Search results for " Principal Component Analysis"

Learning non-linear time-scales with kernel -filters

2009

A family of kernel methods, based on the @c-filter structure, is presented for non-linear system identification and time series prediction. The kernel trick allows us to develop the natural non-linear extension of the (linear) support vector machine (SVM) @c-filter [G. Camps-Valls, M. Martinez-Ramon, J.L. Rojo-Alvarez, E. Soria-Olivas, Robust @c-filter using support vector machines, Neurocomput. J. 62(12) (2004) 493-499.], but this approach yields a rigid system model without non-linear cross relation between time-scales. Several functional analysis properties allow us to develop a full, principled family of kernel @c-filters. The improved performance in several application examples suggest…

Sperm kinematic, head morphometric and kinetic-morphometric subpopulations in the blue fox (Alopex lagopus)

2016

This work provides information on the blue fox ejaculated sperm quality needed for seminal dose calculations. Twenty semen samples, obtained by masturbation, were analyzed for kinematic and morphometric parameters by using CASA-Mot and CASA-Morph system and principal component (PC) analysis. For motility, eight kinematic parameters were evaluated, which were reduced to PC1, related to linear variables, and PC2, related to oscillatory movement. The whole population was divided into three independent subpopulations: SP1, fast cells with linear movement; SP2, slow cells and nonoscillatory motility; and SP3, medium speed cells and oscillatory movement. In almost all cases, the subpopulation dis…

A new methodology for Functional Principal Component Analysis from scarce data. Application to stroke rehabilitation.

2015

Functional Principal Component Analysis (FPCA) is an increasingly used methodology for analysis of biomedical data. This methodology aims to obtain Functional Principal Components (FPCs) from Functional Data (time dependent functions). However, in biomedical data, the most common scenario of this analysis is from discrete time values. Standard procedures for FPCA require obtaining the functional data from these discrete values before extracting the FPCs. The problem appears when there are missing values in a non-negligible sample of subjects, especially at the beginning or the end of the study, because this approach can compromise the analysis due to the need to extrapolate or dismiss subje…

Agronomic, metabolomic and lipidomic characterization of Sicilian Origanum vulgare (L.) ecotypes

2016

Although Origanum vulgare (L.) has been deeply analysed at phytochemical level, poor knowledge is available regarding non-volatile compounds such as lipids. The aim of this work was to characterise five wild Sicilian Origanum ecotypes from an agronomic, metabolomic and lipidomic perspective. Serradifalco presented higher dry weight and inflorescences/plant than the others while Favara had a significantly higher number of branches per plant and more extensive flowered stratum. Metabolomic analysis, performed with LC-MS-TOF, allowed a preliminary characterisation of the non-volatile metabolome of the five oregano ecotypes Origanum vulgare ssp. hirtum. Twenty-five metabolites were identified b…

Estimation of total electricity consumption curves of small areas by sampling in a finite population

2016

International audience; Many studies carried out in the French electricity company EDF are based on the analysis of the total electricity consumption curves of groups of customers. These aggregated electricity consumption curves are estimated by using samples of thousands of curves measured at a small time step and collected according to a sampling design. Small area estimation is very usual in survey sampling. It is often addressed by using implicit or explicit domain models between the interest variable and the auxiliary variables. The goal here is to estimate totals of electricity consumption curves over domains or areas. Three approaches are compared: the rst one consists in modeling th…

Signal-to-noise ratio in reproducing kernel Hilbert spaces

2018

This paper introduces the kernel signal-to-noise ratio (kSNR) for different machine learning and signal processing applications}. The kSNR seeks to maximize the signal variance while minimizing the estimated noise variance explicitly in a reproducing kernel Hilbert space (rkHs). The kSNR gives rise to considering complex signal-to-noise relations beyond additive noise models, and can be seen as a useful signal-to-noise regularizer for feature extraction and dimensionality reduction. We show that the kSNR generalizes kernel PCA (and other spectral dimensionality reduction methods), least squares SVM, and kernel ridge regression to deal with cases where signal and noise cannot be assumed inde…

Functional principal component analysis for multivariate multidimensional environmental data

2015

Data with spatio-temporal structure can arise in many contexts, therefore a considerable interest in modelling these data has been generated, but the complexity of spatio-temporal models, together with the size of the dataset, results in a challenging task. The modelization is even more complex in presence of multivariate data. Since some modelling problems are more natural to think through in functional terms, even if only a finite number of observations is available, treating the data as functional can be useful (Berrendero et al. in Comput Stat Data Anal 55:2619–2634, 2011). Although in Ramsay and Silverman (Functional data analysis, 2nd edn. Springer, New York, 2005) the case of multiva…

A gallery of Chua's Attractors - Part IV

2007

Time Trends in the Joint Distributions of Income and Age

2001

We propose a method of analyzing time changes of joint income-age densities. Change is decomposed into time invariant components which act on the densities as deformations with time varying strength. The functional form of these components is estimated non parametrically from cross sectional data. The method is applied to analyze British household data on income and age for the years 1968–95. It is learned that for the young and middle aged there is a trend towards increasing inequality, while during the early eighties there seems to occur a reversal in the evolution of the income distribution for the old.

Learning with the kernel signal to noise ratio

2012

This paper presents the application of the kernel signal to noise ratio (KSNR) in the context of feature extraction to general machine learning and signal processing domains. The proposed approach maximizes the signal variance while minimizes the estimated noise variance in a reproducing kernel Hilbert space (RKHS). The KSNR can be used in any kernel method to deal with correlated (possibly non-Gaussian) noise. We illustrate the method in nonlinear regression examples, dependence estimation and causal inference, nonlinear channel equalization, and nonlinear feature extraction from high-dimensional satellite images. Results show that the proposed KSNR yields more fitted solutions and extract…