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Jeong Rye Park

Publications and source records attributed to Jeong Rye Park.

6 recordsLinked to original sources
arXiv2026

Denoising data reduction algorithm for Topological Data Analysis

Persistent homology is a central tool in topological data analysis, but its application to large and noisy datasets is often limited by computational cost and the presence of spurious topological features. Noise not only increases data size but also obscures the underlying structure of the data. In this paper, we propose the Refined Characteristic Lattice Algorithm (RCLA), a grid-based method that integrates data reduction with threshold-based denoising in a single procedure. By incorporating a threshold parameter $k$, RCLA removes noise while preserving the essential structure of the data in a single pass. We further provide a theoretical guarantee by proving a stability theorem under a homogeneous Poisson noise model, which bounds the bottleneck distance between the persistence diagrams of the output and the underlying shape with high probability. In addition, we introduce an automatic parameter selection method based on nearest-neighbor statistics. Experimental results demonstrate that RCLA consistently outperforms existing methods, and its effectiveness is further validated on a 3D shape classification task.

cs.CG↗
arXiv2023

Effective data reduction algorithm for topological data analysis

One of the most interesting tools that have recently entered the data science toolbox is topological data analysis (TDA). With the explosion of available data sizes and dimensions, identifying and extracting the underlying structure of a given dataset is a fundamental challenge in data science, and TDA provides a methodology for analyzing the shape of a dataset using tools and prospects from algebraic topology. However, the computational complexity makes it quickly infeasible to process large datasets, especially those with high dimensions. Here, we introduce a preprocessing strategy called the Characteristic Lattice Algorithm (CLA), which allows users to reduce the size of a given dataset as desired while maintaining geometric and topological features in order to make the computation of TDA feasible or to shorten its computation time. In addition, we derive a stability theorem and an upper bound of the barcode errors for CLA based on the bottleneck distance.

cs.CG↗
arXiv2018

Sharp spectral bounds for the edge-connectivity of a regular graph

Let $λ_2(G)$ and $κ'(G)$ be the second largest eigenvalue and the edge-connectivity of a graph $G$, respectively. Let $d$ be a positive integer at least 3. For $t=1$ or 2, Cioaba proved sharp upper bounds for $λ_2(G)$ in a $d$-regular simple graph $G$ to guarantee that $κ'(G) \ge t+1$. In this paper, we settle down for all $t \ge 3$.

math.CO↗
arXiv2018

Sharp conditions for the existence of an even $[a,b]$-factor in a graph

Let $a$ and $b$ be positive integers. An even $[a,b]$-factor of a graph $G$ is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $d_H(v)$ is even and $a \le d_H(v) \le b$. Matsuda conjectured that if $G$ is an $n$-vertex 2-edge-connected graph such that $n \ge 2a+b+\frac{a^2-3a}b - 2$, $δ(G) \ge a$, and $σ_2(G) \ge \frac{2an}{a+b}$, then $G$ has an even $[a,b]$-factor. In this paper, we provide counterexamples, which are highly connected. Furthermore, we give sharp sufficient conditions for a graph to have an even $[a,b]$-factor. For even $an$, we conjecture a lower bound for $λ_1(G)$ in an $n$-vertex graph to have an $[a,b]$-factor, where $λ_1(G)$ is the largest eigenvalue of $G$.

math.CO↗
arXiv2017

The weighted poset metrics and directed graph metrics

Etzion et al. introduced metrics on $\mathbb{F}_2^n$ based on directed graphs on $n$ vertices and developed some basic coding theory on directed graph metric spaces. In this paper, we consider the problem of classifying directed graphs which admit the extended Hamming codes to be a perfect code. We first consider weighted poset metrics as a natural generalization of poset metrics and investigate interrelation between weighted poset metrics and directed graph based metrics. In the next, we classify weighted posets on a set with eight elements and directed graphs on eight vertices which admit the extended Hamming code $\widetilde{\mathcal{H}}_3$ to be a $2$-perfect code. We also construct some families of such structures for any $k \geq 3$. Those families enable us to construct packing or covering codes of radius 2 under certain maps.

math.CO↗