On the usage of the probability integral transform to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems

We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts their shape and position to the real distribution of training data. A two-step process is applied : 1) transformation of the original distribution into a standard uniform distribution by means of the probability integral transform. Since the original distribution is generally unknown, the cumulative distribution function is approximated by computing the q-quantiles of the training set; 2) construction of a Ruspini strong fuzzy partition in the transformed attribute space using a fixed number of equally distributed triangular membership functions. Despite the aforementioned transformation, the definition of every fuzzy set in the original space can be recovered by applying the inverse cumulative distribution function (also known as quantile function). The experimental results reveal that the proposed methodology allows the state-of-the-art multi-way fuzzy decision tree (FMDT) induction algorithm to maintain classification accuracy with up to 6 million fewer leaves.Comment: Appeared in 2018 IEEE International Congress on Big Data (BigData Congress). arXiv admin note: text overlap with arXiv:1902.0935

Economic and financial analysis of Das-Nano Group

El presente trabajo de fin de grado consiste en la aplicación de la metodología del análisis de los estados financieros de una empresa o grupo empresarial. Este análisis se ha realizado con una apertura de miras considerable, sin limitarse al cálculo de una serie de ratios, intentando integrar conceptos como el entorno, tanto externo como interno, y el estudio del patrimonio con el análisis de la rentabilidad y el riesgo. En concreto se ha llevado a cabo el análisis del grupo empresarial GRUPO DAS-NANO, especializado en el sector de la inteligencia artificial. Destacando,sobre todo, en el campo de las soluciones basadas en ondas de terahercios para procesos industriales.This final degree project consists of the application of the methodology of the analysis of the financial statements of a company or business group. This analysis has been carried out with considerable open-mindedness, not limited to the calculation of a series of ratios, trying to integrate concepts such as the environment, both external and internal, and the patrimonial study with the analysis of profitability and risk. Specifically, the analysis of the business group GRUPO DAS-NANO, specialized in the artificial intelligence sector, has been carried out. It stands out, above all, in the field of terahertz wave-based solutions for industrial processes. In order to carry out the financial economic analysis, we have accessed the annual accounts of the group through the SABI database.Graduado o Graduada en Administración y Dirección de Empresas por la Universidad Pública de Navarra (Programa Internacional)Enpresen Administrazio eta Zuzendaritzan Graduatua Nafarroako Unibertsitate Publikoan (Nazioarteko Programa

Enhancing multi-class classification in FARC-HD fuzzy classifier: on the synergy between n-dimensional overlap functions and decomposition strategies

There are many real-world classification problems involving multiple classes, e.g., in bioinformatics, computer vision or medicine. These problems are generally more difficult than their binary counterparts. In this scenario, decomposition strategies usually improve the performance of classifiers. Hence, in this paper we aim to improve the behaviour of FARC-HD fuzzy classifier in multi-class classification problems using decomposition strategies, and more specifically One-vs-One (OVO) and One-vs-All (OVA) strategies. However, when these strategies are applied on FARC-HD a problem emerges due to the low confidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product t-norm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of the fuzzy rules. As a result, robust aggregation strategies in OVO such as the weighted voting obtain poor results with this fuzzy classifier. In order to solve these problems, we propose to adapt the inference system of FARC-HD replacing the product t-norm with overlap functions. To do so, we define n-dimensional overlap functions. The usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in OVO and OVA schemes. Furthermore, we propose a new aggregation strategy for OVO to deal with the problem of the weighted voting derived from the inappropriate confidences provided by FARC-HD for this aggregation method. The quality of our new approach is analyzed using twenty datasets and the conclusions are supported by a proper statistical analysis. In order to check the usefulness of our proposal, we carry out a comparison against some of the state-of-the-art fuzzy classifiers. Experimental results show the competitiveness of our method.This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2011-28488, TIN-2012-33856 and TIN-2013- 40765-P and the Andalusian Research Plan P10-TIC-6858 and P11-TIC-7765