arXiv subjects

Shang-Ying Shiu

Publications and source records attributed to Shang-Ying Shiu.

3 recordsLinked to original sources

arXiv2026

Structure-Preserving Visualization of Complex Systems through Discrete Approximation: An Application to Argo Data

This paper presents a framework for constructing structure-preserving representations of complex systems through discrete approximation, and demonstrates its use in studying the vertical temperature and salinity structures in the mesopelagic zone across the global ocean using the ARGO dataset. Clustering serves as a means of organizing complexity into a finite set of structures that approximate the overall oceanic conditions, and a color encoding design then integrates these structures into a coherent map, with the three color components derived from interpretable geometric features of a profile: its initial level, its magnitude of variation, and its shape. Instead of focusing on specific depth levels or computing zonal averages within selected regions, our approach preserves the full vertical structure of individual profiles and incorporates each profile in the global ocean, capturing both fine-scale profile detail and large-scale spatial variability. By clustering over one million profiles collected over a decade, we identify and characterize representative profile shapes, which form the basis for a visualization strategy that provides an integrated, comprehensive, and interpretable presentation of the large-scale spatial distributions of these oceanic vertical patterns.

stat.ME↗

arXiv2026

cGAP: Generalized Association Plots with HOMALS-Guided Heatmaps for Visualization of High-Dimensional Categorical Data

High-dimensional categorical data arise in genetics, biomedicine, and the social sciences, yet visualization tools for such data remain far less developed than those for continuous variables. Existing methods either scale poorly, rely heavily on low-dimensional displays detached from the original data matrix, or prioritize predictive accuracy over interpretability. To address this gap, we introduce categorical Generalized Association Plots (cGAP), a visualization framework for nominal, ordinal, and binary data that preserves the original data matrix while augmenting it with interpretable geometric structure. cGAP uses Homogeneity Analysis (HOMALS) to embed subjects and category levels in a three-dimensional Euclidean space and maps the embedding to red-green-blue coordinates so that similar patterns receive similar colors. The framework integrates three coordinated views: a HOMALS-guided heatmap of the raw data matrix, a subject proximity matrix, and a variable proximity matrix. Seriation algorithms are then used to reorder rows and columns to reveal coherent clusters, outliers, and local-to-global structure. We also derive barycentric traceability, projection-distortion, and contrast-preservation properties that clarify how embedding geometry is transferred to the display. We demonstrate the versatility of cGAP through applications to student-animal classification data, mammalian dentition profiles, mushroom records from the UCI Machine Learning Repository, and the Clusters of Orthologous Genes database. These examples show that cGAP supports transparent exploratory analysis by maintaining traceability between derived visual structure and the original categorical observations. cGAP provides a full-matrix, heatmap-based visualization environment for investigating complex categorical datasets across scientific domains.

stat.ML↗

arXiv2015

On the strengths of the self-updating process clustering algorithm

We introduce a simple, intuitive and yet powerful algorithm for clustering analysis. This algorithm is an iterative process on the sample space, which arises as an extension of the iteratively generated correlation matrices. It allows for both time-varying and time-invariant operators, therefore can be considered more general than the blurring mean-shift algorithm in which operators are time-invariant. The algorithm stands from the viewpoint of data points and simulates the process how data points move and perform self-clustering, therefore is named Self-Updating Process (SUP). It is particularly competitive for (i) data with noise, (ii) data with large number of clusters and (iii) unbalanced data. When noise is present in the data, the algorithm is able to isolate noisy points while performing clustering simultaneously. Simulation studies and real data applications are presented to demonstrate the performance of SUP.

stat.ME↗