CC BY 4.0