Search results for "PCa"
showing 10 items of 130 documents
Sign and Rank Covariance Matrices: Statistical Properties and Application to Principal Components Analysis
2002
In this paper, the estimation of covariance matrices based on multivariate sign and rank vectors is discussed. Equivariance and robustness properties of the sign and rank covariance matrices are described. We show their use for the principal components analysis (PCA) problem. Limiting efficiencies of the estimation procedures for PCA are compared.
XRF analysis to identify historical photographic processes: The case of some Interguglielmi Jr.’s images from the Palermo Municipal Archive
2017
Abstract In the early period, even though professional photographers worked with similar techniques and products, their artistic and commercial aims determined different choices and led them to follow different, often personal, recipes. For this reason, identification of the techniques through date and name of the photographer or through some visual features like colour, tonality and surface of the image layer, often needs further investigation to be proved. Chemical characterization, carried out in a non or micro destructive way, can be crucial to provide useful information about the original composition, degradation process, realization technique, in obtaining an indirect dating of the ph…
Long gaps in multivariate spatio-temporal data: an approach based on functional data analysis
2015
The main aim of this paper is to perform Functional Principal Component Analysis (FPCA) taking into account spatio-temporal correlation structures, in order to fill in missing values in spatio-temporal multivariate data set. A spatial and a spatio-temporal variant of the classical temporal FPCA is considered; in other words, FPCA is carried out after modeling data with respect to more than one dimension: space (long, lat) or space+time. Moreover, multidimensional FPCA is extended to multivariate context (more than one variable). Information on spatial or spatiotemporal structures are efficiently extracted by applying Generalized Additive Models (GAMs). Both simulation studies and some perfo…
Clustering of waveforms-data based on FPCA direction
2010
The necessity of nding similar features of waveforms data recorded for earthquakes at di erent time instants is here considered, since eventual similarity between these functions could suggest similar behavior of the source process of the corresponding earthquakes. In this paper we develop a clustering algorithm for curves based on directions de ned by an application of PCA to functional data.
Clustering of waveforms based on FPCA direction
2010
Looking for curves similarity could be a complex issue characterized by subjective choices related to continuous transformations of observed discrete data (Chiodi, 1989). Waveforms correlation techniques have been introduced to charac- terize the degree of seismic event similarity (Menke, 1999) and in facilitating more accurate relative locations within similar event clusters by providing more precise timing of seismic wave (P and S) arrivals (Phillips, 1997). In this paper functional analysis (Ramsey, and Silverman, 2006) is considered to highlight common characteristics of waveforms-data and to summarize these charac- teristics by few components, by applying a variant of a classical clust…
Space-time FPCA Algorithm for clustering of multidimensional curves.
2016
In this paper we focus on finding clusters of multidimensional curves with spatio-temporal structure, applying a variant of a k-means algorithm based on the principal component rotation of data. The main advantage of this approach is to combine the clustering functional analysis of the multidimensional data, with smoothing methods based on generalized additive models, that cope with both the spatial and the temporal variability, and with functional principal components that takes into account the dependency between the curves.
Functional Principal components direction to cluster earthquake waveforms
2010
Looking for curves similarity could be a complex issue characterized by subjective choices related to continuous transformations of observed discrete data (Chiodi, 1989). In this paper we combine the aim of finding clusters from a set of individual curves to the functional nature of data, applying a variant of a k-means algorithm based on the principal component rotation of data. We apply a classical clustering method to rotated data, according to the direction of maximum variance. A k-means clustering algorithm based on PCA rotation of data is proposed, as an alternative to methods that require previous interpolation of data based on splines or linear fitting (Garc´ıa- Escudero and Gordali…
FPCA Algorithm For Waveform Clustering
2011
Similar features between waveform data recorded for earthquakes at different time instants could suggest similar behavior of the source process of the corresponding source seismic process. In this paper we combine the aim of finding clusters from a set of individual waveform curves with the functional nature of data, applying a variant of a k-means algorithm based on the principal component rotation of data. This approach overcome the limitation of the cross-correlation, and represents an alternative to methods based on the interpolation of data by splines or linear fitting.
Comparing Spatial and Spatio-temporal FPCA to Impute Large Continuous Gaps in Space
2018
Multivariate spatio-temporal data analysis methods usually assume fairly complete data, while a number of gaps often occur along time or in space. In air quality data long gaps may be due to instrument malfunctions; moreover, not all the pollutants of interest are measured in all the monitoring stations of a network. In literature, many statistical methods have been proposed for imputing short sequences of missing values, but most of them are not valid when the fraction of missing values is high. Furthermore, the limitation of the methods commonly used consists in exploiting temporal only, or spatial only, correlation of the data. The objective of this paper is to provide an approach based …
Comparing FPCA Based on Conditional Quantile Functions and FPCA Based on Conditional Mean Function
2019
In this work functional principal component analysis (FPCA) based on quantile functions is proposed as an alternative to the classical approach, based on the functional mean. Quantile regression characterizes the conditional distribution of a response variable and, in particular, some features like the tails behavior; smoothing splines have also been usefully applied to quantile regression to allow for a more flexible modelling. This framework finds application in contexts involving multiple high frequency time series, for which the functional data analysis (FDA) approach is a natural choice. Quantile regression is then extended to the estimation of functional quantiles and our proposal exp…