Francisco J. Valverde-Albacete

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• Doctor of Engineering
• Associate Professor at Rey Juan Carlos University

Multilabel classification is a recently conceptualized task in machine learning. Contrary to most of the research that has so far focused on classification machinery, we take a data-centric approach and provide an integrative framework that blends qualitative and quantitative descriptions of multilabel data sources. By combining lattice theory, in...

In this paper we provide an embedding of finite lattices into \((\mathbb N, \mid )\), the lattice of divisibility of natural numbers. For that purpose, we explore two representations: vector clocks, a device to provide a virtual time used in distributed systems that has gained traction as a finite lattice representation, and the log-prime function...

In this chapter we hypotesize that Information Semifields are the underlying calculi that brains operate on and we postulate that strong artificial intelligences should try to imitate them. Information semifields have recently been proposed to describe the calculations that pertain to the manipulation of Renyi entropies. These are semifields that e...

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...

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...

We set out to demonstrate that the Rényi entropies are better thought of as operating in a type of non-linear semiring called a positive semifield. We show how the Rényi’s postulates lead to Pap’s g-calculus where the functions carrying out the domain transformation are Rényi’s information function and its inverse. In its turn, Pap’s g-calculus und...

We introduce a framework for the evaluation of multiclass classifiers by exploring their confusion matrices. Instead of using error-counting measures of performance, we concentrate in quantifying the information transfer from true to estimated labels using information-theoretic measures. First, the Entropy Triangle allows us to visualize the balanc...

We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quantities close to it, like the information potential...

We introduce a variant of the R\'enyi entropy definition that aligns it with the well-known H\"older mean: in the new formulation, the r-th order R\'enyi Entropy is the logarithm of the inverse of the r-th order H\"older mean. This brings about new insights into the relationship of the R\'enyi entropy to quantities close to it, like the information...

We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quantities close to it, like the information potential...

We report on progress in characterizing K-valued FCA in algebraic terms, where K is an idempotent semifield. In this data mining-inspired approach, incidences are matrices and sets of objects and attributes are vectors. The algebraization allows us to write matrix-calculus formulae describing the polars and the fixpoint equations for extents and in...

Data transformation, e.g., feature transformation and selection, is an integral part of any machine learning procedure. In this paper, we introduce an information-theoretic model and tools to assess the quality of data transformations in machine learning tasks. In an unsupervised fashion, we analyze the transformation of a discrete, multivariate so...

In this paper we present a new technique for the analysis of data tables by means of Formal Independence Analysis (FIA). This is an analogue of Formal Concept Analysis for the study of independence relations in data, instead of hierarchical relations. A FIA of a context produces, when possible, its block diagonalization by detecting pairs of sets o...

In this paper we use information-theoretic measures to provide a theory and tools to analyze the flow of information from a discrete, multivariate source of information $\overline X$ to a discrete, multivariate sink of information $\overline Y$ joined by a distribution $P_{\overline X \overline Y}$. The first contribution is a decomposition of the...

In this paper we try to analyse the dual-projection approach to weighted 2-mode networks using the tools of\(\mathcal{K}\)-Formal Concept Analysis (\(\mathcal{K}\)-FCA), an extension of FCA for incidences with values in a particular kind of semiring.

We set out to demonstrate that the R\'enyi entropies with parameter $\alpha$ are better thought of as operating in a type of non-linear semiring called a positive semifield. We show how the R\'enyi's postulates lead to Pap's g-calculus where the functions carrying out the domain transformation are Renyi's information function and its inverse. In it...

We report on progress relating \(\mathcal K\)-valued FCA to \(\mathcal K\)-Linear Algebra where \(\mathcal K\) is an idempotent semifield. We first find that the standard machinery of linear algebra points to Galois adjunctions as the preferred construction, which generates either Neighbourhood Lattices of attributes or objects. For the Neighbourho...

We introduce from first principles an analysis of the information content of multivariate distributions as information sources. Specifically, we generalize a balance equation and a visualization device, the Entropy Triangle, for multivariate distributions and find notable differences with similar analyses done on joint distributions as models of in...

Background: Gene 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....

In this paper we try to extend the Galois connection construction of \(\mathcal K\)-Formal Concept Analysis to handle semifields which are not idempotent. Important examples of such algebras are the extended non-negative reals and the extended non-negative rationals, but we provide a construction that suggests that such semifields are much more abu...

We extend a framework for the analysis of classifiers to encompass also the analysis of data sets. Specifically, we generalize a balance equation and a visualization device, the Entropy Triangle, for multivariate distributions, not only bivariate ones. With such tools we analyze a handful of UCI machine learning task to start addressing the questio...

http://www.tandfonline.com/eprint/zjUGqQHW2mIrKR4pGnMC/full

In this paper, we present advances in the modeling of the masking behavior of the human auditory system (HAS) to enhance the robustness of the feature extraction stage in automatic speech recognition (ASR). The solution adopted is based on a nonlinear filtering of a spectro-temporal representation applied simultaneously to both frequency and time d...

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 mo...

A perceptually motivated feature extraction method based on mimicking the masking properties of the cochlea has been recently found to provide enhanced performance when applied to conventional speech recognition back-ends. On the other hand, the introduction of Deep Neural Network (DNN) based acoustic models has produced dramatic improvements in pe...

We report on progress in characterizing K-valued FCA in algebraic terms, where K is an idempotent semifield. In this data mininginspired approach, incidences are matrices and sets of objects and attributes are vectors. The algebraization allows us to write matrixcalculus formulae describing the polars and the fixpoint equations for extents and inte...

This paper deals with the relation between fuzzy implications and Galois connections, trying to raise the awareness that the fuzzy implications are indispensable to generalise Formal Concept Analysis. The concrete goal of the paper is to make evident that Galois connections, which are at the heart of some of the generalizations of Formal Concept An...

Motivated by some spectral results in the characterization of concept lattices we investigate the spectra of reducible matrices over complete idempotent semifields in the framework of naturally-ordered semirings, or dioids. We find non-null eigenvectors for every non-null element in the semifield and conclude that the notion of spectrum has to be r...

In this paper we present advances in the modeling of the masking behavior of the Human Auditory System to enhance the robustness of the feature extraction stage in Automatic Speech Recognition. The solution adopted is based on a non-linear filtering of a spectro-temporal representation applied simultaneously on both the frequency and time domains,...

The most widely spread measure of performance, accuracy, suffers from a paradox: predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. Despite optimizing classification error rate, high accuracy models may fail to capture crucial information transfer in the classification task. We prese...

New auditory-inspired speech processing methods are presented in this paper, combining spectral subtraction and two-dimensional non-linear filtering techniques originally conceived for image processing purposes. In particular, mathematical morphology operations, like erosion and dilation, are applied to noisy speech spectrograms using specifically...

Previous work has shown a relation between L-valued extensions of Formal Concept Analysis and the spectra of some matrices related to L-valued contexts. To clarify this relation, we investigated elsewhere the nature of the spectra of irreducible matrices over idempotent semifields in the framework of dioids, naturally ordered semirings, that encomp...

The implementation of the entropy triangle stemming from the 2011 paper and used for several other papers until 2014.

In this paper we propound the use of a number of entropy-based metrics and a visualization tool for the intrinsic evaluation of Sentiment and Reputation Analysis tasks. We provide a theoretical justification for their use and discuss how they complement other accuracy-based metrics. We apply the proposed techniques to the analysis of TASS-SEPLN and...

Previous work has shown a relation between L-valued extensions of FCA and the spectra of some matrices related to L-valued contexts. We investigate the spectra of reducible matrices over completed idempotent semifields in the framework of dioids, naturally-ordered semirings, that encompass several of those extensions. Considering special sets of ei...

We review previous work using Formal Concept Analysis (FCA) to build Information Retrieval (IR) applications seeking a wider adoption of the FCA paradigm in IR. We conclude that although a number of systems have been built with such paradigm (FCA in IR), the most effective contribution would be to help establish IR on firmer grounds (FCA for IR). S...

In this paper we introduce a Web-based tool for the analysis of Genomic Expression (GE) data based in K-Formal Concept Analysis (KFCA). First we present the task of analysing GE data and then we describe the tool implementing KFCA. As a second contribution, we present a mechanism to visualise a sequence of concept lattices by fixing the intents aga...

We assess the behaviour of 5 different feature extraction methods for an acoustic event classification task - built using the same SVM underlying technology - by means of two different techniques: accuracy and the entropy triangle. The entropy triangle is able to find a classifier instance whose relatively high accuracy stems from an attempt to spe...

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...

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]...

We develop two tools to analyze the behavior of multiple-class, or multi-class, classifiers by means of entropic measures on their confusion matrix or contingency table. First we obtain a balance equation on the entropies that captures interesting properties of the classifier. Second, by normalizing this balance equation we first obtain a 2-simplex...

Confusion matrices have been used as a tool for the analysis of speech perception or human speech recognition (HSR) for decades. However, they are rarely employed in automatic speech recognition (ASR) mainly due to the lack of a systematic procedure for their exploration. The generalization of formal concept analysis employed in this paper provides...

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 reali...

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 t...

In this paper we have used Formal Concept Analysis to elicit a hierarchical structure of human consonant perception task errors. We have used the Native Listeners experiments provided for the Consonant Challenge session of Interspeech 2008 to analyze perception errors comitted in relation to the place of articulation of the consonants being evaluat...

In this article, we introduce a new representation based on lattice theory for lexical data from a lexical-database embodying the frame-semantic approach to language description, FrameNet. We present proof of the abundance of Concept Lattices as proposed in Formal Concept Analysis both in the theory of frames and in its present-day incarnation, the...

In [13] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, -Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. Subsequently, the structural lattice of such generalised contexts was introduced in [15], to provide a limited eq...

In [1] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K\mathcal K -Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. A fundamental result was missing there, namely the second half of the equivalent of the main theorem...

In [14] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. The construction leading to the pair of dually (order) isomorphic lattices can be further manipulated to obtain...

In this chapter we present a formal model that provides an analysis of the batch retrieval phase of a Web retrieval interaction or any other batch retrieval task by decomposing it into three subproblems: first, given a perfect relevance relation in representation space find a system that implements it; second, transform query and document represent...

We introduce in this paper a new experimental design for the supervised clustering of retrieval results to replace rankings. The technique is a mixture of soft and hard techniques built on top of Formal Concept Analysis and a generalisation of the fuzzy semiring, idempotent reflexive semirings. We present first results as to the theoretical design...

In this paper we justify the need for a generalisation of For- mal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstract- ing the Boolean algebra and the notion of extents and intents, respec- ti...

In this chapter we present a formal model that provides an analysis of the batch retrieval phase of a Web retrieval interaction or any other batch retrieval task by decomposing it into three subproblems: first, given a perfect relevance relation in representation space find a system that implements it; second, transform query and document represent...

This paper reports on ongoing work to use Formal Concept Analysis as an auxiliary tool in understanding and visualising the wealth of data produced by lexical-resource building as embodied in the construction of FrameNet, a database to capture the syntax and semantics of language use in Frame Linguistics. We present proof of the abundance of concep...

Los procesos de toma de decisión han alcanzado un gran desarrollo en el entorno Web, en particular en la recuperación de información y el comercio electrónico. No obstante, la carencia de un modelo de datos bien definido en la misma ha traído consigo problemas de difícil solución. En este trabajo enunciamos algunos de estos problemas, y describimos...

The paper deals with personalization of navigation in the educational content, introduced in a competence-based instructional design system InterMediActor. The system constructs an individualized navigation graph for each student and thus suggests the learning objectives the student is most prepared to attain. The navigation tools rely on the graph...

This paper describes a failure alert system and a methodology for content reuse in a new instructional design system called InterMediActor (IMA). IMA provides an environment for instructional content design, production and reuse, and for students’ evaluation based in content specification through a hierarchical structure of competences. The student...

The paper presents a competence-based instructional design system and a way to provide a personalization of navigation in the course content. The navigation aid tool builds on the competence graph and the student model, which includes the elements of uncertainty in the assessment of students. An individualized navigation graph is constructed for ea...

This paper describes the basic architecture and functional principles of a new instructional design system called InterMediActor (IMA) and reports about its implementation state. IMA provides an environment for instructional content design, production and reuse and for student evaluation that is based on the decomposition of the learning objectives...

This paper describes the basic architecture and functional principles of a new instructional design system called InterMediActor (IMA). IMA provides an environment for instructional content design, production and reuse and student evaluation that is based on the decomposition of the learning objectives in a hierarchical structure of competences. Th...

The paper presents a competence-based instructional design system and a way to provide a personalization of navigation in the course content. The navigation aid tool builds on the competence graph and the student model, which includes the elements of uncertainty in the assessment of students. An individualized navigation graph is constructed for ea...

In this paper we introduce a user profile exchange mechanism, called barter or trading without money, that does not make use of countable resources in a dynamic information retrieval environment. We consider a network of inter-connected users, who behave both as information consumers and producers, within a multi-agent system which operates in a pe...

In this paper we introduce one application layer for information processing in the DIET platform, a MAS development platform. This application layer is basically formed of three types of agents, here called "infocytes", designed to cater for the information needs of information providers, requesters and brokers. We have also defined and implemented...

Computer based training or distance education are facing dramatic changes with the advent of standardization efforts, some of them concentrating in maximal reuse. This is of paramount importance for a sustainable -cost affordable- production of educational materials. Reuse in itself should not be a goal, though, since many methodological aspects mi...

We have extended our previous research on a new approach to automatic speech recognition (ASR) in the GSM environment. Instead of recognizing from the decoded speech signal, our system works from the digital speech representation used by the GSM encoder. We have compared the performance of a conventional system and the one we propose on a speaker i...

We present a continuous speech recognition architecture with a tightly coupled language model that tries to improve the dwindling performance of the normal stack decoder with increasing lexicon size. We solve the problem of recognition by means of two mutually recursive functions. The first one uses an auxiliary retrieval function to obtain lexical...

http://www.tsc.uc3m.es/~carmen/KFCADemo.html