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Users want to know the reliability of the recommendations; they do not accept high predictions if there is no reliability evidence. Recommender systems should provide reliability values associated with the predictions. Research into reliability measures requires the existence of simple, plausible and universal reliability quality measures. Research into recommender system quality measures has focused on accuracy. Moreover, novelty, serendipity and diversity have been studied; nevertheless there is an important lack of research into reliability/confidence quality measures. This paper proposes a reliability quality prediction measure (RPI) and a reliability quality recommendation measure (RRI). Both quality measures are based on the hypothesis that the more suitable a reliability measure is, the better accuracy results it will provide when applied. These reliability quality measures show accuracy improvements when appropriated reliability values are associated with their predictions (i.e. high reliability values associated with correct predictions or low reliability values associated with incorrect predictions). The proposed reliability quality metrics will lead to the design of brand new recommender system reliability measures. These measures could be applied to different matrix factorization techniques and to content-based, context-aware and social recommendation approaches. The recommender system reliability measures designed could be tested, compared and improved using the proposed reliability quality metrics.

Recommender Systems (RS) provide a relevant tool to mitigate the information overload problem. A large number of researchers have published hundreds of papers to improve different RS features. It is advisable to use RS frameworks that simplify RS researchers: a) to design and implement recommendations methods and, b) to speed up the execution time of the experiments. In this paper, we present CF4J, a Java library designed to carry out Collaborative Filtering based RS research experiments. CF4J has been designed from researchers to researchers. It allows: a) RS datasets reading, b) full and easy access to data and intermediate or final results, c) to extend their main functionalities, d) to concurrently execute the implemented methods, and e) to provide a thorough evaluation for the implementations by quality measures. In summary, CF4J serves as a library specifically designed for the research trial and error process.

We obtain the kinematic distributions of stars (synthetic model line absorption) and ionized gas (H$\alpha$ line emission) for star-forming regions residing in CALIFA survey tidally perturbed (perturbed) and non-tidally perturbed (control) galaxies. We set the uncertainties of the velocity dispersion by measuring the statistical variability of the datasets themselves. Using these adopted uncertainties and considering the sensitivity of the grating device, we establish thresholds of reliability that allow us to select reliable velocity dispersions. From this selection, we pair the star-forming spaxels between control and perturbed galaxies at the closest shifts in velocity (de-redshifting). We compare their respective distributions of velocity dispersion. In perturbed galaxies, median velocity dispersions for the stellar and gaseous components are minimally higher and equal, respectively, than those in control galaxies. The spread in velocity dispersion and the velocity shift - velocity dispersion space agree with this result. Unlike the well-known trend in strongly interacting systems, the stellar and ionized-gas motions are not disturbed by the influence of close companions. For the gaseous component, this result is due to the poor statistical variability of its data, a consequence of the tightness in velocity dispersion derived from high spectral line intensities. This analysis concludes the series, which previously showed star-forming regions in galaxies with close companions undergoing more prominent gas inflows, resulting in differences in their star formation and consequent metal content.

Recommender systems are intrinsically tied to a reliability/coverage dilemma: The more reliable we desire the forecasts, the more conservative the decision will be and thus, the fewer items will be recommended. This causes a detriment to the predictive capability of the system, as it is only able to estimate potential interest in items for which there is a consensus in their evaluation, rather than being able to estimate potential interest in any item. In this paper, we propose the inclusion of a new term in the learning process of matrix factorization-based recommender systems, called recklessness, that takes into account the variance of the output probability distribution of the predicted ratings. In this way, gauging this recklessness measure we can force more spiky output distribution, enabling the control of the risk level desired when making decisions about the reliability of a prediction. Experimental results demonstrate that recklessness not only allows for risk regulation but also improves the quantity and quality of predictions provided by the recommender system., Comment: 15 pages, 4 figures, 2 tables

Modern society devotes a significant amount of time to digital interaction. Many of our daily actions are carried out through digital means. This has led to the emergence of numerous Artificial Intelligence tools that assist us in various aspects of our lives. One key tool for the digital society is Recommender Systems, intelligent systems that learn from our past actions to propose new ones that align with our interests. Some of these systems have specialized in learning from the behavior of user groups to make recommendations to a group of individuals who want to perform a joint task. In this article, we analyze the current state of Group Recommender Systems and propose two new models that use emerging Deep Learning architectures. Experimental results demonstrate the improvement achieved by employing the proposed models compared to the state-of-the-art models using four different datasets. The source code of the models, as well as that of all the experiments conducted, is available in a public repository.

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., Comment: 16 pages, 4 figures, submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence

Students' perception of excessive difficulty in STEM degrees lowers their motivation and therefore affects their performance. According to prior research, the use of gamification techniques promote engagement, motivation and fun when learning. Badges, which are a distinction that is given as a reward to students, are a well-known gamification tool. This contribution hypothesizes that the use of badges, both physical and virtual, improves student performance and reduces dropout rates. To verify that hypothesis, a case study involving 99 students enrolled in a Databases course of computer engineering degrees was conducted. The results show that the usage of badges improves student performance and reduces dropout rates. However, negligible differences were found between the use of different kind of badges.

Recommendation to groups of users is a challenging subfield of recommendation systems. Its key concept is how and where to make the aggregation of each set of user information into an individual entity, such as a ranked recommendation list, a virtual user, or a multi-hot input vector encoding. This paper proposes an innovative strategy where aggregation is made in the multi-hot vector that feeds the neural network model. The aggregation provides a probabilistic semantic, and the resulting input vectors feed a model that is able to conveniently generalize the group recommendation from the individual predictions. Furthermore, using the proposed architecture, group recommendations can be obtained by simply feedforwarding the pre-trained model with individual ratings; that is, without the need to obtain datasets containing group of user information, and without the need of running two separate trainings (individual and group). This approach also avoids maintaining two different models to support both individual and group learning. Experiments have tested the proposed architecture using three representative collaborative filtering datasets and a series of baselines; results show suitable accuracy improvements compared to the state-of-the-art.

Reliability measures associated with the prediction of the machine learning models are critical to strengthening user confidence in artificial intelligence. Therefore, those models that are able to provide not only predictions, but also reliability, enjoy greater popularity. In the field of recommender systems, reliability is crucial, since users tend to prefer those recommendations that are sure to interest them, that is, high predictions with high reliabilities. In this paper, we propose Restricted Bernoulli Matrix Factorization (ResBeMF), a new algorithm aimed at enhancing the performance of classification-based collaborative filtering. The proposed model has been compared to other existing solutions in the literature in terms of prediction quality (Mean Absolute Error and accuracy scores), prediction quantity (coverage score) and recommendation quality (Mean Average Precision score). The experimental results demonstrate that the proposed model provides a good balance in terms of the quality measures used compared to other recommendation models., Comment: Several changes performed, including a title change. 21 pages, 7 figures, 2 tables

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., Comment: 14 pages, 8 figures, 3 tables

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., Comment: 20 pages, 14 figures, 1 table

The lack of bias management in Recommender Systems leads to minority groups receiving unfair recommendations. Moreover, the trade-off between equity and precision makes it difficult to obtain recommendations that meet both criteria. Here we propose a Deep Learning based Collaborative Filtering algorithm that provides recommendations with an optimum balance between fairness and accuracy without knowing demographic information about the users. Experimental results show that it is possible to make fair recommendations without losing a significant proportion of accuracy., Comment: 18 pages, 9 figures, 4 tables

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., Comment: 28 pages, 8 figures, 8 tables

We present a 2-dimensional chemical evolution code applied to a Milky Way type galaxy, incorporating the role of spiral arms in shaping azimuthal abundance variations, and confront the predicted behaviour with recent observations taken with integral field units. To the usual radial distribution of mass, we add the surface density of the spiral wave and study its effect on star formation and elemental abundances. We compute five different models: one with azimuthal symmetry which depends only on radius, while the other four are subjected to the effect of a spiral density wave. At early times, the imprint of the spiral density wave is carried by both the stellar and star formation surface densities; conversely, the elemental abundance pattern is less affected. At later epochs, however, differences among the models are diluted, becoming almost indistinguishable given current observational uncertainties. At the present time, the largest differences appear in the star formation rate and/or in the outer disc (R$\ge$ 18\,kpc). The predicted azimuthal oxygen abundance patterns for $t \le 2$\,Gyr are in reasonable agreement with recent observations obtained with VLT/MUSE for NGC 6754, Comment: 19 pages, 12 figures, MNRAS to be published

This paper studies the equilibrium of an extended case of the classical Samuelson's multiplier-accelerator model for national economy. This case has incorporated some kind of memory into the system. We assume that total consumption and private investment depend upon the national income values. Then, delayed difference equations of third order are employed to describe the model, while the respective solutions of third order polynomial, correspond to the typical observed business cycles of real economy. We focus on the case that the equilibrium is not unique and provide a method to obtain the optimal equilibrium.

In this paper we revisit the famous classical Samuelson's multiplier-accelerator model for national economy. We reform this model into a singular discrete time system and study its solutions. The advantage of this study gives a better understanding of the structure of the model and more deep and elegant results.

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix. We focus on the optimal solutions of the system and derive easily testable conditions for stability.

In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into consideration the case that the coefficients are square constant matrices with the leading coefficient singular and provide optimal solutions. Numerical examples are given to justify our theory., Comment: arXiv admin note: substantial text overlap with arXiv:1610.00927; substantial text overlap with arXiv:1510.07438 by other authors

In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant matrices with the leading coefficient singular. We provide optimal solutions and numerical examples to justify our theory., Comment: arXiv admin note: text overlap with arXiv:1512.04740

We consider two type of systems, a linear singular discrete time system and a linear singular fractional discrete time system whose coefficients are square constant matrices. By assuming that the input vector changes only at equally space sampling instants we investigate and provide properties for causality between state and inputs and causality between output and inputs., Comment: arXiv admin note: text overlap with arXiv:1406.6669 by other authors