Related papers: Continuous Multidimensional Scaling
We present a novel view of nonlinear manifold learning using derivative-free optimization techniques. Specifically, we propose an extension of the classical multi-dimensional scaling (MDS) method, where instead of performing gradient…
Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
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…
We present the MDS feature learning framework, in which multidimensional scaling (MDS) is applied on high-level pairwise image distances to learn fixed-length vector representations of images. The aspects of the images that are captured by…
This study proposes median consensus embedding (MCE) to address variability in low-dimensional embeddings caused by random initialization in nonlinear dimensionality reduction techniques such as $t$-distributed stochastic neighbor…
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…
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).…
We introduce Non-Euclidean-MDS (Neuc-MDS), an extension of classical Multidimensional Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is to generalize the standard inner product to symmetric bilinear forms…
We develop a formal statistical framework for classical multidimensional scaling (CMDS) applied to noisy dissimilarity data. We establish distributional convergence results for the embeddings produced by CMDS for various noise models, which…
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 embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
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…
Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…
The landmark multi-dimensional scaling (LMDS) is a leading method that embeds new points to an existing coordinate system based on observed distance information. It has long been known as a variant of Nystr\"{o}m algorithm. It was recently…
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…
Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…
The recent rapid growth of the dimension of many datasets means that many approaches to dimension reduction (DR) have gained significant attention. High-performance DR algorithms are required to make data analysis feasible for big and fast…
Progressive dimensionality reduction algorithms allow for visually investigating intermediate results, especially for large data sets. While different algorithms exist that progressively increase the number of data points, we propose an…