Triclustering Algorithms for Three-Dimensional Data Analysis

Abstract

Three-dimensional data are increasingly prevalent across biomedical and social domains. Notable examples are gene-sample-time, individual-feature-time, or node-node-time data, generally referred to as observationattribute-context data. The unsupervised analysis of three-dimensional data can be pursued to discover putative biological modules, disease progression profiles, and communities of individuals with coherent behavior, among other patterns of interest. It is thus key to enhance the understanding of complex biological, individual, and societal systems. In this context, although clustering can be applied to group observations, its relevance is limited since observations in three-dimensional data domains are typically only meaningfully correlated on subspaces of the overall space. Biclustering tackles this challenge but disregards the third dimension. In this scenario, triclustering-the discovery of coherent subspaces within three-dimensional data-has been largely researched to tackle these problems. Despite the diversity of contributions in this field, there still lacks a structured view on the major requirements of triclustering, desirable forms of homogeneity (including coherency, structure, quality, locality, and orthonormality criteria), and algorithmic approaches. This work formalizes the triclustering task and its scope, introduces a taxonomy to categorize the contributions in the field, provides a comprehensive comparison of state-of-the-art triclustering algorithms according to their behavior and output, and lists relevant real-world applications. Finally, it highlights challenges and opportunities to advance the field of triclustering and its applicability to complex three-dimensional data analysis.

Tri-Clustering Based Exploration of Temporal Resolution Impacts on Spatio-Temporal Clusters in Geo-Referenced Time Series

“…Since the tri-clustering algorithm was first proposed in 2005, tri-clustering analysis has been employed for the exploration of patterns in many applications [11,20,21,32,33]. As the first tri-clustering algorithm, TRICLUSTER identifies tri-clusters by using multigraphs of ranges and constrained maximal cliques.…”

“…As a result, it provides both an overview of data at cluster levels and investigation of details on single clusters [9,10]. According to the involved dimensions in the clustering analysis, clustering methods for GTS are categorized as one-way clustering, co-clustering, and tri-clustering methods [11,12].…”

Moving from Formal Towards Coherent Concept Analysis: Why, When and How

“…Pattern-based biclustering algorithms are inherently prepared to efficiently find exhaustive solutions of biclusters and offer the unprecedented possibility to affect their structure, coherency and quality [12,14]. This behavior explains why this class of biclustering algorithms are receiving an increasing attention in recent years [13,18]. BicPAMS [14] consistently combines such state-of-the-art contributions on pattern-based biclustering.…”

“…Depending on the goal, one or more coherence assumptions (Definitions 1 and 2) can be pursued [13,18]. The classic constant coherence can be placed to find groups of documents and topics, where each document has a similar probability to be described by a specific topic.…”

Clustering Methods in Gene Expression Research

“…Данная тема освещена в обзорах [1][2][3], составленных в разное время. В данном обзоре рассмотренные в прошлых обзорах методы кластеризации дополнены новыми методами, появление которых связано с развитием теории машинного обучения и интеллектуального анализа данных.…”