6 papers
Structure-Preserving Reduced-Order Modeling via Low-Rank Transport Signatures
Jiajia Yu, Jingwei Hu, Fengyan Li +3
Parametrized PDEs with density-valued solutions are often difficult to approximate with classical linear reduced-order models, especially in transport-dominated regimes. We introdu…
Advancing Local Clustering on Graphs via Compressive Sensing: Semi-supervised and Unsupervised Methods
Zhaiming Shen, Sung Ha Kang
Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small co…
The Kolmogorov Superposition Theorem can Break the Curse of Dimensionality When Approximating High Dimensional Functions
Ming-Jun Lai, Zhaiming Shen
We explain how to use Kolmogorov Superposition Theorem (KST) to break the curse of dimensionality when approximating a dense class of multivariate continuous functions. We first sh…
Local Clustering for Lung Cancer Image Classification via Sparse Solution Technique
Jackson Hamel, Ming-Jun Lai, Zhaiming Shen +1
In this work, we propose to use a local clustering approach based on the sparse solution technique to study the medical image, especially the lung cancer image classification task.…
The Optimal Linear B-splines Approximation via Kolmogorov Superposition Theorem and its Application
Ming-Jun Lai, Zhaiming Shen
We propose a new approach for approximating functions in via Kolmogorov superposition theorem (KST) based on the linear spline interpolation of the outer function in t…
Maximal Volume Matrix Cross Approximation for Image Compression and Least Squares Solution
Kenneth Allen, Ming-Jun Lai, Zhaiming Shen
We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approxi…