Related papers: Multidimensional Scaling of Noisy High Dimensional…

We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

Noisy labeled data represent a rich source of information that often are easily accessible and cheap to obtain, but label noise might also have many negative consequences if not accounted for. How to fully utilize noisy labels has been…

The human brain distinguishes speech sounds by mapping acoustic signals into a latent perceptual space. This space can be estimated via multidimensional scaling (MDS), preserving the similarity structure in lower dimensions. However,…

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 develop a multidimensional version of Gradient-MUSIC for estimating the frequencies of a nonharmonic signal from noisy samples. The guiding principle is that frequency recovery should be based only on the signal subspace determined by…

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…

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…

This paper reports on the state-of-the-art in application of multidimensional scaling (MDS) techniques to create semantic maps in linguistic research. MDS refers to a statistical technique that represents objects (lexical items, linguistic…

Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However,…

Classical multidimensional scaling (CMDS) is a technique that embeds a set of objects in a Euclidean space given their pairwise Euclidean distances. The main part of CMDS involves double centering a squared distance matrix and using a…

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…

For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…

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,…

Current and future wireless applications strongly rely on precise real-time localization. A number of applications such as smart cities, Internet of Things (IoT), medical services, automotive industry, underwater exploration, public safety,…

Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional…

We reexamine the the classical multidimensional scaling (MDS). We study some special cases, in particular, the exact solution for the sub-space formed by the 3 dimensional principal coordinates is derived. Also we give the extreme case when…

With the recent development of technology, wireless sensor networks (WSN) are becoming an important part of many applications. Knowing the exact location of each sensor in the network is very important issue. Therefore, the localization…

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 is a widely used method in dimensionality reduction and manifold learning. The method takes in a dissimilarity matrix and outputs a low-dimensional configuration matrix based on a spectral decomposition.…