Detecting Features from Confusion Matrices using Generalized Formal Concept Analysis

We claim that the confusion matrices of multiclass problems can be analyzed by means of a generalization of Formal Concept Analysis to obtain symbolic information about the feature sets of the underlying classification task.We prove our claims by analyzing the confusion matrices of human speech perception experiments and comparing our results to those elicited by experts.This work has been supported by Spanish Government-Comisión Interministerial de Ciencia y Tecnología TEC2008-02473/TEC y TEC2008-06382/TEC.Publicad

Supporting scientific knowledge discovery with extended, generalized Formal Concept Analysis

In this paper we fuse together the Landscapes of Knowledge of Wille's and Exploratory Data Analysis by leveraging Formal Concept Analysis (FCA) to support data-induced scientific enquiry and discovery. We use extended FCA first by allowing K-valued entries in the incidence to accommodate other, non-binary types of data, and second with different modes of creating formal concepts to accommodate diverse conceptualizing phenomena. With these extensions we demonstrate the versatility of the Landscapes of Knowledge metaphor to help in creating new scientific and engineering knowledge by providing several successful use cases of our techniques that support scientific hypothesis-making and discovery in a range of domains: semiring theory, perceptual studies, natural language semantics, and gene expression data analysis. While doing so, we also capture the affordances that justify the use of FCA and its extensions in scientific discovery.FJVA and AP were partially supported by EUFP7 project LiMo- SINe (contract288024) for this research. CPM was partially supported by the Spanish Ministry of Economics and Competitiveness projects TEC2014-61729-EXP and TEC2014-53390-P

Inference of mixed information in Formal Concept Analysis

Negative information can be considered twofold: by means of a negation operator or by capturing the absence of information. In this second approach, a new framework have to be developed: from the syntax to the semantics, including the management of such generalized knowledge representation. In this work we traverse all these issues in the framework of formal concept analysis, introducing a new set of inference rules to manage mixed (positive and negative) attributes.TIN2014-59471-P of the Science and Innovation Ministry of Spain, co-funded by the European Regional Development Fund (ERDF). UNIVERSIDAD DE MÁLAGA. Campus de Excelencia Internacional Andalucía Tech

A generalized framework to consider positive and negative attributes in formal concept analysis

In Formal Concept Analysis the classical formal context is analized taking into account only the positive information, i.e. the presence of a property in an object. Nevertheless, the no presence of a property in an object also provides a signi cant knowledge which can only be partially considered with the classical approach. In this work we have modi ed the concept forming operators to allow the treatment of both, positive and negative attributes which come from respectively, the presence and absence of the properties. In this work we de ne the new operators and we prove that they are Galois connections. Finally, we have also studied the correspondence between the formal context in the new framework and the extended concept lattice, providing new interesting properties.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Interpretation of Fuzzy Attribute Subsets in Generalized One-Sided Concept Lattices

In this paper we describe possible interpretation and reduction of fuzzy attributes in Generalized One-sided Concept Lattices (GOSCL). This type of concept lattices represent generalization of Formal Concept Analysis (FCA) suitable for analysis of datatables with different types of attributes. FCA as well as generalized one-sided concept lattices represent conceptual data miningmethods. With growing number of attributes the interpretation of fuzzy subsets may become unclear, hence another interpretation of this fuzzy attribute subsets can be valuable. The originality of the presented method is based on the usage of one-sided concept lattices derived from submodels of former object-attribute model by grouping attributes with the same truth value structure. This leads to new method for attribute reduction in GOSCL environment

Метод формального умножения гиперфункций и его приложение

THE FORMAL MULTIPLICATION OF HYPERFUNCTIONS AND ITS APPLICATIONS. T. URBANOVICH, S. BELYAI.Представлен исторический обзор развития теории обобщенных функций и сравнительный анализ различных подходов к обобщению понятия функции. Рассматриваются гиперфункции Сато как обобщение понятия функции. Анализируется проблема умножения обобщённых функций. Рассматривается проблема умножения гиперфункций. Методом формального умножения гиперфункций решается краевая задача о скачке со степенной правой частью. = The article contains a historical survey of the development of the generalized functions theory and the comparative analysis of different approaches to the generalization of the concept of function. Sato’s hyperfunctions are viewed as generalization of the concept of function. The problem of generalized functions multiplication is considered. The problem of hyperfunctions multiplication is considered. The jump boundary value problem with the power right-hand side is solved by the method of the formal multiplication of hyperfunctions

Gene Expressio Array Exploration Using K-Formal Concept Analysis

Proceeding of: 9th International Conference, ICFCA 2011, Nicosia, Cyprus, May 2-6, 2011.DNA micro-arrays are a mechanism for eliciting gene expression values, the concentration of the transcription products of a set of genes, under different chemical conditions. The phenomena of interest—up-regulation, down-regulation and co-regulation—are hypothesized to stem from the functional relationships among transcription products. In [1,2,3] a generalisation of Formal Concept Analysis was developed with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the usual Boolean carrier set. In this paper, we use (Rmin+)- and (Rmax+) to analyse gene expression data for Arabidopsis thaliana. We introduce the mechanism to render the data in the appropriate algebra and profit by the wealth of different Galois Connections available in Generalized Formal Concept Analysis to carry different analysis for up- and down-regulated genes.Spanish Government-Comision Interministerial de Ciencia y Tecnología projects 2008-06382/TEC and 2008-02473/TEC and the regional projects S-505/TIC/0223 (DGUI-CM) and CCG08-UC3M/TIC- 4457 (Comunidad Aut onoma de Madrid - UC3M)