arXiv subjects

ShengLi Tzeng

Publications and source records attributed to ShengLi Tzeng.

10 recordsLinked to original sources

arXiv2026

Sturm-Liouville-Type Parity and Oscillation of a Cubic Spline Eigenbasis

We study the eigen-structure of the penalty matrix arising from cubic smoothing splines on equally spaced knots. Using purely matrix-theoretic arguments, we show that its positive eigenvalues are simple, that the associated eigenvectors alternate between even and odd, and that the eigenvector for the $k$th largest eigenvalue has exactly $k+1$ sign changes. The approach provides a direct and transparent alternative to existing variational proofs of the oscillation property. These results show that equally spaced knots support a spline basis with both a parity structure and an oscillation pattern.

math.ST↗

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↗

arXiv2023

Assessing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components

In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic that tracks a stable microergodic parameter of the exponential covariance function, allowing us to address the intricate challenges of nonstationary processes that lack repeated measurements. We implement the fused lasso technique to elucidate nonstationary patterns at various resolutions. For prediction purposes, we segment the spatial domain into stationary sub-regions via Voronoi tessellations. Additionally, we devise a robust test for stationarity based on contrasting the sample means of our proposed statistics between two selected Voronoi subregions. The effectiveness of our method is demonstrated through simulation studies and its application to a precipitation dataset in Colorado.

stat.ME↗

arXiv2022

The R Package HCV for Hierarchical Clustering from Vertex-links

The HCV package implements the hierarchical clustering for spatial data. It requires clustering results not only homogeneous in non-geographical features among samples but also geographically close to each other within a cluster. We modified typically used hierarchical agglomerative clustering algorithms to introduce the spatial homogeneity, by considering geographical locations as vertices and converting spatial adjacency into whether a shared edge exists between a pair of vertices. The main function HCV obeying constraints of the vertex links automatically enforces the spatial contiguity property at each step of iterations. In addition, two methods to find an appropriate number of clusters and to report cluster members are also provided.

stat.CO↗

arXiv2021

Interpretable, predictive spatio-temporal models via enhanced Pairwise Directions Estimation

This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to capture nonlinear mean structures without requiring a prespecified parametric model. In addition to prediction as a common interest, this approach emphasizes the exploration of geometric information from the data. The method of Pairwise Directions Estimation (PDE; Lue, 2019) is implemented in our approach as a data-driven function searching for spatial patterns and temporal trends. The benefit of using geometric information from the method of PDE is highlighted, which aids effectively in exploring data structures. We further enhance PDE, referring to it as PDE+, by incorporating kriging to estimate the random effects not explained in the mean functions. Our proposal can not only increase prediction accuracy, but also improve the interpretation for modeling. Two simulation examples are conducted and comparisons are made with four existing methods. The results demonstrate that the proposed PDE+ method is very useful for exploring and interpreting the patterns and trends for spatio-temporal data. Illustrative applications to two real datasets are also presented.

stat.ME↗

arXiv2021

Spatially Adaptive Calibrations of AirBox PM$_{2.5}$ Data

Two networks are available to monitor PM$_{2.5}$ in Taiwan, including the Taiwan Air Quality Monitoring Network (TAQMN) and the AirBox network. The TAQMN, managed by Taiwan's Environmental Protection Administration (EPA), provides high-quality PM$_{2.5}$ measurements at $77$ monitoring stations. More recently, the AirBox network was launched, consisting of low-cost, small internet-of-things (IoT) microsensors (i.e., AirBoxes) at thousands of locations. While the AirBox network provides broad spatial coverage, its measurements are not reliable and require calibrations. However, applying a universal calibration procedure to all AirBoxes does not work well because the calibration curves vary with several factors, including the chemical compositions of PM$_{2.5}$, which are not homogeneous in space. Therefore, different calibrations are needed at different locations with different local environments. Unfortunately, most AirBoxes are not close to EPA stations, making the calibration task challenging. In this article, we propose a spatial model with spatially varying coefficients to account for heteroscedasticity in the data. Our method gives adaptive calibrations of AirBoxes according to their local conditions and provides accurate PM$_{2.5}$ concentrations at any location in Taiwan, incorporating two types of measurements. In addition, the proposed method automatically calibrates measurements from a new AirBox once it is added to the network. We illustrate our approach using hourly PM$_{2.5}$ data in the year 2020. After the calibration, the results show that the PM$_{2.5}$ prediction improves about 37% to 67% in root mean-squared prediction error for matching EPA data. In particular, once the calibration curves are established, we can obtain reliable PM$_{2.5}$ values at any location in Taiwan, even if we ignore EPA data.

stat.ME↗

arXiv2019

Spatial Process Decomposition for Quantitative Imaging Biomarkers Using Multiple Images of Varying Shapes

Quantitative imaging biomarkers (QIB) are extracted from medical images in radiomics for a variety of purposes including noninvasive disease detection, cancer monitoring, and precision medicine. The existing methods for QIB extraction tend to be ad-hoc and not reproducible. In this paper, a general and flexible statistical approach is proposed for handling up to three-dimensional medical images in an objective and principled way. In particular, a model-based spatial process decomposition is developed where the random weights are unique to individual patients for component functions common across patients. Model fitting and selection are based on maximum likelihood, while feature extractions are via optimal prediction of the underlying true image. A simulation study evaluates the properties of the proposed methodology and for illustration, a cancer image data set is analyzed and QIBs are extracted in association with a clinical endpoint.

stat.ME↗

arXiv2018

Empirical Likelihood Based Summary ROC Curve for Meta-Analysis of Diagnostic Studies

Objectives: This study provides an effective model selection method based on the empirical likelihood approach for constructing summary receiver operating characteristic (sROC) curves from meta-analyses of diagnostic studies. Methods: We considered models from combinations of family indices and specific pairs of transformations, which cover several widely used methods for bivariate summary of sensitivity and specificity. Then a final model was selected using the proposed empirical likelihood method. Simulation scenarios were conducted based on different number of studies and different population distributions for the disease and non-disease cases. The performance of our proposal and other model selection criteria was also compared. Results: Although parametric likelihood-based methods are often applied in practice due to its asymptotic property, they fail to consistently choose appropriate models for summary under the limited number of studies. For these situations, our proposed method almost always performs better. Conclusion: When the number of studies is as small as 10 or 5, we recommend choosing a summary model via the proposed empirical likelihood method.

stat.ME↗

arXiv2016

Distance for Functional Data Clustering Based on Smoothing Parameter Commutation

We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each subject as fixed during clustering, we measure the dissimilarity between subjects based on varying curve estimates with commutation of smoothing parameters pair-by-pair (of subjects). The intuitions are that smoothing parameters of smoothing splines reflect inverse signal-to-noise ratios and that applying an identical smoothing parameter the smoothed curves for two similar subjects are expected to be close. The effectiveness of our proposal is shown through simulations comparing to other dissimilarity measures. It also has several pragmatic advantages. First, missing values or irregular time points can be handled directly, thanks to the nature of smoothing splines. Second, conventional clustering method based on dissimilarity can be employed straightforward, and the dissimilarity also serves as a useful tool for outlier detection. Third, the implementation is almost handy since subroutines for smoothing splines and numerical integration are widely available. Fourth, the computational complexity does not increase and is parallel with that in calculating Euclidean distance between curves estimated by smoothing splines.

stat.ME↗

arXiv2015

Multi-Resolution Spatial Random-Effects Models for Irregularly Spaced Data

The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis functions. In this research, we propose a class of basis functions extracted from thin-plate splines. These functions are ordered in terms of their degrees of smoothness with a higher-order function corresponding to larger-scale features and a lower-order one corresponding to smaller-scale details, leading to a parsimonious representation for a nonstationary spatial covariance function. Consequently, only a small to moderate number of functions are needed in a spatial random-effects model. The proposed class of basis functions has several advantages over commonly used ones. First, we do not need to concern about the allocation of the basis functions, but simply select the total number of functions corresponding to a resolution. Second, only a small number of basis functions is usually required, which facilitates computation. Third, estimation variability of model parameters can be considerably reduced, and hence more precise covariance function estimates can be obtained. Fourth, the proposed basis functions depend only on the data locations but not the measurements taken at those locations, and are applicable regardless of whether the data locations are sparse or irregularly spaced. In addition, we derive a simple close-form expression for the maximum likelihood estimates of model parameters in the spatial random-effects model. Some numerical examples are provided to demonstrate the effectiveness of the proposed method.

stat.ME↗