Related papers: A dimensionality reduction technique based on the …
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…
The 2-Wasserstein distance (or RMS distance) is a useful measure of similarity between probability distributions that has exciting applications in machine learning. For discrete distributions, the problem of computing this distance can be…
The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly…
The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local…
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a…
Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…
The central goal of this paper is to establish two commonly available dimensionality reduction (DR) methods i.e. t-distributed Stochastic Neighbor Embedding (t-SNE) and Multidimensional Scaling (MDS) in Matlab and to observe their…
We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…
This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear…
Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a…
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the…
Searching for the $k$-nearest neighbors (KNN) in multimodal data retrieval is computationally expensive, particularly due to the inherent difficulty in comparing similarity measures across different modalities. Recent advances in multimodal…
Dimensionality Reduction (DR) techniques can generate 2D projections and enable visual exploration of cluster structures of high-dimensional datasets. However, different DR techniques would yield various patterns, which significantly affect…