[Paper Review] Towards a Unified Taxonomy of Biclustering Methods

Dmitry I. Ignatov, Bruce W. Watson|arXiv (Cornell University)|Feb 17, 2017

Rough Sets and Fuzzy Logic31 references3 citations

TL;DR

This paper proposes a unified taxonomy for biclustering methods using formal concept analysis (FCA) and attribute exploration to integrate diverse classification schemes from bioinformatics and data mining. By modeling biclustering techniques as formal concepts and applying attribute exploration to complete and validate the taxonomy, the authors establish a comprehensive, extensible framework that reveals missing methodological categories and supports interactive, ontology-like classification of biclustering algorithms.

ABSTRACT

Being an unsupervised machine learning and data mining technique, biclustering and its multimodal extensions are becoming popular tools for analysing object-attribute data in different domains. Apart from conventional clustering techniques, biclustering is searching for homogeneous groups of objects while keeping their common description, e.g., in binary setting, their shared attributes. In bioinformatics, biclustering is used to find genes, which are active in a subset of situations, thus being candidates for biomarkers. However, the authors of those biclustering techniques that are popular in gene expression analysis, may overlook the existing methods. For instance, BiMax algorithm is aimed at finding biclusters, which are well-known for decades as formal concepts. Moreover, even if bioinformatics classify the biclustering methods according to reasonable domain-driven criteria, their classification taxonomies may be different from survey to survey and not full as well. So, in this paper we propose to use concept lattices as a tool for taxonomy building (in the biclustering domain) and attribute exploration as means for cross-domain taxonomy completion.

Motivation & Objective

• To address the lack of a consistent, comprehensive taxonomy for biclustering methods across diverse domains like bioinformatics and data mining.
• To unify existing, often conflicting or incomplete, classification schemes for biclustering algorithms.
• To identify gaps in current biclustering method categorizations by applying attribute exploration to formal concept lattices.
• To develop a reusable, extensible framework for classifying new biclustering methods based on shared attributes and structural properties.
• To enable interactive, visual, and ontology-like exploration of biclustering techniques through concept lattices and nested line diagrams.

Proposed method

• Model biclustering methods as formal concepts within a formal context of objects (methods) and attributes (classification criteria).
• Construct a concept lattice from the formal context to represent hierarchical relationships between biclustering methods.
• Apply attribute exploration—a formal concept analysis technique—to validate and complete the taxonomy by identifying logical implications between classification attributes.
• Use the lattice structure to detect missing or inconsistent method categories, such as non-exhaustive biclusters with one-set discovery strategies.
• Integrate multimodal clustering extensions (e.g., triclustering, n-sets) into the taxonomy by generalizing formal concepts to n-ary relations.
• Support interactive visualization via tree-based, lattice-based, and nested line diagram interfaces for navigating the taxonomy at multiple granularities.

Experimental results

Research questions

• RQ1 How can a unified taxonomy of biclustering methods be constructed from disparate classification schemes in the literature?
• RQ2 Which classification attributes are missing or inconsistent in existing biclustering taxonomies, and how can they be discovered?
• RQ3 To what extent can formal concept analysis and attribute exploration reveal structural gaps in current biclustering method categorizations?
• RQ4 How can the taxonomy be maintained and extended as new biclustering algorithms emerge?
• RQ5 Can the proposed framework support interactive exploration and classification of biclustering methods through visual and logical means?

Key findings

• The authors identify that many widely used biclustering methods in bioinformatics, such as BiMax, are equivalent to formal concepts—maximal submatrices in Boolean matrices—previously known in formal concept analysis since the 1980s.
• Attribute exploration reveals logical inconsistencies and missing categories, such as the absence of methods combining 'one-set discovery strategy' with 'exhaustive bicluster structure', which are logically implied but not yet implemented.
• The taxonomy construction process uncovers that existing classifications are often incomplete, domain-specific, and lack formal validation, leading to redundant or rediscovered algorithmic approaches.
• The use of concept lattices enables hierarchical organization of biclustering methods, revealing general-to-specific relationships and supporting interactive navigation and classification.
• The framework supports ontology-like management of biclustering knowledge, allowing for dynamic expansion and validation of new method categories through expert feedback.
• The integration of multimodal clustering (e.g., triclustering, n-sets) into the taxonomy demonstrates the framework’s extensibility beyond traditional biclustering.