Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with single or finite number of random functions (much smaller than the sample size $n$). In this work, we focus on high-dimensional functional processes where $p$ comparable to, even much larger $n$. Such ubiquitous various...

in this article we consider the sequences of sample and population covariance operators for a sequence of arrays of hilbertian random elements. then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

the aim of this study was to assess the environmental impact of socio-cultural practices on the water quality of river ganga at the foothills of the garhwal himalayas in uttarakhand state, india. the physico-chemical parameters that contributed to the temporal variation and pollution in the river were identified in this study. principal component analysis (pca) and cluster analysis (ca) were us...

background: cutaneous leishmaniasis is one of the most important parasitic diseases in humans. in this disease, one of the responsible organisms is leishmania major, which is transmitted by sandfly vector. there are specific differences in biochemical profiles and metabolite pathways in logarithmic and stationary phases of leishmania parasites. in the present study, 1h nmr spectroscopy was used...

Advances in data collection and storage have tremendously increased the presence of functional data, whose graphical representations are curves, images or shapes. As a new area of statistics, functional data analysis extends existing methodologies and theories from the realms of functional analysis, generalized linear model, multivariate data analysis, nonparametric statistics, regression model...

We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis (MFPCA; Di et al. 2009) was proposed for such data when functions are densely recorded. Here we con...

We describe a principal component analysis (PCA) method for functional magnetic resonance imaging (fMRI) data based on functional data analysis, an advanced nonparametric approach. The data delivered by the fMRI scans are viewed as continuous functions of time sampled at the interscan interval and subject to observational noise, and are used accordingly to estimate an image in which smooth func...

In Functional Data Analysis (FDA), the underlying structure of a raw observation is functional and data are assumed to be sample paths from a single stochastic process. Functional Principal Component Analysis (FPCA) generalizes the standard multivariate Principal Component Analysis (PCA) to the infinite-dimensional case by analyzing the covariance structure of functional data. By approximating ...