정성규 교수

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High Dimension, Low Sample Size (HDLSS)] are becoming increasingly relevant. We investigate the asymptotic behavior of the Principal Component (PC) directions. HDLSS asymptotics are used to study consistency, strong inconsistency and subspace consistency. We show th

We introduce a new geometric framework for the set of symmetric positive-definite (SPD) matrices, aimed at characterizing deformations of SPD matrices by individual scaling of eigenvalues and rotation of eigenvectors of the SPD matrices. To characterize the deformation, the eigenvalue-eigenvector decomposition is used to find alternative representations of SPD matrices and to form a Riemannian manifold so that scaling and rotations of SPD matrices are captured by geodesics on this manifold. The

This paper presents a new and simple decoding algorithm for layered space time block codes such as the two independent Alamouti's codes which are also called the double space-time transmit diversity (DSTTD) system. By using group interference suppression and successive interference cancellation, we can treat DSTTD as two independent space-time block codes (STBC). We can then decode both of these STBC's through a simple maximum likelihood (ML) detector with null space-based interference cancellat

We consider how many components to retain in principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially test skewness of the squared lengths of residual scores that are obtained by removing leading principal components. The residual lengths are asymptotically left-skewed if all principal components with diverging variances are removed, and right-skewed otherwise. The proposed estimator is shown

Motivated by the analysis of torsion (dihedral) angles in the backbone of proteins, we investigate clustering of bivariate angular data on the torus [−π,π)×[−π,π). We show that naive adaptations of clustering methods, designed for vector-valued data, to the torus are not satisfactory and propose a novel clustering approach based on the conformal prediction framework. We construct several prediction sets for toroidal data with guaranteed finite-sample validity, based on a kernel density estimate

Set classification problems arise when classification tasks are based on sets of observations as opposed to individual observations. In set classification, a classification rule is trained with N sets of observations, where each set is labeled with class information, and the prediction of a class label is performed also with a set of observations. Data sets for set classification appear, for example, in diagnostics of disease based on multiple cell nucleus images from a single tissue. Relevant s

A novel interference alignment technique combined with interference cancellation is proposed. A new scenario of single-antenna 2-user X channel with a multiple-antenna relay is considered. The proposed interference alignment and cancellation scheme does not require any wireline links between receivers. In the proposed scheme, interference signals are not decoded. Instead, interference signals are just aligned, and the aligned signal is cancelled out to extract the desired signal. We call the pro

This paper analyzes the linear degrees of freedom (LDoF) for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> × <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> MIMO interference channels with constant channel coefficients. In this correspondence, we interpret the interference alignment problem

Multiblock data, where multiple groups of variables from different sources are observed for a common set of subjects, are routinely collected in many areas of science. Methods for joint factorization of such multiblock data are being developed to explore the potentially joint variation structure of the data. While most of the existing work focuses on delineating joint components, shared across all data blocks, from individual components, which is only relevant to a single data block, we propose