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MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods…

In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes…

Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of…

Deep-feature-based perceptual similarity models have demonstrated strong alignment with human visual perception in Image Quality Assessment (IQA). However, most existing approaches operate at a single spatial scale, implicitly assuming that…

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…

Generative Adversarial Networks (GANs) are an elegant mechanism for data generation. However, a key challenge when using GANs is how to best measure their ability to generate realistic data. In this paper, we demonstrate that an intrinsic…

In the field of 3D dynamic scene reconstruction, how to balance model convergence rate and rendering quality has long been a critical challenge that urgently needs to be addressed, particularly in high-precision modeling of scenes with…

Deep learning models leak significant amounts of information about their training datasets. Previous work has investigated training models with differential privacy (DP) guarantees through adding DP noise to the gradients. However, such…

Unsupervised depth completion aims to recover dense depth from the sparse one without using the ground-truth annotation. Although depth measurement obtained from LiDAR is usually sparse, it contains valid and real distance information,…

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.…

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).…

Semi-supervised classification, where unlabeled data are massive but labeled data are limited, often arises in machine learning applications. We address this challenge under high-dimensional data by leveraging the manifold and cluster…

Multidimensional scaling (MDS) is a dimensionality reduction technique for microbial ecology data analysis that represents the multivariate structure while preserving pairwise distances between samples. While its improvement has enhanced…

Recently, the task of distantly supervised (DS) ultra-fine entity typing has received significant attention. However, DS data is noisy and often suffers from missing or wrong labeling issues resulting in low precision and low recall. This…

Bayesian multidimensional scaling (BMDS) is a probabilistic dimension reduction tool that allows one to model and visualize data consisting of dissimilarities between pairs of objects. Although BMDS has proven useful within, e.g., Bayesian…

Given a matrix $D$ describing the pairwise dissimilarities of a data set, a common task is to embed the data points into Euclidean space. The classical multidimensional scaling (cMDS) algorithm is a widespread method to do this. However,…

The cognitive framework of conceptual spaces proposes to represent concepts as regions in psychological similarity spaces. These similarity spaces are typically obtained through multidimensional scaling (MDS), which converts human…

Weakly-Supervised Semantic Segmentation (WSSS) segments objects without a heavy burden of dense annotation. While as a price, generated pseudo-masks exist obvious noisy pixels, which result in sub-optimal segmentation models trained over…

Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality…

Geodesic distance matrices can reveal shape properties that are largely invariant to non-rigid deformations, and thus are often used to analyze and represent 3-D shapes. However, these matrices grow quadratically with the number of points.…