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We prove a quantitative estimate with a power saving error term for the number of filling closed geodesics of a given topological type and length $\leq L$ on an arbitrary closed, orientable, negatively curved surface. More generally, we prove estimates of the same kind for the number of free homotopy classes of filling closed curves of a given topological type on a closed, orientable surface whose geometric intersection number with respect to a given filling geodesic current is $\leq L$. The proofs rely on recent progress made on the study of the effective dynamics of the mapping class group on Teichm\"uller space and the space of closed curves of a closed, orientable surface, and introduce a novel method for addressing counting problems of mapping class group orbits that naturally yields power saving error terms. This method is also applied to study counting problems of mapping class group orbits of Teichm\"uller space with respect to Thurston's asymmetric metric., Comment: 34 pages, 6 figures. arXiv admin note: text overlap with arXiv:2104.01694

The research in anomaly detection lacks a unified definition of what represents an anomalous instance. Discrepancies in the nature itself of an anomaly lead to multiple paradigms of algorithms design and experimentation. Predictive maintenance is a special case, where the anomaly represents a failure that must be prevented. Related time-series research as outlier and novelty detection or time-series classification does not apply to the concept of an anomaly in this field, because they are not single points which have not been seen previously and may not be precisely annotated. Moreover, due to the lack of annotated anomalous data, many benchmarks are adapted from supervised scenarios. To address these issues, we generalise the concept of positive and negative instances to intervals to be able to evaluate unsupervised anomaly detection algorithms. We also preserve the imbalance scheme for evaluation through the proposal of the Preceding Window ROC, a generalisation for the calculation of ROC curves for time-series scenarios. We also adapt the mechanism from a established time-series anomaly detection benchmark to the proposed generalisations to reward early detection. Therefore, the proposal represents a flexible evaluation framework for the different scenarios. To show the usefulness of this definition, we include a case study of Big Data algorithms with a real-world time-series problem provided by the company ArcelorMittal, and compare the proposal with an evaluation method., Comment: 25 pages, 9 figures, 5 tables

The detection of critical infrastructures in large territories represented by aerial and satellite images is of high importance in several fields such as in security, anomaly detection, land use planning and land use change detection. However, the detection of such infrastructures is complex as they have highly variable shapes and sizes, i.e., some infrastructures, such as electrical substations, are too small while others, such as airports, are too large. Besides, airports can have a surface area either small or too large with completely different shapes, which makes its correct detection challenging. As far as we know, these limitations have not been tackled yet in previous works. This paper presents (1) a smart Critical Infrastructure dataset, named CI-dataset, organised into two scales, small and large scales critical infrastructures and (2) a two-level resolution-independent critical infrastructure detection (DetDSCI) methodology that first determines the spatial resolution of the input image using a classification model, then analyses the image using the appropriate detector for that spatial resolution. The present study targets two representative classes, airports and electrical substations. Our experiments show that DetDSCI methodology achieves up to 37,53% F1 improvement with respect to Faster R-CNN, one of the most influential detection models.

The latest Deep Learning (DL) models for detection and classification have achieved an unprecedented performance over classical machine learning algorithms. However, DL models are black-box methods hard to debug, interpret, and certify. DL alone cannot provide explanations that can be validated by a non technical audience. In contrast, symbolic AI systems that convert concepts into rules or symbols -- such as knowledge graphs -- are easier to explain. However, they present lower generalisation and scaling capabilities. A very important challenge is to fuse DL representations with expert knowledge. One way to address this challenge, as well as the performance-explainability trade-off is by leveraging the best of both streams without obviating domain expert knowledge. We tackle such problem by considering the symbolic knowledge is expressed in form of a domain expert knowledge graph. We present the eXplainable Neural-symbolic learning (X-NeSyL) methodology, designed to learn both symbolic and deep representations, together with an explainability metric to assess the level of alignment of machine and human expert explanations. The ultimate objective is to fuse DL representations with expert domain knowledge during the learning process to serve as a sound basis for explainability. X-NeSyL methodology involves the concrete use of two notions of explanation at inference and training time respectively: 1) EXPLANet: Expert-aligned eXplainable Part-based cLAssifier NETwork Architecture, a compositional CNN that makes use of symbolic representations, and 2) SHAP-Backprop, an explainable AI-informed training procedure that guides the DL process to align with such symbolic representations in form of knowledge graphs. We showcase X-NeSyL methodology using MonuMAI dataset for monument facade image classification, and demonstrate that our approach improves explainability and performance.

Despite the constant advances in computer vision, integrating modern single-image detectors in real-time handgun alarm systems in video-surveillance is still debatable. Using such detectors still implies a high number of false alarms and false negatives. In this context, most existent studies select one of the latest single-image detectors and train it on a better dataset or use some pre-processing, post-processing or data-fusion approach to further reduce false alarms. However, none of these works tried to exploit the temporal information present in the videos to mitigate false detections. This paper presents a new system, called MULTI Confirmation-level Alarm SysTem based on Convolutional Neural Networks (CNN) and Long Short Term Memory networks (LSTM) (MULTICAST), that leverages not only the spacial information but also the temporal information existent in the videos for a more reliable handgun detection. MULTICAST consists of three stages, i) a handgun detection stage, ii) a CNN-based spacial confirmation stage and iii) LSTM-based temporal confirmation stage. The temporal confirmation stage uses the positions of the detected handgun in previous instants to predict its trajectory in the next frame. Our experiments show that MULTICAST reduces by 80% the number of false alarms with respect to Faster R-CNN based-single-image detector, which makes it more useful in providing more effective and rapid security responses.

We show that the action of the mapping class group on the space of closed curves of a closed surface effectively tracks the corresponding action on Teichm\"uller space in the following sense: for all but quantitatively few mapping classes, the information of how a mapping class moves a given point of Teichm\"uller space determines, up to a power saving error term, how it changes the geometric intersection numbers of a given closed curve with respect to arbitrary geodesic currents. Applications include an effective estimate describing the speed of convergence of Teichm\"uller geodesic rays to the boundary at infinity of Teichm\"uller space, an effective estimate comparing the Teichm\"uller and Thurston metrics along mapping class group orbits of Teichm\"uller space, and, in the sequel, effective estimates for countings of filling closed geodesics on closed, negatively curved surfaces., Comment: 55 pages, 20 figures

Transfer Optimization is an incipient research area dedicated to solving multiple optimization tasks simultaneously. Among the different approaches that can address this problem effectively, Evolutionary Multitasking resorts to concepts from Evolutionary Computation to solve multiple problems within a single search process. In this paper we introduce a novel adaptive metaheuristic algorithm to deal with Evolutionary Multitasking environments coined as Adaptive Transfer-guided Multifactorial Cellular Genetic Algorithm (AT-MFCGA). AT-MFCGA relies on cellular automata to implement mechanisms in order to exchange knowledge among the optimization problems under consideration. Furthermore, our approach is able to explain by itself the synergies among tasks that were encountered and exploited during the search, which helps us to understand interactions between related optimization tasks. A comprehensive experimental setup is designed to assess and compare the performance of AT-MFCGA to that of other renowned evolutionary multitasking alternatives (MFEA and MFEA-II). Experiments comprise 11 multitasking scenarios composed of 20 instances of 4 combinatorial optimization problems, yielding the largest discrete multitasking environment solved to date. Results are conclusive in regard to the superior quality of solutions provided by AT-MFCGA with respect to the rest of the methods, which are complemented by a quantitative examination of the genetic transferability among tasks throughout the search process., Comment: 31 pages, 4 figures, paper accepted for being published in Information Sciences journal

We prove a quantitative estimate with a power saving error term for the number of points in a mapping class group orbit of Teichm\"uller space that lie within a Teichm\"uller metric ball of given center and large radius. Estimates of the same kind are also proved for sector and bisector counts. These estimates effectivize asymptotic counting results of Athreya, Bufetov, Eskin, and Mirzakhani., Comment: Updated title, abstract, and introduction. Improved quality of figures. Other minor changes. 51 pages, 5 figures

Data stream mining extracts information from large quantities of data flowing fast and continuously (data streams). They are usually affected by changes in the data distribution, giving rise to a phenomenon referred to as concept drift. Thus, learning models must detect and adapt to such changes, so as to exhibit a good predictive performance after a drift has occurred. In this regard, the development of effective drift detection algorithms becomes a key factor in data stream mining. In this work we propose CU RIE, a drift detector relying on cellular automata. Specifically, in CU RIE the distribution of the data stream is represented in the grid of a cellular automata, whose neighborhood rule can then be utilized to detect possible distribution changes over the stream. Computer simulations are presented and discussed to show that CU RIE, when hybridized with other base learners, renders a competitive behavior in terms of detection metrics and classification accuracy. CU RIE is compared with well-established drift detectors over synthetic datasets with varying drift characteristics.

Much has been said about the fusion of bio-inspired optimization algorithms and Deep Learning models for several purposes: from the discovery of network topologies and hyper-parametric configurations with improved performance for a given task, to the optimization of the model's parameters as a replacement for gradient-based solvers. Indeed, the literature is rich in proposals showcasing the application of assorted nature-inspired approaches for these tasks. In this work we comprehensively review and critically examine contributions made so far based on three axes, each addressing a fundamental question in this research avenue: a) optimization and taxonomy (Why?), including a historical perspective, definitions of optimization problems in Deep Learning, and a taxonomy associated with an in-depth analysis of the literature, b) critical methodological analysis (How?), which together with two case studies, allows us to address learned lessons and recommendations for good practices following the analysis of the literature, and c) challenges and new directions of research (What can be done, and what for?). In summary, three axes - optimization and taxonomy, critical analysis, and challenges - which outline a complete vision of a merger of two technologies drawing up an exciting future for this area of fusion research., Comment: 64 pages, 18 figures, under review for its consideration in Information Fusion journal

Distributed linguistic representations are powerful tools for modelling the uncertainty and complexity of preference information in linguistic decision making. To provide a comprehensive perspective on the development of distributed linguistic representations in decision making, we present the taxonomy of existing distributed linguistic representations. Then, we review the key elements of distributed linguistic information processing in decision making, including the distance measurement, aggregation methods, distributed linguistic preference relations, and distributed linguistic multiple attribute decision making models. Next, we provide a discussion on ongoing challenges and future research directions from the perspective of data science and explainable artificial intelligence., Comment: 37 pages

Decision making models are constrained by taking the expert evaluations with pre-defined numerical or linguistic terms. We claim that the use of sentiment analysis will allow decision making models to consider expert evaluations in natural language. Accordingly, we propose the Sentiment Analysis based Multi-person Multi-criteria Decision Making (SA-MpMcDM) methodology for smarter decision aid, which builds the expert evaluations from their natural language reviews, and even from their numerical ratings if they are available. The SA-MpMcDM methodology incorporates an end-to-end multi-task deep learning model for aspect based sentiment analysis, named DOC-ABSADeepL model, able to identify the aspect categories mentioned in an expert review, and to distill their opinions and criteria. The individual evaluations are aggregated via the procedure named criteria weighting through the attention of the experts. We evaluate the methodology in a case study of restaurant choice using TripAdvisor reviews, hence we build, manually annotate, and release the TripR-2020 dataset of restaurant reviews. We analyze the SA-MpMcDM methodology in different scenarios using and not using natural language and numerical evaluations. The analysis shows that the combination of both sources of information results in a higher quality preference vector.

Federated learning, as a distributed learning that conducts the training on the local devices without accessing to the training data, is vulnerable to Byzatine poisoning adversarial attacks. We argue that the federated learning model has to avoid those kind of adversarial attacks through filtering out the adversarial clients by means of the federated aggregation operator. We propose a dynamic federated aggregation operator that dynamically discards those adversarial clients and allows to prevent the corruption of the global learning model. We assess it as a defense against adversarial attacks deploying a deep learning classification model in a federated learning setting on the Fed-EMNIST Digits, Fashion MNIST and CIFAR-10 image datasets. The results show that the dynamic selection of the clients to aggregate enhances the performance of the global learning model and discards the adversarial and poor (with low quality models) clients., Comment: 10 pages

Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data. However, some properties can cause datasets to be problematic to classify. In order to evaluate a dataset a priori, data complexity metrics have been used extensively. They provide information regarding different intrinsic characteristics of the data, which serve to evaluate classifier compatibility and a course of action that improves performance. However, most complexity metrics focus on just one characteristic of the data, which can be insufficient to properly evaluate the dataset towards the classifiers' performance. In fact, class overlap, a very detrimental feature for the classification process (especially when imbalance among class labels is also present) is hard to assess. This research work focuses on revisiting complexity metrics based on data morphology. In accordance to their nature, the premise is that they provide both good estimates for class overlap, and great correlations with the classification performance. For that purpose, a novel family of metrics have been developed. Being based on ball coverage by classes, they are named after Overlap Number of Balls. Finally, some prospects for the adaptation of the former family of metrics to singular (more complex) problems are discussed., Comment: 23 pages, 9 figures, preprint

The high demand of artificial intelligence services at the edges that also preserve data privacy has pushed the research on novel machine learning paradigms that fit those requirements. Federated learning has the ambition to protect data privacy through distributed learning methods that keep the data in their data silos. Likewise, differential privacy attains to improve the protection of data privacy by measuring the privacy loss in the communication among the elements of federated learning. The prospective matching of federated learning and differential privacy to the challenges of data privacy protection has caused the release of several software tools that support their functionalities, but they lack of the needed unified vision for those techniques, and a methodological workflow that support their use. Hence, we present the Sherpa.ai Federated Learning framework that is built upon an holistic view of federated learning and differential privacy. It results from the study of how to adapt the machine learning paradigm to federated learning, and the definition of methodological guidelines for developing artificial intelligence services based on federated learning and differential privacy. We show how to follow the methodological guidelines with the Sherpa.ai Federated Learning framework by means of a classification and a regression use cases., Comment: 46 pages, 5 figures

In many machine learning tasks, learning a good representation of the data can be the key to building a well-performant solution. This is because most learning algorithms operate with the features in order to find models for the data. For instance, classification performance can improve if the data is mapped to a space where classes are easily separated, and regression can be facilitated by finding a manifold of data in the feature space. As a general rule, features are transformed by means of statistical methods such as principal component analysis, or manifold learning techniques such as Isomap or locally linear embedding. From a plethora of representation learning methods, one of the most versatile tools is the autoencoder. In this paper we aim to demonstrate how to influence its learned representations to achieve the desired learning behavior. To this end, we present a series of learning tasks: data embedding for visualization, image denoising, semantic hashing, detection of abnormal behaviors and instance generation. We model them from the representation learning perspective, following the state of the art methodologies in each field. A solution is proposed for each task employing autoencoders as the only learning method. The theoretical developments are put into practice using a selection of datasets for the different problems and implementing each solution, followed by a discussion of the results in each case study and a brief explanation of other six learning applications. We also explore the current challenges and approaches to explainability in the context of autoencoders. All of this helps conclude that, thanks to alterations in their structure as well as their objective function, autoencoders may be the core of a possible solution to many problems which can be modeled as a transformation of the feature space.

Autoencoders are techniques for data representation learning based on artificial neural networks. Differently to other feature learning methods which may be focused on finding specific transformations of the feature space, they can be adapted to fulfill many purposes, such as data visualization, denoising, anomaly detection and semantic hashing. This work presents these applications and provides details on how autoencoders can perform them, including code samples making use of an R package with an easy-to-use interface for autoencoder design and training, \texttt{ruta}. Along the way, the explanations on how each learning task has been achieved are provided with the aim to help the reader design their own autoencoders for these or other objectives., Comment: This manuscript was accepted as conference paper in IWINAC 2019. The final authenticated publication is available online at https://doi.org/10.1007/978-3-030-19651-6_40

Bio-inspired optimization (including Evolutionary Computation and Swarm Intelligence) is a growing research topic with many competitive bio-inspired algorithms being proposed every year. In such an active area, preparing a successful proposal of a new bio-inspired algorithm is not an easy task. Given the maturity of this research field, proposing a new optimization technique with innovative elements is no longer enough. Apart from the novelty, results reported by the authors should be proven to achieve a significant advance over previous outcomes from the state of the art. Unfortunately, not all new proposals deal with this requirement properly. Some of them fail to select appropriate benchmarks or reference algorithms to compare with. In other cases, the validation process carried out is not defined in a principled way (or is even not done at all). Consequently, the significance of the results presented in such studies cannot be guaranteed. In this work we review several recommendations in the literature and propose methodological guidelines to prepare a successful proposal, taking all these issues into account. We expect these guidelines to be useful not only for authors, but also for reviewers and editors along their assessment of new contributions to the field., Comment: 81 pages, 4 figures

Multitasking optimization is an incipient research area which is lately gaining a notable research momentum. Unlike traditional optimization paradigm that focuses on solving a single task at a time, multitasking addresses how multiple optimization problems can be tackled simultaneously by performing a single search process. The main objective to achieve this goal efficiently is to exploit synergies between the problems (tasks) to be optimized, helping each other via knowledge transfer (thereby being referred to as Transfer Optimization). Furthermore, the equally recent concept of Evolutionary Multitasking (EM) refers to multitasking environments adopting concepts from Evolutionary Computation as their inspiration for the simultaneous solving of the problems under consideration. As such, EM approaches such as the Multifactorial Evolutionary Algorithm (MFEA) has shown a remarkable success when dealing with multiple discrete, continuous, single-, and/or multi-objective optimization problems. In this work we propose a novel algorithmic scheme for Multifactorial Optimization scenarios - the Multifactorial Cellular Genetic Algorithm (MFCGA) - that hinges on concepts from Cellular Automata to implement mechanisms for exchanging knowledge among problems. We conduct an extensive performance analysis of the proposed MFCGA and compare it to the canonical MFEA under the same algorithmic conditions and over 15 different multitasking setups (encompassing different reference instances of the discrete Traveling Salesman Problem). A further contribution of this analysis beyond performance benchmarking is a quantitative examination of the genetic transferability among the problem instances, eliciting an empirical demonstration of the synergies emerged between the different optimization tasks along the MFCGA search process., Comment: Accepted for its presentation at WCCI 2020

This paper proposes a new model based on Fuzzy k-Nearest Neighbors for classification with monotonic constraints, Monotonic Fuzzy k-NN (MonFkNN). Real-life data-sets often do not comply with monotonic constraints due to class noise. MonFkNN incorporates a new calculation of fuzzy memberships, which increases robustness against monotonic noise without the need for relabeling. Our proposal has been designed to be adaptable to the different needs of the problem being tackled. In several experimental studies, we show significant improvements in accuracy while matching the best degree of monotonicity obtained by comparable methods. We also show that MonFkNN empirically achieves improved performance compared with Monotonic k-NN in the presence of large amounts of class noise., Comment: Accepted in Neurocomputing

Given a connected, oriented, complete, finite area hyperbolic surface $X$ of genus $g$ with $n$ punctures, Mirzakhani showed that the number of multi-geodesics on $X$ of total hyperbolic length $\leq L$ in the mapping class group orbit of a given simple or filling closed multi-curve is asymptotic as $L \to \infty$ to a polynomial in $L$ of degree $6g-6+2n$. We establish asymptotics of the same kind for countings of multi-geodesics in mapping class group orbits of simple or filling closed multi-curves that keep track of the hyperbolic lengths of individual components, proving and generalizing a conjecture of Wolpert. In the simple case we consider more precise countings that also keep track of the class of the multi-geodesics in the space of projective measured geodesic laminations. We provide a unified geometric and topological description of the leading terms of the asymptotics of all the countings considered. Our proofs combine techniques and results from several papers of Mirzakhani as well as ideas introduced by Margulis in his thesis., Comment: 40 pages, 6 figures

In recent years, Multifactorial Optimization (MFO) has gained a notable momentum in the research community. MFO is known for its inherent capability to efficiently address multiple optimization tasks at the same time, while transferring information among such tasks to improve their convergence speed. On the other hand, the quantum leap made by Deep Q Learning (DQL) in the Machine Learning field has allowed facing Reinforcement Learning (RL) problems of unprecedented complexity. Unfortunately, complex DQL models usually find it difficult to converge to optimal policies due to the lack of exploration or sparse rewards. In order to overcome these drawbacks, pre-trained models are widely harnessed via Transfer Learning, extrapolating knowledge acquired in a source task to the target task. Besides, meta-heuristic optimization has been shown to reduce the lack of exploration of DQL models. This work proposes a MFO framework capable of simultaneously evolving several DQL models towards solving interrelated RL tasks. Specifically, our proposed framework blends together the benefits of meta-heuristic optimization, Transfer Learning and DQL to automate the process of knowledge transfer and policy learning of distributed RL agents. A thorough experimentation is presented and discussed so as to assess the performance of the framework, its comparison to the traditional methodology for Transfer Learning in terms of convergence, speed and policy quality , and the intertask relationships found and exploited over the search process., Comment: 8 pages, 5 figures, submitted to IEEE Conference on Evolutionary Computation 2020 (IEEE CEC)

In recent years, bio-inspired optimization methods, which mimic biological processes to solve complex problems, have gained popularity in recent literature. The proliferation of proposals prove the growing interest in this field. The increase in nature- and bio-inspired algorithms, applications, and guidelines highlights growing interest in this field. However, the exponential rise in the number of bio-inspired algorithms poses a challenge to the future trajectory of this research domain. Along the five versions of this document, the number of approaches grows incessantly, and where having a new biological description takes precedence over real problem-solving. This document presents two comprehensive taxonomies. One based on principles of biological similarity, and the other one based on operational aspects associated with the iteration of population models that initially have a biological inspiration. Therefore, these taxonomies enable researchers to categorize existing algorithmic developments into well-defined classes, considering two criteria: the source of inspiration, and the behavior exhibited by each algorithm. Using these taxonomies, we classify 518 algorithms based on nature-inspired and bio-inspired principles. Each algorithm within these categories is thoroughly examined, allowing for a critical synthesis of design trends and similarities, and identifying the most analogous classical algorithm for each proposal. From our analysis, we conclude that a poor relationship is often found between the natural inspiration of an algorithm and its behavior. Furthermore, similarities in terms of behavior between different algorithms are greater than what is claimed in their public disclosure: specifically, we show that more than one-fourth of the reviewed solvers are versions of classical algorithms. The conclusions from the analysis of the algorithms lead to several learned lessons., Comment: 89 pages, 9 figures

We apply the Walborn [Walborn S P, Taketani B G, Salles A, Toscano F and de Matos Filho R L 2009 Entropic Entanglement Criteria for Continuous Variables Phys. Rev. Lett. 103 160505] Shannon Entropic Entanglement Criterion (SEEC), to simple harmonic oscillators, a system typically discussed in undergraduate quantum mechanics courses. In particular, we investigate the entanglement of a system of coupled harmonic oscillators. A simple form of entanglement criterion in terms of their interaction is found. It is shown that a pair of interacting ground state coupled oscillators are more likely to be entangled for weaker coupling strengths while coupled oscillators in excited states entangle at higher coupling strengths. Interacting oscillators are more likely to be entangled as their interaction increases., Comment: 15 pages

With the advent of huges volumes of data produced in the form of fast streams, real-time machine learning has become a challenge of relevance emerging in a plethora of real-world applications. Processing such fast streams often demands high memory and processing resources. In addition, they can be affected by non-stationary phenomena (concept drift), by which learning methods have to detect changes in the distribution of streaming data, and adapt to these evolving conditions. A lack of efficient and scalable solutions is particularly noted in real-time scenarios where computing resources are severely constrained, as it occurs in networks of small, numerous, interconnected processing units (such as the so-called Smart Dust, Utility Fog, or Swarm Robotics paradigms). In this work we propose LUNAR, a streamified version of cellular automata devised to successfully meet the aforementioned requirements. It is able to act as a real incremental learner while adapting to drifting conditions. Extensive simulations with synthetic and real data will provide evidence of its competitive behavior in terms of classification performance when compared to long-established and successful online learning methods., Comment: 36 pages, 6 figures, 4 tables

Differences in data size per class, also known as imbalanced data distribution, have become a common problem affecting data quality. Big Data scenarios pose a new challenge to traditional imbalanced classification algorithms, since they are not prepared to work with such amount of data. Split data strategies and lack of data in the minority class due to the use of MapReduce paradigm have posed new challenges for tackling the imbalance between classes in Big Data scenarios. Ensembles have shown to be able to successfully address imbalanced data problems. Smart Data refers to data of enough quality to achieve high performance models. The combination of ensembles and Smart Data, achieved through Big Data preprocessing, should be a great synergy. In this paper, we propose a novel Smart Data driven Decision Trees Ensemble methodology for addressing the imbalanced classification problem in Big Data domains, namely SD_DeTE methodology. This methodology is based on the learning of different decision trees using distributed quality data for the ensemble process. This quality data is achieved by fusing Random Discretization, Principal Components Analysis and clustering-based Random Oversampling for obtaining different Smart Data versions of the original data. Experiments carried out in 21 binary adapted datasets have shown that our methodology outperforms Random Forest.

Given a simple closed curve $\gamma$ on a connected, oriented, closed surface $S$ of negative Euler characteristic, Mirzakhani showed that the set of points in the moduli space of hyperbolic structures on $S$ having a simple closed geodesic of length $L$ of the same topological type as $\gamma$ equidistributes with respect to a natural probability measure as $L \to \infty$. We prove several generalizations of Mirzakhani's result and discuss some of the technical aspects ommited in her original work. The dynamics of the earthquake flow play a fundamental role in the arguments in this paper., Comment: 41 pages

In the last years, Artificial Intelligence (AI) has achieved a notable momentum that may deliver the best of expectations over many application sectors across the field. For this to occur, the entire community stands in front of the barrier of explainability, an inherent problem of AI techniques brought by sub-symbolism (e.g. ensembles or Deep Neural Networks) that were not present in the last hype of AI. Paradigms underlying this problem fall within the so-called eXplainable AI (XAI) field, which is acknowledged as a crucial feature for the practical deployment of AI models. This overview examines the existing literature in the field of XAI, including a prospect toward what is yet to be reached. We summarize previous efforts to define explainability in Machine Learning, establishing a novel definition that covers prior conceptual propositions with a major focus on the audience for which explainability is sought. We then propose and discuss about a taxonomy of recent contributions related to the explainability of different Machine Learning models, including those aimed at Deep Learning methods for which a second taxonomy is built. This literature analysis serves as the background for a series of challenges faced by XAI, such as the crossroads between data fusion and explainability. Our prospects lead toward the concept of Responsible Artificial Intelligence, namely, a methodology for the large-scale implementation of AI methods in real organizations with fairness, model explainability and accountability at its core. Our ultimate goal is to provide newcomers to XAI with a reference material in order to stimulate future research advances, but also to encourage experts and professionals from other disciplines to embrace the benefits of AI in their activity sectors, without any prior bias for its lack of interpretability., Comment: 67 pages, 13 figures, accepted for its publication in Information Fusion

The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provides a comprehensive survey on works that employ Deep Learning models to solve the task of MOT on single-camera videos. Four main steps in MOT algorithms are identified, and an in-depth review of how Deep Learning was employed in each one of these stages is presented. A complete experimental comparison of the presented works on the three MOTChallenge datasets is also provided, identifying a number of similarities among the top-performing methods and presenting some possible future research directions., Comment: Accepted in Neurocomputing, 2019. New in v4: updated license in compliance with Elsevier policy. Main text: 29 pages, 10 figures, 7 tables. Summary table in appendix at the end of the paper

Given integers $g,n \geq 0$ satisfying $2-2g-n < 0$, let $\mathcal{M}_{g,n}$ be the moduli space of connected, oriented, complete, finite area hyperbolic surfaces of genus $g$ with $n$ cusps. We study the global behavior of the Mirzakhani function $B \colon \mathcal{M}_{g,n} \to \mathbf{R}_{\geq 0}$ which assigns to $X \in \mathcal{M}_{g,n}$ the Thurston measure of the set of measured geodesic laminations on $X$ of hyperbolic length $\leq 1$. We improve bounds of Mirzakhani describing the behavior of this function near the cusp of $\mathcal{M}_{g,n}$ and deduce that $B$ is square-integrable with respect to the Weil-Petersson volume form. We relate this knowledge of $B$ to statistics of counting problems for simple closed hyperbolic geodesics., Comment: 28 pages

We show that the number of square-tiled surfaces of genus $g$, with $n$ marked points, with one or both of its horizontal and vertical foliations belonging to fixed mapping class group orbits, and having at most $L$ squares, is asymptotic to $L^{6g-6+2n}$ times a product of constants appearing in Mirzakhani's count of simple closed hyperbolic geodesics. Many of the results in this paper reflect recent discoveries of Delecroix, Goujard, Zograf, and Zorich, but the approach considered here is very different from theirs. We follow conceptual and geometric methods inspired by Mirzakhani's work., Comment: 27 pages, 3 figures

Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this topic and a comprehensive experimental analysis of the most-known algorithms. We start by describing the distance metric learning problem and its main mathematical foundations, divided into three main blocks: convex analysis, matrix analysis and information theory. Then, we will describe a representative set of the most popular distance metric learning methods used in classification. All the algorithms studied in this paper will be evaluated with exhaustive testing in order to analyze their capabilities in standard classification problems, particularly considering dimensionality reduction and kernelization. The results, verified by Bayesian statistical tests, highlight a set of outstanding algorithms. Finally, we will discuss several potential future prospects and challenges in this field. This tutorial will serve as a starting point in the domain of distance metric learning from both a theoretical and practical perspective., Comment: 36 pages with appendices