Spatially Weighted Principal Component Analysis for Imaging Classification

The aim of this paper is to develop a supervised dimension reduction framework, called Spatially Weighted Principal Component Analysis (SWPCA), for high dimensional imaging classification. Two main challenges in imaging classification are the high dimensionality of the feature space and the complex spatial structure of imaging data. In SWPCA, we introduce two sets of novel weights including global and local spatial weights, which enable a selective treatment of individual features and incorporation of the spatial structure of imaging data and class label information. We develop an e cient two-stage iterative SWPCA algorithm and its penalized version along with the associated weight determination. We use both simulation studies and real data analysis to evaluate the finite-sample performance of our SWPCA. The results show that SWPCA outperforms several competing principal component analysis (PCA) methods, such as supervised PCA (SPCA), and other competing methods, such as sparse discriminant analysis (SDA)

Robust principal components for hyperspectral data analysis

Remote sensing data present peculiar features and characteristics that may make their statistical processing and analysis a difficult task. Among them, it can be mentioned the volume of data involved, the redundancy, the presence of unexpected values that arise mainly due to noisy pixels and background objects whose responses to the sensor are very different from those of their neighbours. Sometimes, the volume of data and number of variables involved is so large that any statistical analysis becomes unmanageable if data are not condensed in some way. A commonly used method to deal with this situation is Principal Component Analysis (PCA) based on classical statistics: sample mean and covariance matrices. The drawback in using sample covariance or correlation matrices as measures of variability is their high sensitivity to spurious values. In this work we analyse and evaluate the use of some Robust Principal Component techniques and make a comparison of Robust and Classical PCs performances when applied to satellite data provided by the hyperspectral sensor AVIRIS (Airborne Visible/Infrared Imaging Spectrometer). We conclude that some robust approaches are the most reliable and precise when applied as a data reduction technique before performing supervised image classification. © 2009 Springer Berlin Heidelberg.Fil: Lucini, María Magdalena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; ArgentinaFil: Frery, Alejandro César. Universidade Federal de Alagoas; Brasi

Investigação do Modo Sul em dados de precipitação no período de 1982 a 2006 no estado do Rio Grande do Sul Research of "modo sul" on rainfall data during the period from 1982 to 2006 in Rio Grande do Sul state

Este trabalho apresenta o estudo de um modo de variabilidade que influencia a precipitação no Sul do Brasil e é chamado Modo Sul de precipitação. Será mostrado que a ocorrência de máximos (e mínimos) do Modo Sul de precipitação pode estar relacionada à ocorrência de eventos extremos no Rio Grande do Sul, como vendavais, enchentes, granizo e estiagens Utilizando a análise de componentes principais em dados de precipitação diária filtrados na banda 10-50 dias, são encontrados campos espaciais e temporais que representam a máxima variância de determinadas variabilidades, e neles são detectados Modos de Variabilidade de precipitação. Desta maneira, foi possível determinar este modo de variabilidade, que aparece bem configurado na região do Rio Grande do Sul. A série de componentes principais foi usada para a escolha desses eventos. O Modo Sul foi calculado para o período de 01/03/1982 à 31/05/2006. Foi possível identificar que os eventos extremos chuvosos ocorreram em maior número do que os eventos extremos secos. Na análise decadal verificou-se um aumento no número de eventos, quando comparada às décadas de 80, 90 e 2000. Vale ressaltar que o número de eventos da década de 2000 em relação à década de 80 (proporcionalmente) foi o mais expressivo.<br>This work presents a study of a rainfall variability mode that acts in southern Brazil and is called "Modo Sul" of precipitation. It was tried to show that the occurrences of maximum (and minimum) of the "Modo Sul" of precipitation are related to the occurrence of extreme events in Rio Grande do Sul, as windstorm, flood, hail and drought. Using principal component analysis of daily filtered precipitation data for the 10-50 day band we found spatial pattern and temporal series that represent the maximum variance of certain variabilities, which are the modes of precipitation variability. Thus, it was possible to determine the mode of variability that appears well established in Rio Grande do Sul. The principal component series was used to select the extreme events. The "Modo Sul" was calculated for the period from 01/03/1982 to 31/05/2006. It was possible to realize that the extreme rainy events were more frequent than extreme dry events. In a decadal analysis an increase in the number of events was found when comparing the 80s, 90s and 2000. It is noteworthy that the number of events of 2000s compared with the 80s was proportionally the most expressive