A series of microarray experiments produces observations of differential expression for thousands of genes across multiple conditions. Principal component analysis(PCA) has been widely used in multivariate data analysis to reduce the dimensionality of the data in order to simplify subsequent analysis and allow for summarization of the data in a parsimonious manner. PCA, which can be implemented...

Channel-state-information (CSI) feedback methods are considered, especially for massive or very large-scale multipleinput multiple-output (MIMO) systems. To extract essential information from the CSI without redundancy that arises from the highly correlated antennas, a receiver transforms (sparsifies) a correlated CSI vector to an uncorrelated sparse CSI vector by using a Karhunen-Loève transfo...

l=1 σlulv T l (1) ∀ l σl ∈ R, σl ≥ 0 (2) ∀ l, l 〈ul, ul′〉 = 〈vl, vl′〉 = δ(l, l) (3) To prove this consider the matrix AA ∈ R. Set ul to be the l’th eigenvector of AA . By definition we have that AAul = λlul. Since AA T is positive semidefinite we have λl ≥ 0. Since AA is symmetric we have that ∀ l, l 〈ul, ul′〉 = δ(l, l). Set σl = √ λl and vl = 1 σl Aul. Now we can compute the following: 〈vl, vl...

Statistical and computational techniques for revealing the internal structure that underlies the set of random correlated data exists in a great variety at present; and target decomposition theorems, either in the coherent or incoherent formulation, are well established. In spite of this fact a rather innovative and new concept is presented in this contribution. In turn the Principal Component ...

We recently presented a new asynchronous demodulation method for phase-sampling interferometry. The method is based in the principal component analysis (PCA) technique. In the former work, the PCA method was derived heuristically. In this work, we present an in-depth analysis of the PCA demodulation method.

A phenomenological study of solubility has been conducted using a combination of quantitative structure-property relationship (QSPR) and principal component analysis (PCA). A solubility database of 4540 experimental data points was used that utilized available experimental data into a matrix of 154 solvents times 397 solutes. Methodology in which QSPR and PCA are combined was developed to predi...

We introduce a novel algorithm to compute nonnegative sparse principal components of positive semidefinite (PSD) matrices. Our algorithm comes with approximation guarantees contingent on the spectral profile of the input matrix A: the sharper the eigenvalue decay, the better the quality of the approximation. If the eigenvalues decay like any asymptotically vanishing function, we can approximate...

The main shortage of principle component analysis (PCA) based anomaly detection models is their interpretability. In this paper, our goal is to propose an interpretable PCAbased model for anomaly detection and interpretation. The propose ASPCAmodel constructs principal components with sparse and orthogonal loading vectors to represent the abnormal subspace, and uses them to interpret detected a...

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. We study the asymptotic properties of these sparse PC directions for scenarios with fixed sample size and increasing dimension (i.e. High Dimension,...

Lipid lateral organization in binary-constituent monolayers consisting of fluorescent and nonfluorescent lipids has been investigated by acquiring multiple emission spectra during measurement of each force-area isotherm. The emission spectra reflect BODIPY-labeled lipid surface concentration and lateral mixing with different nonfluorescent lipid species. Using principal component analysis (PCA)...