A spatial-type interval-valued median for random intervals

© 2018 Informa UK Limited, trading as Taylor & Francis Group. To estimate the central tendency or location of a sample of interval-valued data, a standard statistic is the interval-valued sample mean. Its strong sensitivity to outliers or data changes motivates the search for more robust alternatives. In this respect, a more robust location statistic is studied in this paper. This measure is inspired by the concept of spatial median and makes use of the versatile generalized Bertoluzza's metric between intervals, the so-called dθ distance. The problem of minimizing the mean dθ distance to the values the random interval takes, which defines the spatial-type dθ-median, is analysed. Existence and uniqueness of the sample version are shown. Furthermore, the robustness of this proposal is investigated by deriving its finite sample breakdown point. Finally, a real-life example from the Economics field illustrates the robustness of the sample dθ-median, and simulation studies show some comparisons with respect to the mean and several recently introduced robust location measures for interval-valued data.status: publishe

Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Archetypes for histogram-valued data

Il principale sviluppo innovativo del lavoro è quello di propone una estensione dell'analisi archetipale per dati ad istogramma. Per quanto concerne l'impianto metodologico nell'approccio all'analisi di dati ad istogramma, che sono di natura complessa, il presente lavora utilizza le intuizioni della "Symbolic Data Analysis" (SDA) e le relazioni intrinseche tra dati valutati ad intervallo e dati valutati ad istogramma. Dopo aver discusso la tecnica sviluppata in ambiente Matlab, il suo funzionamento e le sue proprietà su di un esempio di comodo, tale tecnica viene proposta, nella sezione applicativa, come strumento per effettuare una analisi di tipo "benchmarking" quantitativo. Nello specifico, si propongono i principali risultati ottenuti da una applicazione degli archetipi per dati ad istogramma ad un caso di benchmarking interno del sistema scolastico, utilizzando dati provenienti dal test INVALSI relativi all'anno scolastico 2015/2016. In questo contesto l'unità di analisi è considerata essere la singola scuola, definita operativamente attraverso le distribuzioni dei punteggi dei propri alunni valutate, congiuntamente, sotto forma di oggetti simbolici ad istogramma

On the consistency of a spatial-type interval-valued median for random intervals

The sample $d_\theta$-median is a robust estimator of the central tendency or location of an interval-valued random variable. While the interval-valued sample mean can be highly influenced by outliers, this spatial-type interval-valued median remains much more reliable. In this paper, we show that under general conditions the sample $d_\theta$-median is a strongly consistent estimator of the $d_\theta$-median of an interval-valued random variable.Comment: 14 page

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

A Survey of Adaptive Resonance Theory Neural Network Models for Engineering Applications

This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a general picture of the architectures developed by researchers over the past 30 years. The learning dynamics of these ART models are briefly described, and their distinctive characteristics such as code representation, long-term memory and corresponding geometric interpretation are discussed. Useful engineering properties of ART (speed, configurability, explainability, parallelization and hardware implementation) are examined along with current challenges. Finally, a compilation of online software libraries is provided. It is expected that this overview will be helpful to new and seasoned ART researchers

Sistemas granulares evolutivos

Orientador: Fernando Antonio Campos GomideTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Recentemente tem-se observado um crescente interesse em abordagens de modelagem computacional para lidar com fluxos de dados do mundo real. Métodos e algoritmos têm sido propostos para obtenção de conhecimento a partir de conjuntos de dados muito grandes e, a princípio, sem valor aparente. Este trabalho apresenta uma plataforma computacional para modelagem granular evolutiva de fluxos de dados incertos. Sistemas granulares evolutivos abrangem uma variedade de abordagens para modelagem on-line inspiradas na forma com que os humanos lidam com a complexidade. Esses sistemas exploram o fluxo de informação em ambiente dinâmico e extrai disso modelos que podem ser linguisticamente entendidos. Particularmente, a granulação da informação é uma técnica natural para dispensar atenção a detalhes desnecessários e enfatizar transparência, interpretabilidade e escalabilidade de sistemas de informação. Dados incertos (granulares) surgem a partir de percepções ou descrições imprecisas do valor de uma variável. De maneira geral, vários fatores podem afetar a escolha da representação dos dados tal que o objeto representativo reflita o significado do conceito que ele está sendo usado para representar. Neste trabalho são considerados dados numéricos, intervalares e fuzzy; e modelos intervalares, fuzzy e neuro-fuzzy. A aprendizagem de sistemas granulares é baseada em algoritmos incrementais que constroem a estrutura do modelo sem conhecimento anterior sobre o processo e adapta os parâmetros do modelo sempre que necessário. Este paradigma de aprendizagem é particularmente importante uma vez que ele evita a reconstrução e o retreinamento do modelo quando o ambiente muda. Exemplos de aplicação em classificação, aproximação de função, predição de séries temporais e controle usando dados sintéticos e reais ilustram a utilidade das abordagens de modelagem granular propostas. O comportamento de fluxos de dados não-estacionários com mudanças graduais e abruptas de regime é também analisado dentro do paradigma de computação granular evolutiva. Realçamos o papel da computação intervalar, fuzzy e neuro-fuzzy em processar dados incertos e prover soluções aproximadas de alta qualidade e sumário de regras de conjuntos de dados de entrada e saída. As abordagens e o paradigma introduzidos constituem uma extensão natural de sistemas inteligentes evolutivos para processamento de dados numéricos a sistemas granulares evolutivos para processamento de dados granularesAbstract: In recent years there has been increasing interest in computational modeling approaches to deal with real-world data streams. Methods and algorithms have been proposed to uncover meaningful knowledge from very large (often unbounded) data sets in principle with no apparent value. This thesis introduces a framework for evolving granular modeling of uncertain data streams. Evolving granular systems comprise an array of online modeling approaches inspired by the way in which humans deal with complexity. These systems explore the information flow in dynamic environments and derive from it models that can be linguistically understood. Particularly, information granulation is a natural technique to dispense unnecessary details and emphasize transparency, interpretability and scalability of information systems. Uncertain (granular) data arise from imprecise perception or description of the value of a variable. Broadly stated, various factors can affect one's choice of data representation such that the representing object conveys the meaning of the concept it is being used to represent. Of particular concern to this work are numerical, interval, and fuzzy types of granular data; and interval, fuzzy, and neurofuzzy modeling frameworks. Learning in evolving granular systems is based on incremental algorithms that build model structure from scratch on a per-sample basis and adapt model parameters whenever necessary. This learning paradigm is meaningful once it avoids redesigning and retraining models all along if the system changes. Application examples in classification, function approximation, time-series prediction and control using real and synthetic data illustrate the usefulness of the granular approaches and framework proposed. The behavior of nonstationary data streams with gradual and abrupt regime shifts is also analyzed in the realm of evolving granular computing. We shed light upon the role of interval, fuzzy, and neurofuzzy computing in processing uncertain data and providing high-quality approximate solutions and rule summary of input-output data sets. The approaches and framework introduced constitute a natural extension of evolving intelligent systems over numeric data streams to evolving granular systems over granular data streamsDoutoradoAutomaçãoDoutor em Engenharia Elétric

QCBA: Postoptimization of Quantitative Attributes in Classifiers based on Association Rules

The need to prediscretize numeric attributes before they can be used in association rule learning is a source of inefficiencies in the resulting classifier. This paper describes several new rule tuning steps aiming to recover information lost in the discretization of numeric (quantitative) attributes, and a new rule pruning strategy, which further reduces the size of the classification models. We demonstrate the effectiveness of the proposed methods on postoptimization of models generated by three state-of-the-art association rule classification algorithms: Classification based on Associations (Liu, 1998), Interpretable Decision Sets (Lakkaraju et al, 2016), and Scalable Bayesian Rule Lists (Yang, 2017). Benchmarks on 22 datasets from the UCI repository show that the postoptimized models are consistently smaller -- typically by about 50% -- and have better classification performance on most datasets