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Metric Multidimensional scaling (MDS) is a classical method for generating meaningful (non-linear) low-dimensional embeddings of high-dimensional data. MDS has a long history in the statistics, machine learning, and graph drawing…

Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…

Classical multidimensional scaling (MDS) is a method for visualizing high-dimensional point clouds by mapping to low-dimensional Euclidean space. This mapping is defined in terms of eigenfunctions of a matrix of interpoint dissimilarities.…

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…

This paper presents an efficient algorithm, naming Centralized Searching and Decentralized Optimization (CSDO), to find feasible solution for large-scale Multi-Vehicle Trajectory Planning (MVTP) problem. Due to the intractable growth of…

Failure-Directed Search (FDS) is a significant complete generic search algorithm used in Constraint Programming (CP) to efficiently explore the search space, proven particularly effective on scheduling problems. This paper analyzes FDS's…

Multiple-proposal MCMC algorithms have recently gained attention for their potential to improve performance, especially through parallel implementation on modern hardware. We introduce Stereographic Multiple-Try Metropolis (SMTM), a novel…

As a crucial component of most modern deep recommender systems, feature embedding maps high-dimensional sparse user/item features into low-dimensional dense embeddings. However, these embeddings are usually assigned a unified dimension,…

While classical forms of stochastic gradient descent algorithm treat the different coordinates in the same way, a framework allowing for adaptive (non uniform) coordinate sampling is developed to leverage structure in data. In a non-convex…

This work presents the convergence rate analysis of stochastic variants of the broad class of direct-search methods of directional type. It introduces an algorithm designed to optimize differentiable objective functions $f$ whose values can…

High-dimensional design spaces underpin a wide range of physics-based modeling and computational design tasks in science and engineering. These problems are commonly formulated as constrained black-box searches over rugged objective…

We introduce Joint Multidimensional Scaling, a novel approach for unsupervised manifold alignment, which maps datasets from two different domains, without any known correspondences between data instances across the datasets, to a common…

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).…

This paper proposes a novel modulation and coding scheme (MCS) selection framework that integrates mutual information (MI) prediction based on vector similarity search (VSS) for massive multi-user multiple-input multiple-output orthogonal…

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…

Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its…

Multidimensional Scaling (MDS) is one of the first fundamental manifold learning methods. It can be categorized into several methods, i.e., classical MDS, kernel classical MDS, metric MDS, and non-metric MDS. Sammon mapping and Isomap can…

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…

Feature embeddings are one of the most essential steps when training deep learning based Click-Through Rate prediction models, which map high-dimensional sparse features to dense embedding vectors. Classic human-crafted embedding size…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…