This is an expository paper that reviews recent developments on optimal estimation of structured high-dimensional covariance and precision matrices. Minimax rates of convergence for estimating several classes of structured covariance and precision matrices, including bandable, Toeplitz, and sparse covariance matrices as well as sparse precision matrices, are given under the spectral norm loss. ...

The development of the technology makes it possible to measure large amount of genes expressions simultaneously. Since biological functions are mostly coordinated by multiple genes, called “gene pathway”, it is interesting to identify differential gene pathways which are associated with clinical phenotype. Principal component analysis has been proposed to identify differential gene pathways in ...

This paper considers a sparse spiked covariancematrix model in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of convergence for estimating the spiked covariance matrix under the spectral norm is established, which requires significantly different techniques from those fo...

Robust Principal Component Analysis (RPCA) is a technique to decompose signals into sparse and low rank components, and has recently drawn the attention of the MIR field for the problem of separating leading vocals from accompaniment, with appealing results obtained on small excerpts of music. However, the performance of the method drops when processing entire music tracks. We present an adapti...

We study sparse principal components analysis in high dimensions , where p (the number of variables) can be much larger than n (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We prove optimal, non-asymptotic lower and upper bounds on the minimax subspace estimation error under two differe...

detecting anomalies is an important challenge for intrusion detection and fault diagnosis in wireless sensor networks (wsns). to address the problem of outlier detection in wireless sensor networks, in this paper we present a pca-based centralized approach and a dpca-based distributed energy-efficient approach for detecting outliers in sensed data in a wsn. the outliers in sensed data can be ca...

linseed is an important oilseed and fibre crop predominantly grown in india. the aim of the present research was to evaluate genetic diversity and patterns of relationships among the 58 genotypes through 10 morphological traits and 12 polymorphic microsatellite (ssr) markers. euclidean analysis of agro-morphological traits grouped the 58 genotypes into four clusters of which cluster i was the l...

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, intuitive accessible manner, basic principles underlying PCA its applications. Next, present a systematic, though no exclusive, survey some representative works illustrating poten...

selecting within local pomegranate accessions is the main method used to identify new cultivars. total of 76 pomegranate accessions from hatay, turkey, were collected and their morpho-pomological and chemical characteristics were determined. the results showed that there was significant diversity among the accessions in terms of fruit quality parameters. several accessions were notable for thei...