We consider a problem involving estimation of a high-dimensional covariance matrix that is the sum of a diagonal matrix and a low-rank matrix, and making a decision based on the resulting estimate. Such problems arise, for example, in portfolio management, where a common approach employs principal component analysis (PCA) to estimate factors used in constructing the low-rank term of the covaria...

Given a set of signals, a classical construction of an optimal truncatable basis for optimally representing the signals, is the principal component analysis (PCA for short) approach. When the information about the signals one would like to represent is a more general property, like smoothness, a different basis should be considered. One example is the Fourier basis which is optimal for represen...

We consider the online version of the well known Principal Component Analysis (PCA) problem. In standard PCA, the input to the problem is a set of vectors X = [x1, . . . , xn] in Rd×n and a target dimension k < d; the output is a set of vectors Y = [y1, . . . , yn] in Rk×n that minimize minΦ ‖X − ΦY ‖F where Φ is restricted to be an isometry. The global minimum of this quantity, OPTk, is obtain...

Efficient and compact representation of images is a fundamental problem in computer vision. Principal Component Analysis (PCA) has been widely used for image representation and has been successfully applied to many computer vision algorithms. In this paper, we propose a method that uses Haar-like binary box functions to span a subspace which approximates the PCA subspace. The proposed method ca...

We propose fast and scalable statistical methods for the analysis of hundreds or thousands of high dimensional vectors observed at multiple visits. The proposed inferential methods do not require loading the entire data set at once in the computer memory and instead use only sequential access to data. This allows deployment of our methodology on low-resource computers where computations can be ...

The primary purpose of this study was to use functional principal component analysis (FPCA) to analyze Hoffman-reflex (H-reflex) recruitment curves. Smoothed and interpolated recruitment curves from 38 participants were used for analysis. Standard methods were used to calculate three discrete variables (i.e., H(max)/M(max) ratio, H(th), H(slp)). FPCA was then used to extract principal component...

With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of “functional data”, which have become a commonly encountered type of data. Functional Data Analysis (FDA) encompasses the statistical methodology for such data. Broadly interpreted, FDA deals with the analysi...

We study the utilization of functional metrics for learning of functional data. In particular we investigate the metrics based on the Sobelev metric which can be related top a respective inner product. This offers capabilities for adequate data processing of functional data taking into acccount the dependencies within the functional data vectors. We outline these possibilities and give the math...

This paper focuses on the analysis of spatially correlated functional data. We propose a parametric model for spatial correlation and the between-curve correlation is modeled by correlating functional principal component scores of the functional data. Additionally, in the sparse observation framework, we propose a novel approach of spatial principal analysis by conditional expectation to explic...