Search results for "Principal Component Analysis"
showing 10 items of 486 documents
Gamma Kernel Intensity Estimation in Temporal Point Processes
2011
In this article, we propose a nonparametric approach for estimating the intensity function of temporal point processes based on kernel estimators. In particular, we use asymmetric kernel estimators characterized by the gamma distribution, in order to describe features of observed point patterns adequately. Some characteristics of these estimators are analyzed and discussed both through simulated results and applications to real data from different seismic catalogs.
Functional Principal Component Analysis for the explorative analysis of multisite-multivariate air pollution time series with long gaps
2013
The knowledge of the urban air quality represents the first step to face air pollution issues. For the last decades many cities can rely on a network of monitoring stations recording concentration values for the main pollutants. This paper focuses on functional principal component analysis (FPCA) to investigate multiple pollutant datasets measured over time at multiple sites within a given urban area. Our purpose is to extend what has been proposed in the literature to data that are multisite and multivariate at the same time. The approach results to be effective to highlight some relevant statistical features of the time series, giving the opportunity to identify significant pollutants and…
On the usage of joint diagonalization in multivariate statistics
2022
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…
Using Unfold-PCA for batch-to-batch start-up process understanding and steady-state identification in a sequencing batch reactor
2007
In chemical and biochemical processes, steady-state models are widely used for process assessment, control and optimisation. In these models, parameter adjustment requires data collected under nearly steady-state conditions. Several approaches have been developed for steady-state identification (SSID) in continuous processes, but no attempt has been made to adapt them to the singularities of batch processes. The main aim of this paper is to propose an automated method based on batch-wise unfolding of the three-way batch process data followed by a principal component analysis (Unfold-PCA) in combination with the methodology of Brown and Rhinehart 2 for SSID. A second goal of this paper is to…
Classification of flavonoid compounds by using entropy of information theory
2013
A total of 74 flavonoid compounds are classified into a periodic table by using an algorithm based on the entropy of information theory. Seven features in hierarchical order are used to classify structurally the flavonoids. From these features, the first three mark the group or column, while the last four are used to indicate the row or period in a table of periodic classification. Those flavonoids in the same group and period are suggested to show maximum similarity in properties. Furthermore, those with only the same group will present moderate similarity. In this report, the flavonoid compounds in the table, whose experimental data in bioactivity and antioxidant properties have been prev…
Applications of Kernel Methods
2009
In this chapter, we give a survey of applications of the kernel methods introduced in the previous chapter. We focus on different application domains that are particularly active in both direct application of well-known kernel methods, and in new algorithmic developments suited to a particular problem. In particular, we consider the following application fields: biomedical engineering (comprising both biological signal processing and bioinformatics), communications, signal, speech and image processing.
Semiparametric Models with Functional Responses in a Model Assisted Survey Sampling Setting : Model Assisted Estimation of Electricity Consumption Cu…
2010
This work adopts a survey sampling point of view to estimate the mean curve of large databases of functional data. When storage capacities are limited, selecting, with survey techniques a small fraction of the observations is an interesting alternative to signal compression techniques. We propose here to take account of real or multivariate auxiliary information available at a low cost for the whole population, with semiparametric model assisted approaches, in order to improve the accuracy of Horvitz-Thompson estimators of the mean curve. We first estimate the functional principal components with a design based point of view in order to reduce the dimension of the signals and then propose s…
Use of linear discriminant analysis applied to vibrational spectroscopy data to characterize commercial varnishes employed for art purposes.
2007
An improvement of methodologies for characterising synthetic resins used in varnishes employed for art purposes has been suggested. Several kinds of standard of the most common polymeric resins (acrylic, vinyl, poly(vinyl alcohol), alkyd, cellulose nitrate, latex, polyester, polyurethane, epoxy, organosilicic, and ketonic) were analyzed by Fourier transform infrared (FTIR) spectroscopy. Synthetic resins characterization is based on the mathematical treatment of their whole spectrum, dividing it in 13 sections, avoiding the one-by-one interpretation of the absorption bands. The mathematical model takes as variables the maximal absorbance of each section, and each synthetic standard resin as …
Comparison of different assembly and annotation tools on analysis of simulated viral metagenomic communities in the gut
2013
Abstract Background The main limitations in the analysis of viral metagenomes are perhaps the high genetic variability and the lack of information in extant databases. To address these issues, several bioinformatic tools have been specifically designed or adapted for metagenomics by improving read assembly and creating more sensitive methods for homology detection. This study compares the performance of different available assemblers and taxonomic annotation software using simulated viral-metagenomic data. Results We simulated two 454 viral metagenomes using genomes from NCBI's RefSeq database based on the list of actual viruses found in previously published metagenomes. Three different ass…
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…