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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 (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 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.
Francisco José Valverde-Albacete; Carmen Peláez-Moreno. Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields. Mathematics 2021, 9, 173 .
AMA StyleFrancisco José Valverde-Albacete, Carmen Peláez-Moreno. Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields. Mathematics. 2021; 9 (2):173.
Chicago/Turabian StyleFrancisco José Valverde-Albacete; Carmen Peláez-Moreno. 2021. "Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields." Mathematics 9, no. 2: 173.
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.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. The Singular Value Decomposition over Completed Idempotent Semifields. Mathematics 2020, 8, 1577 .
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. The Singular Value Decomposition over Completed Idempotent Semifields. Mathematics. 2020; 8 (9):1577.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2020. "The Singular Value Decomposition over Completed Idempotent Semifields." Mathematics 8, no. 9: 1577.
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 under Rényi’s information function transforms the set of positive reals into a family of semirings where “standard” product has been transformed into sum and “standard” sum into a power-emphasized sum. Consequently, the transformed product has an inverse whence the structure is actually that of a positive semifield. Instances of this construction lead to idempotent analysis and tropical algebra as well as to less exotic structures. We conjecture that this is one of the reasons why tropical algebra procedures, like the Viterbi algorithm of dynamic programming, morphological processing, or neural networks are so successful in computational intelligence applications. But also, why there seem to exist so many computational intelligence procedures to deal with “information” at large.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. The Rényi Entropies Operate in Positive Semifields. Entropy 2019, 21, 780 .
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. The Rényi Entropies Operate in Positive Semifields. Entropy. 2019; 21 (8):780.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2019. "The Rényi Entropies Operate in Positive Semifields." Entropy 21, no. 8: 780.
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 balance of mutual information, variation of information and the deviation from uniformity in the true and estimated label distributions. Next the Entropy-Modified Accuracy allows us to rank classifiers by performance while the Normalized Information Transfer rate allows us to evaluate classifiers by the amount of information accrued during learning. Finally, if the question rises to elucidate which errors are systematically committed by the classifier, we use a generalization of Formal Concept Analysis to elicit such knowledge. All such techniques can be applied either to artificially or biologically embodied classifiers---e.g. human performance on perceptual tasks. We instantiate the framework in a number of examples to provide guidelines for the use of these tools in the case of assessing single classifiers or populations of them---whether induced with the same technique or not---either on single tasks or in a set of them. These include UCI tasks and the more complex KDD cup 99 competition on Intrusion Detection.
Francisco J. Valverde-Albacete; Carmen Pelaez-Moreno. A Framework for Supervised Classification Performance Analysis with Information-Theoretic Methods. IEEE Transactions on Knowledge and Data Engineering 2019, 32, 2075 -2087.
AMA StyleFrancisco J. Valverde-Albacete, Carmen Pelaez-Moreno. A Framework for Supervised Classification Performance Analysis with Information-Theoretic Methods. IEEE Transactions on Knowledge and Data Engineering. 2019; 32 (11):2075-2087.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Pelaez-Moreno. 2019. "A Framework for Supervised Classification Performance Analysis with Information-Theoretic Methods." IEEE Transactions on Knowledge and Data Engineering 32, no. 11: 2075-2087.
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 and the partition function of statistical mechanics. We also provide expressions that allow us to calculate the Rényi entropies from the Shannon cross-entropy and the escort probabilities. Finally, we discuss why shifting the Rényi entropy is fruitful in some applications.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. The Case for Shifting the Renyi Entropy. Entropy 2019, 21, 46 .
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. The Case for Shifting the Renyi Entropy. Entropy. 2019; 21 (1):46.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2019. "The Case for Shifting the Renyi Entropy." Entropy 21, no. 1: 46.
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 intents. Adopting also the point of view of the theory of linear operators between vector spaces we explore the similarities and differences of the idempotent semimodules of extents and intents with the subspaces related to a linear operator in standard algebra. This allows us to shed some light into Formal Concept Analysisfrom the point of view of the theory of linear operators over idempotent semimodules. In the opposite direction, we state the importance of FCA-related concepts for dual order homomorphisms of linear spaces over idempotent semifields, specially congruences, the lattices of extents, intents and formal concepts.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. K-Formal Concept Analysis as linear algebra over idempotent semifields. Information Sciences 2018, 467, 579 -603.
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. K-Formal Concept Analysis as linear algebra over idempotent semifields. Information Sciences. 2018; 467 ():579-603.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2018. "K-Formal Concept Analysis as linear algebra over idempotent semifields." Information Sciences 467, no. : 579-603.
In this paper we investigate into analogue of a Singular Value Decomposition for rectangular matrices over a complete idempotent semifields (i-SVD), many of whose 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. We carry on further the task of eliciting the relation between i-SVD and the extension of Formal Concept Analysis to complete idempotent semifields ($\mathcal{K}$-FCA) started in prior work. We find out that for each relation with entries considered in a complete idempotent semifield, for each of the four types of Galois connections defined by the relation, there are two basis of left- and right-singular vectors to choose from for reconstructing the matrix. These are each of the join-dense or meet-dense sets object or attribute concepts of the concept lattice created by the connection. We suggest why these can never form an orthonormal basis, and refer to prior art describing the spectral lattices of such matrices for meaningful representations in the idempotent settings.
Francisco J. Valverde-Albacete; Carmen Pelaez-Moreno. On the Relation between Semifield-Valued FCA and the Idempotent Singular Value Decomposition. 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) 2018, 1 -8.
AMA StyleFrancisco J. Valverde-Albacete, Carmen Pelaez-Moreno. On the Relation between Semifield-Valued FCA and the Idempotent Singular Value Decomposition. 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). 2018; ():1-8.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Pelaez-Moreno. 2018. "On the Relation between Semifield-Valued FCA and the Idempotent Singular Value Decomposition." 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) , no. : 1-8.
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 source of information X¯ into a discrete, multivariate sink of information Y¯ related by a distribution PX¯Y¯. The first contribution is a decomposition of the maximal potential entropy of (X¯,Y¯), which we call a balance equation, into its (a) non-transferable, (b) transferable, but not transferred, and (c) transferred parts. Such balance equations can be represented in (de Finetti) entropy diagrams, our second set of contributions. The most important of these, the aggregate channel multivariate entropy triangle, is a visual exploratory tool to assess the effectiveness of multivariate data transformations in transferring information from input to output variables. We also show how these decomposition and balance equations also apply to the entropies of X¯ and Y¯, respectively, and generate entropy triangles for them. As an example, we present the application of these tools to the assessment of information transfer efficiency for Principal Component Analysis and Independent Component Analysis as unsupervised feature transformation and selection procedures in supervised classification tasks.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle. Entropy 2018, 20, 498 .
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle. Entropy. 2018; 20 (7):498.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2018. "Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle." Entropy 20, no. 7: 498.
In this paper we propose a new lens through which to observe the information contained in a formal context. Instead of focusing on the hierarchical relation between objects or attributes induced by their incidence, we focus on the “unrelatedness” of the objects with respect to those attributes with which they are not incident. The crucial order concept for this is that of maximal anti-chain and the corresponding representation capabilities are provided by Behrendt’s theorem. With these tools we introduce the fundamental theorem of Formal Independence Analysis and use it to provide an example of what its affordances are for the analysis of data tables. We also discuss its relation to Formal Concept Analysis.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno; Inma P. Cabrera; Pablo Cordero; Manuel Ojeda-Aciego. Formal Independence Analysis. Programmieren für Ingenieure und Naturwissenschaftler 2018, 596 -608.
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno, Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego. Formal Independence Analysis. Programmieren für Ingenieure und Naturwissenschaftler. 2018; ():596-608.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno; Inma P. Cabrera; Pablo Cordero; Manuel Ojeda-Aciego. 2018. "Formal Independence Analysis." Programmieren für Ingenieure und Naturwissenschaftler , no. : 596-608.
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 maximal potential entropy of $(\overline X, \overline Y)$ that we call a balance equation, that can also be split into decompositions for the entropies of $\overline X$ and $\overline Y$ respectively. Such balance equations accept normalizations that allow them to be represented in de Finetti entropy diagrams, our second contribution. The most important of these, the aggregate Channel Multivariate Entropy Triangle CMET is an exploratory tool to assess the efficiency of multivariate channels. We also present a practical contribution in the application of these balance equations and diagrams to the assessment of information transfer efficiency for PCA and ICA as feature transformation and selection procedures in machine learning applications.
Francisco J. Valverde-Albacete; Carmen Pelaez-Moreno. The Channel Multivariate Entropy Triangle and Balance Equation. 2017, 1 .
AMA StyleFrancisco J. Valverde-Albacete, Carmen Pelaez-Moreno. The Channel Multivariate Entropy Triangle and Balance Equation. . 2017; ():1.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Pelaez-Moreno. 2017. "The Channel Multivariate Entropy Triangle and Balance Equation." , no. : 1.
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. For this purpose, we first revisit the isomorphisms between 2-mode networks with formal contexts. In the quest for similar relations when the networks have non-Boolean weights, we relate the dual-projection method to both the Singular Value Decomposition and the Eigenvalue Problem of matrices with values in such algebras, as embodied in Kleinberg’s Hubs and Authorities (HITS) algorithm. To recover a relation with multi-valued extensions of FCA, we introduce extensions of the HITS algorithm to calculate the influence of nodes in a network whose adjacency matrix takes values over dioids, zerosumfree semirings with a natural order. In this way, we show the original HITS algorithm to be a particular instance of the generic construction, but also the advantages of working in idempotent semifields, instances of dioids. Subsequently, we also make some connections with extended\(\mathcal{K}\)-FCA, where the particular kind of dioid is an idempotent semifield, and provide theoretical reasoning and evidence that the type of knowledge extracted from a matrix by one procedure and the other are different.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. A Formal Concept Analysis Look at the Analysis of Affiliation Networks. Lecture Notes in Social Networks 2017, 171 -195.
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. A Formal Concept Analysis Look at the Analysis of Affiliation Networks. Lecture Notes in Social Networks. 2017; ():171-195.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2017. "A Formal Concept Analysis Look at the Analysis of Affiliation Networks." Lecture Notes in Social Networks , no. : 171-195.
We provide crucial insights into a recently proposed Shannon-type entropy balance equation for multivariate joint distributions.The decomposition can be plotted in an entropy ternary diagram.Each axis of the ternary diagram provides specific information about the distributions.We use both tools in the exploratory analysis of machine learning datasets.These tools are applicable to supervised and unsupervised tasks. 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 information channels.As an example application, we extend a framework for the analysis of classifiers to also encompass the analysis of data sets. With such tools we analyze a handful of UCI machine learning task to start addressing the question of how well do datasets convey the information they are supposed to capture about the phenomena they stand for.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. The evaluation of data sources using multivariate entropy tools. Expert Systems with Applications 2017, 78, 145 -157.
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. The evaluation of data sources using multivariate entropy tools. Expert Systems with Applications. 2017; 78 ():145-157.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2017. "The evaluation of data sources using multivariate entropy tools." Expert Systems with Applications 78, no. : 145-157.
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 Neighbourhood of objects we provide the adjoints, their respective closure and interior operators and the general structure of the lattices, both of objects and attributes. Next, these results and those previous on Galois connections are set against the backdrop of Extended Formal Concept Analysis. Our results show that for a \(\mathcal K\)-valued formal context (G, M, R)—where \(|G| = g\), \(|M| = m\) and \(R \in K^{g\times {m}}\)—there are only two different “shapes” of lattices each of which comes in four different “colours”, suggesting a notion of a 4-concept associated to a formal concept. Finally, we draw some conclusions as to the use of these as data exploration constructs, allowing many different “readings” on the contextualized data.
Francisco José Valverde-Albacete; Carmen Peláez-Moreno. The Linear Algebra in Extended Formal Concept Analysis Over Idempotent Semifields. Transactions on Petri Nets and Other Models of Concurrency XV 2017, 10308, 211 -227.
AMA StyleFrancisco José Valverde-Albacete, Carmen Peláez-Moreno. The Linear Algebra in Extended Formal Concept Analysis Over Idempotent Semifields. Transactions on Petri Nets and Other Models of Concurrency XV. 2017; 10308 ():211-227.
Chicago/Turabian StyleFrancisco José Valverde-Albacete; Carmen Peláez-Moreno. 2017. "The Linear Algebra in Extended Formal Concept Analysis Over Idempotent Semifields." Transactions on Petri Nets and Other Models of Concurrency XV 10308, no. : 211-227.
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. This is often addressed by means of Gene Set Enrichment Analysis (GSEA). We 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 [Formula: see text]-Formal Concept Analysis ([Formula: see text]-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. The 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.
Jose M González-Calabozo; Francisco J Valverde-Albacete; Carmen Peláez-Moreno. Interactive knowledge discovery and data mining on genomic expression data with numeric formal concept analysis. BMC Bioinformatics 2016, 17, 374 .
AMA StyleJose M González-Calabozo, Francisco J Valverde-Albacete, Carmen Peláez-Moreno. Interactive knowledge discovery and data mining on genomic expression data with numeric formal concept analysis. BMC Bioinformatics. 2016; 17 (1):374.
Chicago/Turabian StyleJose M González-Calabozo; Francisco J Valverde-Albacete; Carmen Peláez-Moreno. 2016. "Interactive knowledge discovery and data mining on genomic expression data with numeric formal concept analysis." BMC Bioinformatics 17, no. 1: 374.
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 question of how information gets transformed through machine learning classification tasks.
Francisco José Valverde-Albacete; Carmen Peláez-Moreno. The Multivariate Entropy Triangle and Applications. Algorithms and Data Structures 2016, 647 -658.
AMA StyleFrancisco José Valverde-Albacete, Carmen Peláez-Moreno. The Multivariate Entropy Triangle and Applications. Algorithms and Data Structures. 2016; ():647-658.
Chicago/Turabian StyleFrancisco José Valverde-Albacete; Carmen Peláez-Moreno. 2016. "The Multivariate Entropy Triangle and Applications." Algorithms and Data Structures , no. : 647-658.
We present a methodology for scientific enquiry based in Formal Concept Analysis.We adopt the \"Landscapes of Knowledge\" metaphor for Exploratory Data Analysis.We provide use cases to demonstrate the affordances of the methodology.The use cases encompass gene expression data and classifier assessment.The use cases also include abstract algebra and information extraction and indexing. 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.
Francisco J. Valverde-Albacete; José María González-Calabozo; Anselmo Peñas; Carmen Peláez-Moreno. Supporting scientific knowledge discovery with extended, generalized Formal Concept Analysis. Expert Systems with Applications 2016, 44, 198 -216.
AMA StyleFrancisco J. Valverde-Albacete, José María González-Calabozo, Anselmo Peñas, Carmen Peláez-Moreno. Supporting scientific knowledge discovery with extended, generalized Formal Concept Analysis. Expert Systems with Applications. 2016; 44 ():198-216.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; José María González-Calabozo; Anselmo Peñas; Carmen Peláez-Moreno. 2016. "Supporting scientific knowledge discovery with extended, generalized Formal Concept Analysis." Expert Systems with Applications 44, no. : 198-216.
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 domains - as if it were an image - using mathematical morphology operations. A particularly important component of this architecture is the so-called structuring element (SE) that in the present contribution is designed as a single three-dimensional pattern using physiological facts, in such a way that closely resembles the masking phenomena taking place in the cochlea. A proper choice of spectro-temporal representation lends validity to the model throughout the whole frequency spectrum and intensity spans assuming the variability of the masking properties of the HAS in these two domains. The best results were achieved with the representation introduced as part of the power normalized cepstral coefficients (PNCC) together with a spectral subtraction step. This method has been tested on Aurora 2, Wall Street Journal and ISOLET databases including both classical hidden Markov model (HMM) and hybrid artificial neural networks (ANN)-HMM back-ends. In these, the proposed front-end analysis provides substantial and significant improvements compared to baseline techniques: up to 39.5% relative improvement compared to MFCC, and 18.7% compared to PNCC in the Aurora 2 database.
Fernando De La Calle Silos; Francisco J. Valverde Albacete; Ascensión Gallardo-Antolín; Carmen Peláez-Moreno; E La Calle Silos F.; Gallardo-Antolin A.; Pelaez-Moreno C.. Morphologically Filtered Power-Normalized Cochleograms as Robust, Biologically Inspired Features for ASR. IEEE/ACM Transactions on Audio, Speech, and Language Processing 2015, 23, 2070 -2080.
AMA StyleFernando De La Calle Silos, Francisco J. Valverde Albacete, Ascensión Gallardo-Antolín, Carmen Peláez-Moreno, E La Calle Silos F., Gallardo-Antolin A., Pelaez-Moreno C.. Morphologically Filtered Power-Normalized Cochleograms as Robust, Biologically Inspired Features for ASR. IEEE/ACM Transactions on Audio, Speech, and Language Processing. 2015; 23 (11):2070-2080.
Chicago/Turabian StyleFernando De La Calle Silos; Francisco J. Valverde Albacete; Ascensión Gallardo-Antolín; Carmen Peláez-Moreno; E La Calle Silos F.; Gallardo-Antolin A.; Pelaez-Moreno C.. 2015. "Morphologically Filtered Power-Normalized Cochleograms as Robust, Biologically Inspired Features for ASR." IEEE/ACM Transactions on Audio, Speech, and Language Processing 23, no. 11: 2070-2080.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. The spectra of irreducible matrices over completed idempotent semifields. Fuzzy Sets and Systems 2015, 271, 46 -69.
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. The spectra of irreducible matrices over completed idempotent semifields. Fuzzy Sets and Systems. 2015; 271 ():46-69.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2015. "The spectra of irreducible matrices over completed idempotent semifields." Fuzzy Sets and Systems 271, no. : 46-69.
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 performance. In particular, we found that Deep Maxout Networks, a modification of DNNs' feed-forward architecture that uses a max-out activation function, provides enhanced robustness to environmental noise. In this paper, we present preliminary experiments on the combination of these two elements that already show how the DMN-based back-end is capable of taking advantage of these auditorily inspired features making the whole system more robust and also suggesting that human-like representations of speech keep playing an important role in DNN-based automatic speech recognition systems.
F. De-La-Calle-Silos; Francisco J. Valverde-Albacete; A. Gallardo-Antolin; C. Pelaez-Moreno; E-La-Calle-Silos F.; Valverde-Albacete F.J.. Preliminary experiments on the robustness of biologically motivated features for DNN-based ASR. 2015 4th International Work Conference on Bioinspired Intelligence (IWOBI) 2015, 169 -176.
AMA StyleF. De-La-Calle-Silos, Francisco J. Valverde-Albacete, A. Gallardo-Antolin, C. Pelaez-Moreno, E-La-Calle-Silos F., Valverde-Albacete F.J.. Preliminary experiments on the robustness of biologically motivated features for DNN-based ASR. 2015 4th International Work Conference on Bioinspired Intelligence (IWOBI). 2015; ():169-176.
Chicago/Turabian StyleF. De-La-Calle-Silos; Francisco J. Valverde-Albacete; A. Gallardo-Antolin; C. Pelaez-Moreno; E-La-Calle-Silos F.; Valverde-Albacete F.J.. 2015. "Preliminary experiments on the robustness of biologically motivated features for DNN-based ASR." 2015 4th International Work Conference on Bioinspired Intelligence (IWOBI) , no. : 169-176.
We report on progress in characterizing \(\mathcal K\)-valued FCA in algebraic terms, where \(\mathcal K\) 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 intents. Adopting also the point of view of the theory of linear operators between vector spaces we explore the similarities and differences of the idempotent semimodules of extents and intents with the subspaces related to a linear operator in standard algebra. This allows us to shed some new light into Formal Concept Analysis from the point of view of the theory of linear operators over idempotent semimodules.
Francisco J. Valverde-Albacete; Carmen Peláez-Moreno. The Linear Algebra in Formal Concept Analysis over Idempotent Semifields. Transactions on Petri Nets and Other Models of Concurrency XV 2015, 97 -113.
AMA StyleFrancisco J. Valverde-Albacete, Carmen Peláez-Moreno. The Linear Algebra in Formal Concept Analysis over Idempotent Semifields. Transactions on Petri Nets and Other Models of Concurrency XV. 2015; ():97-113.
Chicago/Turabian StyleFrancisco J. Valverde-Albacete; Carmen Peláez-Moreno. 2015. "The Linear Algebra in Formal Concept Analysis over Idempotent Semifields." Transactions on Petri Nets and Other Models of Concurrency XV , no. : 97-113.