Related papers: Spectral Generalized Multi-Dimensional Scaling
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Species distribution models (SDMs) aim to predict the distribution of species by relating occurrence data with environmental variables. Recent applications of deep learning to SDMs have enabled new avenues, specifically the inclusion of…
This study addresses the challenge of online 3D model generation for neural rendering using an RGB image stream. Previous research has tackled this issue by incorporating Neural Radiance Fields (NeRF) or 3D Gaussian Splatting (3DGS) as…
Identifying molecules from mass spectrometry (MS) data remains a fundamental challenge due to the semantic gap between physical spectral peaks and underlying chemical structures. Existing deep learning approaches often treat spectral…
Integrating inverse rendering with multi-view photometric stereo (MVPS) yields more accurate 3D reconstructions than the inverse rendering approaches that rely on fixed environment illumination. However, efficient inverse rendering with…
This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
In this work, a unified framework for gradient-free Multidimensional Scaling (MDS) based on Coordinate Search (CS) is proposed. This family of algorithms is an instance of General Pattern Search (GPS) methods which avoid the explicit…
Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., $t$-SNE, UMAP) or global (e.g., MDS, PCA) structure of the…
Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In…
Recovering 3D information from scenes via multi-view stereo reconstruction (MVS) and novel view synthesis (NVS) is inherently challenging, particularly in scenarios involving sparse-view setups. The advent of 3D Gaussian Splatting (3DGS)…
Multifractal scaling (MFS) refers to structures that can be described as a collection of interwoven fractal subsets which exhibit power-law spatial scaling behavior with a range of scaling exponents (concentration, or singularity,…
A satellite image is a remotely sensed image data, where each pixel represents a specific location on earth. The pixel value recorded is the reflection radiation from the earth's surface at that location. Multispectral images are those that…
It is vital to infer a signed distance function (SDF) in multi-view based surface reconstruction. 3D Gaussian splatting (3DGS) provides a novel perspective for volume rendering, and shows advantages in rendering efficiency and quality.…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
We propose a novel multi-scale template matching method which is robust against both scaling and rotation in unconstrained environments. The key component behind is a similarity measure referred to as scalable diversity similarity (SDS).…
Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to…
Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…
Ultrafast multidimensional spectroscopies are powerful tools that can access charge and energy flow in complex materials, shifting chemical kinetics, and even many-body interactions in correlated matter. However, current implementations…