arXiv subjects

Yongho Jeon

Publications and source records attributed to Yongho Jeon.

4 recordsLinked to original sources

arXiv2025

DOD: Detection of outliers in high dimensional data with distance of distances

Reliable outlier detection in high-dimensional data is crucial in modern science, yet it remains a challenging task. Traditional methods often break down in these settings due to their reliance on asymptotic behaviors with respect to sample size under fixed dimension. Furthermore, many modern alternatives introduce sophisticated statistical treatments and computational complexities. To overcome these issues, our approach leverages intuitive geometric properties of high-dimensional space, effectively turning the curse of dimensionality into an advantage. We propose two new outlyingness statistics based on observation's relational patterns with all other points, measured via pairwise distances or inner products. We establish a theoretical foundation for our statistics demonstrating that as the dimension grows, our statistics create a non-vanishing margin that asymptotically separates outliers from non-outliers. Based on this foundation, we develop practical outlier detection procedures, including a simple clustering-based algorithm and a distribution-free test using random rotations. Through simulation experiments and real data applications, we demonstrate that our proposed methods achieve a superior balance between detection power and false positive control, outperforming existing methods and establishing their practical utility in high-dimensional settings.

stat.ME↗

arXiv2020

Sparse Functional Linear Discriminant Analysis

Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the dimensionality of the problem. On the other hand, there is a growing interest in interpretability of the analysis, which favors a simple and sparse solution. In this work, we propose a new approach that incorporates a type of sparsity that identifies non-zero sub-domains in the functional setting, offering a solution that is easier to interpret without compromising performance. With the need to embed additional constraints in the solution, we reformulate the functional linear discriminant analysis as a regularization problem with an appropriate penalty. Inspired by the success of $\ell_1$-type regularization at inducing zero coefficients for scalar variables, we develop a new regularization method for functional linear discriminant analysis that incorporates an $L^1$-type penalty, $\int |f|$, to induce zero regions. We demonstrate that our formulation has a well defined solution that contains zero regions, achieving a functional sparsity in the sense of domain selection. In addition, the misclassification probability of the regularized solution is shown to converge to the Bayes error if the data are Gaussian. Our method does not presume that the underlying function has zero regions in the domain, but produces a sparse estimator that consistently estimates the true function whether or not the latter is sparse. Numerical comparisons with existing methods demonstrate this property in finite samples with both simulated and real data examples.

stat.ME↗

arXiv2017

Penalized Orthogonal Iteration for Sparse Estimation of Generalized Eigenvalue Problem

We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA), multiclass linear discriminant analysis (LDA), canonical correlation analysis (CCA), sufficient dimension reduction (SDR) and invariant co-ordinate selection. We propose to modify the standard generalized orthogonal iteration with a sparsity-inducing penalty for the eigenvectors. To achieve this goal, we generalize the equation-solving step of orthogonal iteration to a penalized convex optimization problem. The resulting algorithm, called penalized orthogonal iteration, provides accurate estimation of the true eigenspace, when it is sparse. Also proposed is a computationally more efficient alternative, which works well for PCA and LDA problems. Numerical studies reveal that the proposed algorithms are competitive, and that our tuning procedure works well. We demonstrate applications of the proposed algorithm to obtain sparse estimates for PCA, multiclass LDA, CCA and SDR. Supplementary materials are available online.

stat.ME↗

arXiv2016

Sparse Generalized Eigenvalue Problem with Application to Canonical Correlation Analysis for Integrative Analysis of Methylation and Gene Expression Data

We present a method for individual and integrative analysis of high dimension, low sample size data that capitalizes on the recurring theme in multivariate analysis of projecting higher dimensional data onto a few meaningful directions that are solutions to a generalized eigenvalue problem. We propose a general framework, called SELP (Sparse Estimation with Linear Programming), with which one can obtain a sparse estimate for a solution vector of a generalized eigenvalue problem. We demonstrate the utility of SELP on canonical correlation analysis for an integrative analysis of methylation and gene expression profiles from a breast cancer study, and we identify some genes known to be associated with breast carcinogenesis, which indicates that the proposed method is capable of generating biologically meaningful insights. Simulation studies suggest that the proposed method performs competitive in comparison with some existing methods in identifying true signals in various underlying covariance structures.

stat.ME↗