Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Designing labeled graph classifiers by exploiting the R\'enyi entropy of the dissimilarity representation

Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowadays available and tested for various datasets of labeled graphs. However, the design of effective learning procedures operating in the space of labeled graphs is still a challenging problem, especially from the computational complexity viewpoint. In this paper, we present a major improvement of a general-purpose classifier for graphs, which is conceived on an interplay between dissimilarity representation, clustering, information-theoretic techniques, and evolutionary optimization algorithms. The improvement focuses on a specific key subroutine devised to compress the input data. We prove different theorems which are fundamental to the setting of the parameters controlling such a compression operation. We demonstrate the effectiveness of the resulting classifier by benchmarking the developed variants on well-known datasets of labeled graphs, considering as distinct performance indicators the classification accuracy, computing time, and parsimony in terms of structural complexity of the synthesized classification models. The results show state-of-the-art standards in terms of test set accuracy and a considerable speed-up for what concerns the computing time.Comment: Revised versio

A Short Survey on Data Clustering Algorithms

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial analysis. Formally speaking, given a set of data instances, a clustering algorithm is expected to divide the set of data instances into the subsets which maximize the intra-subset similarity and inter-subset dissimilarity, where a similarity measure is defined beforehand. In this work, the state-of-the-arts clustering algorithms are reviewed from design concept to methodology; Different clustering paradigms are discussed. Advanced clustering algorithms are also discussed. After that, the existing clustering evaluation metrics are reviewed. A summary with future insights is provided at the end

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Spectral and spatial methods for the classification of urban remote sensing data

Lors de ces travaux, nous nous sommes intéressés au problème de la classification supervisée d'images satellitaires de zones urbaines. Les données traitées sont des images optiques à très hautes résolutions spatiales: données panchromatiques à très haute résolution spatiale (IKONOS, QUICKBIRD, simulations PLEIADES) et des images hyperspectrales (DAIS, ROSIS). Deux stratégies ont été proposées. La première stratégie consiste en une phase d'extraction de caractéristiques spatiales et spectrales suivie d'une phase de classification. Ces caractéristiques sont extraites par filtrages morphologiques : ouvertures et fermetures géodésiques et filtrages surfaciques auto-complémentaires. La classification est réalisée avec les machines à vecteurs supports (SVM) non linéaires. Nous proposons la définition d'un noyau spatio-spectral utilisant de manière conjointe l'information spatiale et l'information spectrale extraites lors de la première phase. La seconde stratégie consiste en une phase de fusion de données pre- ou post-classification. Lors de la fusion postclassification, divers classifieurs sont appliqués, éventuellement sur plusieurs données issues d'une même scène (image panchromat ique, image multi-spectrale). Pour chaque pixel, l'appartenance à chaque classe est estimée à l'aide des classifieurs. Un schéma de fusion adaptatif permettant d'utiliser l'information sur la fiabilité locale de chaque classifieur, mais aussi l'information globale disponible a priori sur les performances de chaque algorithme pour les différentes classes, est proposé. Les différents résultats sont fusionnés à l'aide d'opérateurs flous. Les méthodes ont été validées sur des images réelles. Des améliorations significatives sont obtenues par rapport aux méthodes publiées dans la litterature