Person:
Gómez González, Daniel

First Name

Daniel

Last Name

Gómez González

URI

https://hdl.handle.net/20.500.14352/77430

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Estudios estadísticos

Department

Estadística y Ciencia de los Datos

Area

Estadística e Investigación Operativa

Identifiers

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Now showing 1 - 10 of 17

On measuring features importance in Machine Learning models in a two-dimensional representation scenario
(2022) Gutiérrez García-Pardo, Inmaculada; Santos, Daniel; Castro Cantalejo, Javier; Gómez González, Daniel; Espínola Vílchez, María Rosario; Guevara Gil, Juan Antonio
Abstract: There is a wide range of papers in the literature about the explanation of machine learning models in which Shapley value is considered to measure the importance of the features in these models. We can distinguish between these which set their basis on the cooperative game theory principles, and these focused on fuzzy measures. It is important to mention that all of these approaches only provide a crisp value (or a fix point) to measure the importance of a feature in a specific model. The reason is that an aggregation process of the different marginal contributions produces a single output for each variable. Nevertheless, and because of the relations between features, we cannot distinguish the case in which we do not know all the features. To this aim, we propose a disaggregated model which allows the analysis of the importance of the features, regarding the available information. This new proposal can be viewed as a generalization of all previous measures found in literature providing a two dimensional graph which, in a very intuitive and visual way, provides this rich disaggregated information. This information may be aggregated with several aggregation functions with which obtain new measures to establish the importance of the features. Specifically, the aggregation by the sum results in the Shapley value. We also explain the characteristics of those graphics in different scenarios of the relations among features, to raise this useful information at a glance.
Allocating slacks in stochastic PERT network
(Central European journal of operations research, 2014) Castro Cantalejo, Javier; Gómez González, Daniel; Tejada Cazorla, Juan Antonio
The SPERT problem was defined, in a game theory framework, as the fair allocation of the slack or float among the activities in a PERT network previous to the execution of the project. Previous approaches tackle with this problem imposing that the durations of the activities are deterministic. In this paper, we extend the SPERT problem into a stochastic framework defining a new solution that tries also to maintain the good performance of some other approaches that have been defined for the deterministic case. Afterward, we present a polynomial algorithm for this new solution that also could be used for the calculation of other approaches founded in the deterministic SPERT literature.
Multiple bipolar fuzzy measures: an application to community detection problems for networks with additional information
(International Journal of Computational Intelligence Systems, 2020) Gutiérrez García-Pardo, Inmaculada; Gómez González, Daniel; Castro Cantalejo, Javier; Espínola Vílchez, María Rosario
In this paper we introduce the concept of multiple bipolar fuzzy measures as a generalization of a bipolar fuzzy measure. We also propose a new definition of a group, which is based on the multidimensional bipolar fuzzy relations of its elements. Taking into account this information, we provide a novel procedure (based on the well-known Louvain algorithm) to deal with community detection problems. This new method considers the multidimensional bipolar information provided by multiple bipolar fuzzy measures, as well as the information provided by a graph. We also give some detailed computational tests, obtained from the application of this algorithm in several benchmark models.
A new edge betweenness measure using a game theoretical approach: an application to hierarchical community cetection
(Mathematics, 2021) Espínola Vílchez, María Rosario; Gómez González, Daniel; Castro Cantalejo, Javier; Gutiérrez García-Pardo, Inmaculada; Jiménez-Losada, Andrés; Goubko, Mikhail
In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.
A new approach to Color Edge Detection
(Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019), 2019) Flores Vidal, Pablo Arcadio; Gómez González, Daniel; Castro Cantalejo, Javier; Villarino, Guillermo; Montero, Javier
Most edge detection algorithms deal only with grayscale images, and the way of adapting them to use with RGB images is an open problem. In this work, we explore different ways of aggregating the color information of a RGB image for edges extraction, and this is made by means of well-known edge detection algorithms. In this research, it is been used the set of images from Berkeley. In order to evaluate the algorithm’s performance, F measure is computed. The way that color information -the different channels- is aggregated is proved to be relevant for the edge detection task. Moreover, post-aggregation of channels performed significatively better than the classic approach (pre-aggregation of channels).
New Aggregation Approaches with HSV to Color Edge Detection
(International Journal of Computational Intelligence Systems, 2022) Flores Vidal, Pablo Arcadio; Gómez González, Daniel; Castro Cantalejo, Javier; Montero, Javier
The majority of edge detection algorithms only deal with grayscale images, while their use with color images remains an open problem. This paper explores different approaches to aggregate color information of RGB and HSV images for edge extraction purposes through the usage of the Sobel operator and Canny algorithm. This paper makes use of Berkeley’s image data set, and to evaluate the performance of the different aggregations, the F-measure is computed. Higher potential of aggregations with HSV channels than with RGB channels is found. This article also shows that depending on the type of image used, RGB or HSV, some methods are more appropriate than others.
From fuzzy information to community detection: an approach to social networks analysis with soft information
(Mathematics, 2022) Gutiérrez García-Pardo, Inmaculada; Gómez González, Daniel; Castro Cantalejo, Javier; Espínola Vílchez, María Rosario; Wierzchoń, Sławomir T.
On the basis of network analysis, and within the context of modeling imprecision or vague information with fuzzy sets, we propose an innovative way to analyze, aggregate and apply this uncertain knowledge into community detection of real-life problems. This work is set on the existence of one (or multiple) soft information sources, independent of the network considered, assuming this extra knowledge is modeled by a vector of fuzzy sets (or a family of vectors). This information may represent, for example, how much some people agree with a specific law, or their position against several politicians. We emphasize the importance of being able to manage the vagueness which usually appears in real life because of the common use of linguistic terms. Then, we propose a constructive method to build fuzzy measures from fuzzy sets. These measures are the basis of a new representation model which combines the information of a network with that of fuzzy sets, specifically when it comes to linguistic terms. We propose a specific application of that model in terms of finding communities in a network with additional soft information. To do so, we propose an efficient algorithm and measure its performance by means of a benchmarking process, obtaining high-quality results.
A project game for PERT networks
(Operations Research Letters, 2007) Castro Cantalejo, Javier; Gómez González, Daniel; Tejada Cazorla, Juan Antonio
An important topic in PERT networks is how to allocate the total expedition (or delay) for situations in which the project is not executed as planned. In order to do that we define a TU project game that satisfies some desirable properties from the management project and game theory point of view.
Improving polynomial estimation of the Shapley value by stratified random sampling with optimum allocation
(Computers & Operations Research, 2017) Castro Cantalejo, Javier; Gómez González, Daniel; Molina, Elienda; Tejada Cazorla, Juan Antonio
In this paper, we propose a refinement of the polynomial method based on sampling theory proposed by Castro et al. (2009) to estimate the Shapley value for cooperative games. In addition to analyzing the variance of the previously proposed estimation method, we employ stratified random sampling with optimum allocation in order to reduce the variance. We examine some desirable statistical features of the stratified approach and provide some computational results by analyzing the gains due to stratification, which are around 30% on average and more than 80% in the best case.
Fuzzy measures: a solution to deal with community detection problems for networks with additional information
(Journal of Intelligent & Fuzzy Systems, 2020) Gutiérrez García-Pardo, Inmaculada; Gómez González, Daniel; Castro Cantalejo, Javier; Espínola Vílchez, María Rosario; Kahraman, Cengiz
In this work we introduce the notion of the weighted graph associated with a fuzzy measure. Having a finite set of elements between which there exists an affinity fuzzy relation, we propose the definition of a group based on that affinity fuzzy relation between the individuals. Then, we propose an algorithm based on the Louvain’s method to deal with community detection problems with additional information independent of the graph. We also provide a particular method to solve community detection problems over extended fuzzy graphs. Finally, we test the performance of our proposal by means of some detailed computational tests calculated in several benchmark models.