Related papers: Multidimensional Scaling: Approximation and Comple…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
Efficient motion planning for high-dimensional robotic systems, such as manipulators and mobile manipulators, is critical for real-time operation and reliable deployment. Although advances in planning algorithms have enhanced scalability to…
This paper proposes Neural-MMGS, a novel neural 3DGS framework for multimodal large-scale scene reconstruction that fuses multiple sensing modalities in a per-gaussian compact, learnable embedding. While recent works focusing on large-scale…
Computing classical centrality measures such as betweenness and closeness is computationally expensive on large-scale graphs. In this work, we introduce an efficient force layout algorithm that embeds a graph into a low-dimensional space,…
Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…
Visualizing graphs using virtual physical models is probably the most heavily used technique for drawing graphs in practice. There are many algorithms that are efficient and produce high-quality layouts. If one requires that the layout also…
Maximum Inner Product Search (MIPS) for high-dimensional vectors is pivotal across databases, information retrieval, and artificial intelligence. Existing methods either reduce MIPS to Nearest Neighbor Search (NNS) while suffering from…
Data augmentation has been an indispensable tool to improve the performance of deep neural networks, however the augmentation can hardly transfer among different tasks and datasets. Consequently, a recent trend is to adopt AutoML technique…
This article presents an empirical validation of the functional multidimensional scaling model, a novel approach that improves the smoothness of time-varying dissimilarities in a low-dimensional space, embedding a modified Adam stochastic…
In the Weighted Triangle-Free 2-Matching problem (WTF2M), we are given an undirected edge-weighted graph. Our goal is to compute a maximum-weight subgraph that is a 2-matching (i.e., no node has degree more than $2$) and triangle-free…
It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
Monocular 3D object detection is very challenging in autonomous driving due to the lack of depth information. This paper proposes a one-stage monocular 3D object detection algorithm based on multi-scale depth stratification, which uses the…
Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like…