Related papers: A Spectral Framework for Multi-Scale Nonlinear Dim…

In this paper, we propose a learning-based framework for non-rigid shape registration without correspondence supervision. Traditional shape registration techniques typically rely on correspondences induced by extrinsic proximity, therefore…

Dimensionality reduction is essential in simulation-based shape design, where high-dimensional parameterizations hinder optimization, surrogate modeling, and systematic design-space exploration. Parametric Model Embedding (PME) addresses…

Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…

Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to…

We introduce Uniform Manifold Approximation with Two-phase Optimization (UMATO), a dimensionality reduction (DR) technique that improves UMAP to capture the global structure of high-dimensional data more accurately. In UMATO, optimization…

Diminished reality (DR) refers to the removal of real objects from the environment by virtually replacing them with their background. Modern DR frameworks use inpainting to hallucinate unobserved regions. While recent deep learning-based…

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…

Graph Neural Networks have become the preferred tool to process graph data, with their efficacy being boosted through graph data augmentation techniques. Despite the evolution of augmentation methods, issues like graph property distortions…

Deep learning has demonstrated remarkable achievements in medical image segmentation. However, prevailing deep learning models struggle with poor generalization due to (i) intra-class variations, where the same class appears differently in…

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…

Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability…

Neural Radiance Field (NeRF)-based segmentation methods focus on object semantics and rely solely on RGB data, lacking intrinsic material properties. This limitation restricts accurate material perception, which is crucial for robotics,…

Implicit Neural Representations (INRs) have garnered significant attention for their ability to model complex signals in various domains. Recently, INR-based frameworks have shown promise in neural video compression by embedding video…

In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

In contrast to classical techniques for exploratory analysis of high-dimensional data sets, such as principal component analysis (PCA), neighbor embedding (NE) techniques tend to better preserve the local structure/topology of…

Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation…

We propose Neural-DynamicReconstruction (NDR), a template-free method to recover high-fidelity geometry and motions of a dynamic scene from a monocular RGB-D camera. In NDR, we adopt the neural implicit function for surface representation…

We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived…

Locality preserving projections (LPP) are a classical dimensionality reduction method based on data graph information. However, LPP is still responsive to extreme outliers. LPP aiming for vectorial data may undermine data structural…