Related papers: Modified Multidimensional Scaling and High Dimensi…
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…
Multidimensional Scaling (MDS) is a classical technique for embedding data in low dimensions, still in widespread use today. Originally introduced in the 1950's, MDS was not designed with high-dimensional data in mind; while it remains…
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…
Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…
Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…
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…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
Subspace clustering is the classical problem of clustering a collection of data samples that approximately lie around several low-dimensional subspaces. The current state-of-the-art approaches for this problem are based on the…
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…
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…
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…
We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and,…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
Modeling of high-dimensional data is very important to categorize different classes. We develop a new mixture model called Multinomial cluster-weighted model (MCWM). We derive the identifiability of a general class of MCWM. We estimate the…
Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is…
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.…
Deep Metric Learning (DML) plays a critical role in various machine learning tasks. However, most existing deep metric learning methods with binary similarity are sensitive to noisy labels, which are widely present in real-world data. Since…
In current research, machine and deep learning solutions for the classification of temporal data are shifting from single-channel datasets (univariate) to problems with multiple channels of information (multivariate). The majority of these…
Deep neural networks (DNNs) offer a means of addressing the challenging task of clustering high-dimensional data. DNNs can extract useful features, and so produce a lower dimensional representation, which is more amenable to clustering…
Clustering in high dimension spaces is a difficult task; the usual distance metrics may no longer be appropriate under the curse of dimensionality. Indeed, the choice of the metric is crucial, and it is highly dependent on the dataset…