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Ángel González-Prieto

Publications and source records attributed to Ángel González-Prieto.

At least 37 records · Page 2Linked to original sources
arXiv2023

Quantization of algebraic invariants through Topological Quantum Field Theories

In this paper we investigate the problem of constructing Topological Quantum Field Theories (TQFTs) to quantize algebraic invariants. We exhibit necessary conditions for quantizability based on Euler characteristics. In the case of surfaces, also provide a partial answer in terms of sufficient conditions by means of almost-TQFTs and almost-Frobenius algebras for wide TQFTs. As an application, we show that the Poincaré polynomial of $G$-representation varieties is not a quantizable invariant by means of a monoidal TQFTs for any algebraic group $G$ of positive dimension.

math.QA↗
arXiv2023

An evaluation framework for dimensionality reduction through sectional curvature

Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality metrics have been studied in the literature, in the field of dimensionality reduction only a few over-simplistic metrics has been proposed. In this work, we aim to introduce the first highly non-trivial dimensionality reduction performance metric. This metric is based on the sectional curvature behaviour arising from Riemannian geometry. To test its feasibility, this metric has been used to evaluate the performance of the most commonly used dimension reduction algorithms in the state of the art. Furthermore, to make the evaluation of the algorithms robust and representative, using curvature properties of planar curves, a new parameterized problem instance generator has been constructed in the form of a function generator. Experimental results are consistent with what could be expected based on the design and characteristics of the evaluated algorithms and the features of the data instances used to feed the method.

cs.LG↗
arXiv2023

Stratification of $\mathrm{SU}(r)$-character varieties of twisted Hopf links

We describe the geometry of the character variety of representations of the fundamental group of the complement of a Hopf link with $n$ twists, namely $Γ_{n}=\langle x,y \,| \, [x^n,y]=1 \rangle$ into the group $\mathrm{SU}(r)$. For arbitrary rank, we provide geometric descriptions of the loci of irreducible and totally reducible representations. In the case $r = 2$, we provide a complete geometric description of the character variety, proving that this $\mathrm{SU}(2)$-character variety is a deformation retract of the larger $\mathrm{SL}(2,\mathbb{C})$-character variety, as conjectured by Florentino and Lawton. In the case $r = 3$, we also describe different strata of the $\mathrm{SU}(3)$-character variety according to the semi-simple type of the representation.

math.GT↗
arXiv2022

Dynamics of Fourier Modes in Torus Generative Adversarial Networks

Generative Adversarial Networks (GANs) are powerful Machine Learning models capable of generating fully synthetic samples of a desired phenomenon with a high resolution. Despite their success, the training process of a GAN is highly unstable and typically it is necessary to implement several accessory heuristics to the networks to reach an acceptable convergence of the model. In this paper, we introduce a novel method to analyze the convergence and stability in the training of Generative Adversarial Networks. For this purpose, we propose to decompose the objective function of the adversary min-max game defining a periodic GAN into its Fourier series. By studying the dynamics of the truncated Fourier series for the continuous Alternating Gradient Descend algorithm, we are able to approximate the real flow and to identify the main features of the convergence of the GAN. This approach is confirmed empirically by studying the training flow in a $2$-parametric GAN aiming to generate an unknown exponential distribution. As byproduct, we show that convergent orbits in GANs are small perturbations of periodic orbits so the Nash equillibria are spiral attractors. This theoretically justifies the slow and unstable training observed in GANs.

cs.LG↗
arXiv2022

Geometry of $\mathrm{SU}(3)$-character varieties of torus knots

We describe the geometry of the character variety of representations of the knot group $Γ_{m,n}=\langle x,y| x^n=y^m\rangle$ into the group $\mathrm{SU}(3)$, by stratifying the character variety into strata correspoding to totally reducible representations, representations decomposing into a $2$-dimensional and a $1$-dimensional representation, and irreducible representations, the latter of two types depending on whether the matrices have distinct eigenvalues, or one of the matrices has one eigenvalue of multiplicity $2$. We describe how the closure of each stratum meets lower strata, and use this to compute the compactly supported Euler characteristic, and to prove that the inclusion of the character variety for $\mathrm{SU}(3)$ into the character variety for $\mathrm{SL}(3,\mathbb{C})$ is a homotopy equivalence.

math.GT↗
arXiv2022

Providing reliability in Recommender Systems through Bernoulli Matrix Factorization

Beyond accuracy, quality measures are gaining importance in modern recommender systems, with reliability being one of the most important indicators in the context of collaborative filtering. This paper proposes Bernoulli Matrix Factorization (BeMF), which is a matrix factorization model, to provide both prediction values and reliability values. BeMF is a very innovative approach from several perspectives: a) it acts on model-based collaborative filtering rather than on memory-based filtering, b) it does not use external methods or extended architectures, such as existing solutions, to provide reliability, c) it is based on a classification-based model instead of traditional regression-based models, and d) matrix factorization formalism is supported by the Bernoulli distribution to exploit the binary nature of the designed classification model. The experimental results show that the more reliable a prediction is, the less liable it is to be wrong: recommendation quality improves after the most reliable predictions are selected. State-of-the-art quality measures for reliability have been tested, which shows that BeMF outperforms previous baseline methods and models.

cs.LG↗
arXiv2021

Improving the quality of generative models through Smirnov transformation

Solving the convergence issues of Generative Adversarial Networks (GANs) is one of the most outstanding problems in generative models. In this work, we propose a novel activation function to be used as output of the generator agent. This activation function is based on the Smirnov probabilistic transformation and it is specifically designed to improve the quality of the generated data. In sharp contrast with previous works, our activation function provides a more general approach that deals not only with the replication of categorical variables but with any type of data distribution (continuous or discrete). Moreover, our activation function is derivable and therefore, it can be seamlessly integrated in the backpropagation computations during the GAN training processes. To validate this approach, we evaluate our proposal against two different data sets: a) an artificially rendered data set containing a mixture of discrete and continuous variables, and b) a real data set of flow-based network traffic data containing both normal connections and cryptomining attacks. To evaluate the fidelity of the generated data, we analyze both their results in terms of quality measures of statistical nature and also regarding the use of these synthetic data to feed a nested machine learning-based classifier. The experimental results evince a clear outperformance of the GAN network tuned with this new activation function with respect to both a naïve mean-based generator and a standard GAN. The quality of the data is so high that the generated data can fully substitute real data for training the nested classifier without a fall in the obtained accuracy. This result encourages the use of GANs to produce high-quality synthetic data that are applicable in scenarios in which data privacy must be guaranteed.

cs.LG↗
arXiv2021

Synthetic flow-based cryptomining attack generation through Generative Adversarial Networks

Due to the growing rise of cyber attacks in the Internet, flow-based data sets are crucial to increase the performance of the Machine Learning (ML) components that run in network-based intrusion detection systems (IDS). To overcome the existing network traffic data shortage in attack analysis, recent works propose Generative Adversarial Networks (GANs) for synthetic flow-based network traffic generation. Data privacy is appearing more and more as a strong requirement when processing such network data, which suggests to find solutions where synthetic data can fully replace real data. Because of the ill-convergence of the GAN training, none of the existing solutions can generate high-quality fully synthetic data that can totally substitute real data in the training of IDS ML components. Therefore, they mix real with synthetic data, which acts only as data augmentation components, leading to privacy breaches as real data is used. In sharp contrast, in this work we propose a novel deterministic way to measure the quality of the synthetic data produced by a GAN both with respect to the real data and to its performance when used for ML tasks. As a byproduct, we present a heuristic that uses these metrics for selecting the best performing generator during GAN training, leading to a stopping criterion. An additional heuristic is proposed to select the best performing GANs when different types of synthetic data are to be used in the same ML task. We demonstrate the adequacy of our proposal by generating synthetic cryptomining attack traffic and normal traffic flow-based data using an enhanced version of a Wasserstein GAN. We show that the generated synthetic network traffic can completely replace real data when training a ML-based cryptomining detector, obtaining similar performance and avoiding privacy violations, since real data is not used in the training of the ML-based detector.

cs.CR↗
arXiv2021

Deep Variational Models for Collaborative Filtering-based Recommender Systems

Deep learning provides accurate collaborative filtering models to improve recommender system results. Deep matrix factorization and their related collaborative neural networks are the state-of-art in the field; nevertheless, both models lack the necessary stochasticity to create the robust, continuous, and structured latent spaces that variational autoencoders exhibit. On the other hand, data augmentation through variational autoencoder does not provide accurate results in the collaborative filtering field due to the high sparsity of recommender systems. Our proposed models apply the variational concept to inject stochasticity in the latent space of the deep architecture, introducing the variational technique in the neural collaborative filtering field. This method does not depend on the particular model used to generate the latent representation. In this way, this approach can be applied as a plugin to any current and future specific models. The proposed models have been tested using four representative open datasets, three different quality measures, and state-of-art baselines. The results show the superiority of the proposed approach in scenarios where the variational enrichment exceeds the injected noise effect. Additionally, a framework is provided to enable the reproducibility of the conducted experiments.

cs.IR↗
arXiv2021

Applying Inter-rater Reliability and Agreement in Grounded Theory Studies in Software Engineering

In recent years, the qualitative research on empirical software engineering that applies Grounded Theory is increasing. Grounded Theory (GT) is a technique for developing theory inductively e iteratively from qualitative data based on theoretical sampling, coding, constant comparison, memoing, and saturation, as main characteristics. Large or controversial GT studies may involve multiple researchers in collaborative coding, which requires a kind of rigor and consensus that an individual coder does not. Although many qualitative researchers reject quantitative measures in favor of other qualitative criteria, many others are committed to measuring consensus through Inter-Rater Reliability (IRR) and/or Inter-Rater Agreement (IRA) techniques to develop a shared understanding of the phenomenon being studied. However, there are no specific guidelines about how and when to apply IRR/IRA during the iterative process of GT, so researchers have been using ad hoc methods for years. This paper presents a process for systematically applying IRR/IRA in GT studies that meets the iterative nature of this qualitative research method, which is supported by a previous systematic literature review on applying IRR/RA in GT studies in software engineering. This process allows researchers to incrementally generate a theory while ensuring consensus on the constructs that support it and, thus, improving the rigor of qualitative research. This formalization helps researchers to apply IRR/IRA to GT studies when various raters are involved in coding. Measuring consensus among raters promotes communicability, transparency, reflexivity, replicability, and trustworthiness of the research.

cs.SE↗
arXiv2021

The point counting problem in representation varieties of torus knots

We compute the motive of the variety of representations of the torus knot of type (m,n) into the affine groups $AGL_1$ and $AGL_2$ for an arbitrary field $k$. In the case that $k = F_q$ is a finite field this gives rise to the count of the number of points of the representation variety, while for $k = C$ this calculation returns the E-polynomial of the representation variety. We discuss the interplay between these two results in sight of Katz theorem that relates the point count polynomial with the E-polynomial. In particular, we shall show that several point count polynomials exist for these representation varieties, depending on the arithmetic between m,n and the characteristic of the field, whereas only one of them agrees with the actual E-polynomial.

math.AG↗
arXiv2021

Machine learning for risk assessment in gender-based crime

Gender-based crime is one of the most concerning scourges of contemporary society. Governments worldwide have invested lots of economic and human resources to radically eliminate this threat. Despite these efforts, providing accurate predictions of the risk that a victim of gender violence has of being attacked again is still a very hard open problem. The development of new methods for issuing accurate, fair and quick predictions would allow police forces to select the most appropriate measures to prevent recidivism. In this work, we propose to apply Machine Learning (ML) techniques to create models that accurately predict the recidivism risk of a gender-violence offender. The relevance of the contribution of this work is threefold: (i) the proposed ML method outperforms the preexisting risk assessment algorithm based on classical statistical techniques, (ii) the study has been conducted through an official specific-purpose database with more than 40,000 reports of gender violence, and (iii) two new quality measures are proposed for assessing the effective police protection that a model supplies and the overload in the invested resources that it generates. Additionally, we propose a hybrid model that combines the statistical prediction methods with the ML method, permitting authorities to implement a smooth transition from the preexisting model to the ML-based model. This hybrid nature enables a decision-making process to optimally balance between the efficiency of the police system and aggressiveness of the protection measures taken.

cs.CY↗
arXiv2021

Why are many businesses instilling a DevOps culture into their organization?

Context: DevOps can be defined as a cultural movement to improve and accelerate the delivery of business value by making the collaboration between development and operations effective. Although this movement is relatively recent, there exist an intensive research around DevOps. However, the real reasons why companies move to DevOps and the results they expect to obtain have been paid little attention in real contexts. Objective: This paper aims to help practitioners and researchers to better understand the context and the problems that many companies face day to day in their organizations when they try to accelerate software delivery and the main drivers that move these companies to adopting DevOps. Method: We conducted an exploratory study by leveraging in depth, semi-structured interviews to relevant stakeholders of 30 multinational software-intensive companies, together industrial workshops and observations at organizations' facilities that supported triangulation. Additionally, we conducted an inter-coder agreement analysis, which is not usually addressed in qualitative studies in software engineering, to increase reliability and reduce authors bias of the drawn findings. Results: The research explores the problems and expected outcomes that moved companies to adopt DevOps and reveals a set of patterns and anti-patterns about the reasons why companies are instilling a DevOps culture. Conclusions: This study aims to strengthen evidence and support practitioners in making better informed about which problems trigger a DevOps transition and most common expected results.

cs.SE↗
arXiv2021

Reliability in Software Engineering Qualitative Research through Inter-Coder Agreement: A guide using Krippendorff's $α$ & Atlas.ti

In recent years, the research on empirical software engineering that uses qualitative data analysis (e.g., cases studies, interview surveys, and grounded theory studies) is increasing. However, most of this research does not deep into the reliability and validity of findings, specifically in the reliability of coding in which these methodologies rely on, despite there exist a variety of statistical techniques known as Inter-Coder Agreement (ICA) for analyzing consensus in team coding. This paper aims to establish a novel theoretical framework that enables a methodological approach for conducting this validity analysis. This framework is based on a set of coefficients for measuring the degree of agreement that different coders achieve when judging a common matter. We analyze different reliability coefficients and provide detailed examples of calculation, with special attention to Krippendorff's $α$ coefficients. We systematically review several variants of Krippendorff's $α$ reported in the literature and provide a novel common mathematical framework in which all of them are unified through a universal $α$ coefficient. Finally, this paper provides a detailed guide of the use of this theoretical framework in a large case study on DevOps culture. We explain how $α$ coefficients are computed and interpreted using a widely used software tool for qualitative analysis like Atlas.ti. We expect that this work will help empirical researchers, particularly in software engineering, to improve the quality and trustworthiness of their studies.

cs.SE↗
arXiv2021

DevOps Team Structures: Characterization and Implications

Context: DevOps can be defined as a cultural movement to improve and accelerate the delivery of business value by making the collaboration between development and operations effective. Objective: This paper aims to help practitioners and researchers to better understand the organizational structure and characteristics of teams adopting DevOps. Method: We conducted an exploratory study by leveraging in depth, semi-structured interviews to relevant stakeholders of 31 multinational software-intensive companies, together with industrial workshops and observations at organizations' facilities that supported triangulation. We used Grounded Theory as qualitative research method to explore the structure and characteristics of teams, and statistical analysis to discover their implications in software delivery performance. Results: We describe a taxonomy of team structure patterns that shows emerging, stable and consolidated product teams that are classified according to six variables, such as collaboration frequency, product ownership sharing, autonomy, among others, as well as their implications on software delivery performance. These teams are often supported by horizontal teams (DevOps platform teams, Centers of Excellence, and chapters) that provide them with platform technical capability, mentoring and evangelization, and even temporarily facilitate human resources. Conclusion: This study aims to strengthen evidence and support practitioners in making better informed about organizational team structures by analyzing their main characteristics and implications in software delivery performance.

cs.SE↗
arXiv2020

On character varieties of singular manifolds

In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic varieties, of $G$-representation varieties over manifolds with conic singularities, which we will call nodefolds. This construction is valid for any algebraic group $G$, in any dimension and also in the parabolic setting. In particular, this TQFT allow us to compute the virtual classes of representation varieties over complex singular planar curves. In addition, in the case $G = \mathrm{SL}_{2}(k)$, the virtual class of the associated character variety over a nodal closed orientable surface is computed both in the non-parabolic and in the parabolic scenarios.

math.AG↗
arXiv2020

Deep Learning feature selection to unhide demographic recommender systems factors

Extracting demographic features from hidden factors is an innovative concept that provides multiple and relevant applications. The matrix factorization model generates factors which do not incorporate semantic knowledge. This paper provides a deep learning-based method: DeepUnHide, able to extract demographic information from the users and items factors in collaborative filtering recommender systems. The core of the proposed method is the gradient-based localization used in the image processing literature to highlight the representative areas of each classification class. Validation experiments make use of two public datasets and current baselines. Results show the superiority of DeepUnHide to make feature selection and demographic classification, compared to the state of art of feature selection methods. Relevant and direct applications include recommendations explanation, fairness in collaborative filtering and recommendation to groups of users.

cs.IR↗