Supporting scientific knowledge discovery with extended, generalized Formal Concept Analysis

Valverde-Albacete, Francisco J.; González-Calabozo, José María; Peñas, Anselmo; Peláez-Moreno, Carmen

doi:10.1016/j.eswa.2015.09.022

Cited by 24 publications

(11 citation statements)

References 40 publications

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“…Of course, this manner of proceeding belongs in Exploratory Data Analysis (EDA) [10] which propounds cycles of exploration and inferencing, hence these phases of analysis could be iterated, mingled or carried in parallel. We have already discussed at length the "affordances" of FCA for EDA [11]. In this light, the presence of FIA and FEA are two more tools at the disposal of practitioners, providing the systematic approach that FCA pioneered.…”

Section: Discussionmentioning

confidence: 99%

Formal Equivalence Analysis

Albacete¹,

Peláez-Moreno²,

Ojeda‐Aciego³

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Following R. Wille's lead and suggestion we set out to design a new kind of view onto a formal context analogous but different to Formal Concept Analysis and Formal Independent Analysis. In this instance, we choose to analyse the information in the incidence table in terms of the partitions induced on the sets of objects and attributes by the same functions of single attributes and objects of the context. These functions constitute a left adjunction between sets of objects and attributes and we later lift this left adjunction to partitions of the objects and attributes. Therefore we refer to this new view onto the formal context as Formal Equivalence Analysis. Rather than looking on the effect of these partitions on set representation, as in Rough Sets, we try to make explicit the information in the context.

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Section: Discussionmentioning

confidence: 99%

Formal Equivalence Analysis

Albacete¹,

Peláez-Moreno²,

Ojeda‐Aciego³

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…The reader should be aware that since this methodology cannot be used as a tool for Confirmatory or Predictive Data Analysis by itself, an empirical verification of the hypothesis gained in the exploration should be carried out as a subsequent step. We believe, nevertheless, that the framework we promote is specially suited to support scientific knowledge discovery in GED [ 28 ] given the usual lack of ground-truth in this type of data. This leads us to the enduring dilemma of obtaining quality indicators in an EDA framework.…”

Section: Discussionmentioning

confidence: 99%

“…As very early noted by Godin and collaborators [ 34 , 35 ] a Formal Concept Analysis-based lattice can be turned into a content-based indexing device onto other knowledge resources. This affordance plays an important role in supporting the exploration of a scientific experiment and specifically for GED analysis [ 28 ]. A more in-depth analysis of affordances of FCA for the analysis and synthesis of Information Retrieval systems is [ 36 ].…”

Section: Methodsmentioning

confidence: 99%

“…The proposal is well-founded and completes the “landscapes of knowledge” metaphor providing a sound basis for EDA over non-boolean data with FCA that enables exploring the data at different resolutions [ 28 ]. As we sweep over those resolutions, the output is a sequence of gene expression lattices, where the researcher can see how clusters evolve, enabling a more detailed and less rigid understanding of the behavior some genes may share under different conditions.…”

Section: Introductionmentioning

confidence: 99%

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Interactive knowledge discovery and data mining on genomic expression data with numeric formal concept analysis

2016

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BackgroundGene Expression Data (GED) analysis poses a great challenge to the scientific community that can be framed into the Knowledge Discovery in Databases (KDD) and Data Mining (DM) paradigm. Biclustering has emerged as the machine learning method of choice to solve this task, but its unsupervised nature makes result assessment problematic. This is often addressed by means of Gene Set Enrichment Analysis (GSEA).ResultsWe put forward a framework in which GED analysis is understood as an Exploratory Data Analysis (EDA) process where we provide support for continuous human interaction with data aiming at improving the step of hypothesis abduction and assessment. We focus on the adaptation to human cognition of data interpretation and visualization of the output of EDA.First, we give a proper theoretical background to bi-clustering using Lattice Theory and provide a set of analysis tools revolving around -Formal Concept Analysis (-FCA), a lattice-theoretic unsupervised learning technique for real-valued matrices.By using different kinds of cost structures to quantify expression we obtain different sequences of hierarchical bi-clusterings for gene under- and over-expression using thresholds. Consequently, we provide a method with interleaved analysis steps and visualization devices so that the sequences of lattices for a particular experiment summarize the researcher’s vision of the data. This also allows us to define measures of persistence and robustness of biclusters to assess them.Second, the resulting biclusters are used to index external omics databases—for instance, Gene Ontology (GO)—thus offering a new way of accessing publicly available resources. This provides different flavors of gene set enrichment against which to assess the biclusters, by obtaining their p-values according to the terminology of those resources.We illustrate the exploration procedure on a real data example confirming results previously published.ConclusionsThe GED analysis problem gets transformed into the exploration of a sequence of lattices enabling the visualization of the hierarchical structure of the biclusters with a certain degree of granularity. The ability of FCA-based bi-clustering methods to index external databases such as GO allows us to obtain a quality measure of the biclusters, to observe the evolution of a gene throughout the different biclusters it appears in, to look for relevant biclusters—by observing their genes and what their persistence is—to infer, for instance, hypotheses on their function.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1234-z) contains supplementary material, which is available to authorized users.

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“…These developments were extensively based in previous work in the (completed and incomplete) tropical and schedule algebras [8,9,13,14,[26][27][28][29]. It was instantiated with the minimax algebra and applied to, for example, the analysis of genomic [30], and positive data [31], or even Exploratory Data Analysis [32]. Note that a similar approach to extending FCA had previously been developed for matrices with entries in a fuzzy-semiring, today grouped under the name FCA in a fuzzy setting [33][34][35], but fuzzy semirings are not idempotent semifields, except for 2 2 itself.…”

Section: K-formal Concept Analysis As Linear Algebra Over Idempotent Semifieldsmentioning

confidence: 99%

Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields

Valverde-Albacete

Peláez-Moreno

2021

Mathematics

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Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings. At the heart of FCA lies a Galois connection between two powersets. In this paper we extend the FCA formalism to include all four Galois connections between four different semivectors spaces over idempotent semifields, at the same time. The result is K¯-four-fold Formal Concept Analysis (K¯-4FCA) where K¯ is the idempotent semifield biasing the analysis. Since complete idempotent semifields come in dually-ordered pairs—e.g., the complete max-plus and min-plus semirings—the basic construction shows dual-order-, row–column- and Galois-connection-induced dualities that appear simultaneously a number of times to provide the full spectrum of variability. Our results lead to a fundamental theorem of K¯-four-fold Formal Concept Analysis that properly defines quadrilattices as 4-tuples of (order-dually) isomorphic lattices of vectors and discuss its relevance vis-à-vis previous formal conceptual analyses and some affordances of their results.

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Supporting scientific knowledge discovery with extended, generalized Formal Concept Analysis

Cited by 24 publications

References 40 publications

Formal Equivalence Analysis

Formal Equivalence Analysis

Interactive knowledge discovery and data mining on genomic expression data with numeric formal concept analysis

Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields

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