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

Estudio de un sistema de reconocimiento biométrico mediante firma manuscrita online basado en SVM usando Análisis Formal de Conceptos

10 pages, 8 figures.-- Contributed to: V Jornadas de Reconocimiento Biométrico de Personas (JRBP 2010, Huesca, Spain, Sep 2-3, 2010).En el presente artículo se pretende estudiar las prestaciones de un sistema de reconocimiento biométrico mediante firma manuscrita usando la teoría de Análisis Formal de Conceptos (FCA). Se usará la modalidad online de la firma manuscrita, con un algoritmo basado en Máquinas de Vectores Soporte (SVM). Para analizar el desempeño del sistema se realizará un estudio de su matriz de confusión usando el Análisis de Conceptos Formales, y se procederá a extraer conclusiones sobre el sistema.Publicad

On Concept Lattices as Information Channels

Proceedings of: 11th International Conference on Concept Lattices and Their Applications (CLA 2014). Kosice, Slovakia, October 07-10, 2014.This paper explores the idea that a concept lattice is an information channel between objects and attributes. For this purpose we study the behaviour of incidences in L-formal contexts where L is the range of an information-theoretic entropy function. Examples of such data abound in machine learning and data mining, e.g. confusion matrices of multi-class classifers or document-term matrices. We use a wellmotivated information-theoretic heuristic, the maximization of mutual information, that in our conclusions provides a favour of feature selection providing and information-theory explanation of an established practice in Data Mining, Natural Language Processing and Information Retrieval applications, viz. stop-wording and frequency thresholding. We also introduce a post-clustering class identi cation in the presence of confusions and a favour of term selection for a multi-label document classifcation task.FJVA and AP are supported by EU FP7 project LiMoSINe (contract 288024) for this work. CPM has been supported by the Spanish Government-Comisión Interministerial de Ciencia y Tecnología project TEC2011-26807.Publicad

Software Evolution Understanding: Automatic Extraction of Software Identifiers Map for Object-Oriented Software Systems

Software companies usually develop a set of product variants within the same family that share certain functions and differ in others. Variations across software variants occur to meet different customer requirements. Thus, software product variants evolve overtime to cope with new requirements. A software engineer who deals with this family may find it difficult to understand the evolution scenarios that have taken place over time. In addition, software identifier names are important resources to understand the evolution scenarios in this family. This paper introduces an automatic approach called Juana’s approach to detect the evolution scenario across two product variants at the source code level and identifies the common and unique software identifier names across software variants source code. Juana’s approach refers to common and unique identifier names as a software identifiers map and computes it by comparing software variants to each other. Juana considers all software identifier names such as package, class, attribute, and method. The novelty of this approach is that it exploits common and unique identifier names across the source code of software variants, to understand the evolution scenarios across software family in an efficient way. For validity, Juana was applied on ArgoUML and Mobile Media software variants. The results of this evaluation validate the relevance and the performance of the approach as all evolution scenarios were correctly detected via a software identifiers map

Construction d'une ontologie à partir d'un corpus de textes avec l'ACF

National audienceNous présentons dans cet article une méthodologie semi-automatique de construction d'ontologie à partir de corpus de textes sur un domaine spécifique. Cette méthodologie repose en premier lieu sur la classification d'objets d'après les propriétés qu'ils partagent, en utilisant l'analyse de concepts formels (ACF) pour la construction d'un treillis de concepts. Ce treillis va servir à construire un noyau d'ontologie. Cependant, les objets sont aussi définis par les relations qu'ils entretiennent entre eux. Donc, en second lieu, nous proposons une méthode originale qui enrichit cette ontologie avec des relations transversales en utilisant une nouvelle méthode : l'analyse relationnelle de concepts (ARC). Chaque concept de l'ontologie résultante est défini puis représenté en Logique de Descriptions (LDs). Le domaine d'application de cette méthodologie est le domaine de l'astronomie

Four-fold Formal Concept Analysis based on Complete Idempotent Semifields

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

The Singular Value Decomposition over Completed Idempotent Semifields

In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD). These algebras are already complete lattices and many of their instances—the complete schedule algebra or completed max-plus semifield, the tropical algebra, and the max-times algebra—are useful in a range of applications, e.g., morphological processing. We further the task of eliciting the relation between i-SVD and the extension of Formal Concept Analysis to complete idempotent semifields (K-FCA) started in a prior work. We find out that for a matrix with entries considered in a complete idempotent semifield, the Galois connection at the heart of K-FCA provides two basis of left- and right-singular vectors to choose from, for reconstructing the matrix. These are join-dense or meet-dense sets of object or attribute concepts of the concept lattice created by the connection, and they are almost surely not pairwise orthogonal. We conclude with an attempt analogue of the fundamental theorem of linear algebra that gathers all results and discuss it in the wider setting of matrix factorization.This research was funded by the Spanish Government-MinECo project TEC2017-84395-P and the Dept. of Research and Innovation of Madrid Regional Authority project EMPATIA-CM (Y2018/TCS-5046)

Extending Conceptualisation Modes for Generalised Formal Concept Analysis

Formal Concept Analysis (FCA) is an exploratory data analysis technique for boolean relations based on lattice theory. Its main result is the existence of a dual order isomorphism between two set lattices induced by a binary relation between a set of objects and a set of attributes. Pairs of dually isomorphic sets of objects and attributes, called formal concepts, form a concept lattice, but actually model only a conjunctive mode of conceptualisation. In this paper we augment this formalism in two ways: first we extend FCA to consider different modes of conceptualisation by changing the basic dual isomorphism in a modal-logic motivated way. This creates the three new types of concepts and lattices of extended FCA, viz., the lattice of neighbourhood of objects, that of attributes and the lattice of unrelatedness. Second, we consider incidences with values in idempotent semirings—concretely the completed max-plus or schedule algebra View the MathML source—and focus on generalising FCA to try and replicate the modes of conceptualisation mentioned above. To provide a concrete example of the use of these techniques, we analyse the performance of multi-class classifiers by conceptually analysing their confusion matrices.Spanish Government-Comisión Interministerial de Ciencia y Tecnología project 2008–06382/TEC and 2008–02473/TEC and the regional project (Comunidad Autónoma de Madrid – UC3M) CCG08-UC3M/TIC-4457Publicad

Efficient Axiomatization of OWL 2 EL Ontologies from Data by means of Formal Concept Analysis: (Extended Version)

We present an FCA-based axiomatization method that produces a complete EL TBox (the terminological part of an OWL 2 EL ontology) from a graph dataset in at most exponential time. We describe technical details that allow for efficient implementation as well as variations that dispense with the computation of extremely large axioms, thereby rendering the approach applicable albeit some completeness is lost. Moreover, we evaluate the prototype on real-world datasets.This is an extended version of an article accepted at AAAI 2024