Detecting spatial patterns with the cumulant function. Part I: The theory

In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF) decomposition, is often applied on this purpose, it can only provide meaningful results if the underlying multivariate distribution is Gaussian. Indeed, PCA is based on optimizing second order moments quantities and the covariance matrix can only capture the full dependence structure for multivariate Gaussian vectors. Whenever the application at hand can not satisfy this normality hypothesis (e.g. precipitation data), alternatives and/or improvements to PCA have to be developed and studied. To go beyond this second order statistics constraint that limits the applicability of the PCA, we take advantage of the cumulant function that can produce higher order moments information. This cumulant function, well-known in the statistical literature, allows us to propose a new, simple and fast procedure to identify spatial patterns for non-Gaussian data. Our algorithm consists in maximizing the cumulant function. To illustrate our approach, its implementation for which explicit computations are obtained is performed on three family of of multivariate random vectors. In addition, we show that our algorithm corresponds to selecting the directions along which projected data display the largest spread over the marginal probability density tails.Comment: 9 pages, 3 figure

A taxonomy framework for unsupervised outlier detection techniques for multi-type data sets

The term "outlier" can generally be defined as an observation that is significantly different from the other values in a data set. The outliers may be instances of error or indicate events. The task of outlier detection aims at identifying such outliers in order to improve the analysis of data and further discover interesting and useful knowledge about unusual events within numerous applications domains. In this paper, we report on contemporary unsupervised outlier detection techniques for multiple types of data sets and provide a comprehensive taxonomy framework and two decision trees to select the most suitable technique based on data set. Furthermore, we highlight the advantages, disadvantages and performance issues of each class of outlier detection techniques under this taxonomy framework

Online real-time crowd behavior detection in video sequences

Automatically detecting events in crowded scenes is a challenging task in Computer Vision. A number of offline approaches have been proposed for solving the problem of crowd behavior detection, however the offline assumption limits their application in real-world video surveillance systems. In this paper, we propose an online and real-time method for detecting events in crowded video sequences. The proposed approach is based on the combination of visual feature extraction and image segmentation and it works without the need of a training phase. A quantitative experimental evaluation has been carried out on multiple publicly available video sequences, containing data from various crowd scenarios and different types of events, to demonstrate the effectiveness of the approach