We review and extend some statistical tools that have proved useful for analysing functional data. Functional data analysis primarily is designed for the analysis of random trajectories and infinite-dimensional data, and there exists a need for the development of adequate statistical estimation and inference techniques. While this field is in flux, some methods have proven useful. These include...

We introduce the concept of mixture inner product spaces associated with a given separable Hilbert space, which feature an infinite-dimensional mixture of finite-dimensional vector spaces and are dense in the underlying Hilbert space. Any Hilbert valued random element can be arbitrarily closely approximated by mixture inner product space valued random elements. While this concept can be applied...

Functional data analysis is concerned with inherently infinite-dimensional data objects and therefore can be viewed as part of the methodology for Big Data. The size of functional data may vary from terabytes as encountered in fMRI (functional magnetic resonance imaging ) and other applications in brain imaging to just a few kilobytes in longitudinal data with small or modest sample sizes. In t...

introduction: the accuracy of analyzing functional mri (fmri) data is usually decreases in the presence of noise and artifact sources. a common solution in for analyzing fmri data having high noise is to use suitable preprocessing methods with the aim of data denoising. some effects of preprocessing methods on the parametric methods such as general linear model (glm) have previously been evalua...

spatial patterns are useful descriptors of the horizontal structure in a plant population and may change over time as the individual components of the population grow or die out. but, whether this is the case for desert woody annuals is largely unknown. in the present investigation, the variations in spatial patterns of tribulus terrestris during different pulse events in semi-arid area of the ...

the writers of this research have studied seven variables including: precipitation, relative humidity, sunny hours, temperature average, temperature minimum, temperature maximum and sea level pressure, at sanandaj air station during 1964-1994. sanandaj air station has nearly 10966 days of complete data for these variables. a principal component analysis (pca) has been applied on this data; then...

the field study was conducted in one district of educational-experimental forest at tehran university (kheirood-kenar forest) in the north of iran. eighty-five soil profiles were dug in the site of study and several chemical and physical soil properties were considered. these factors included: soil ph, soil texture, bulk density, organic carbon, total nitrogen, extractable phosphorus and depth ...

the principle of dimensionality reduction with pca is the representation of the dataset ‘x’in terms of eigenvectors ei ∈ rn  of its covariance matrix. the eigenvectors oriented in the direction with the maximum variance of x in rn carry the most      relevant information of x. these eigenvectors are called principal components [8]. assume that n images in a set are originally represented in mat...