Related papers: Multidimensional scaling informed by $F$-statistic…
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…
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
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…
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).…
Feature selection is a crucial step in machine learning, especially for high-dimensional datasets, where irrelevant and redundant features can degrade model performance and increase computational costs. This paper proposes a novel…
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…
Missing data present challenges in data analysis. Naive analyses such as complete-case and available-case analysis may introduce bias and loss of efficiency, and produce unreliable results. Multiple imputation (MI) is one of the most widely…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
Molecular dynamics (MD) simulations are powerful tools for elucidating the macroscopic physical properties of materials from microscopic atomic behaviors. However, the massive, high-dimensional datasets generated by MD simulations pose a…
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…
The minimum covariance determinant (MCD) estimator is ubiquitous in multivariate analysis, the critical step of which is to select a subset of a given size with the lowest sample covariance determinant. The concentration step (C-step) is a…
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)…
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…
High-dimensional compositional data, such as those from human microbiome studies, pose unique statistical challenges due to the simplex constraint and excess zeros. While dimension reduction is indispensable for analyzing such data,…
With the development of next generation sequencing technology, researchers have now been able to study the microbiome composition using direct sequencing, whose output are bacterial taxa counts for each microbiome sample. One goal of…
The continuing advances of omic technologies mean that it is now more tangible to measure the numerous features collectively reflecting the molecular properties of a sample. When multiple omic methods are used, statistical and computational…
Big Bayes is the computationally intensive co-application of big data and large, expressive Bayesian models for the analysis of complex phenomena in scientific inference and statistical learning. Standing as an example, Bayesian…
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…
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 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…