Related papers: Dimensionality Reduction using Elastic Measures

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

Developing interpretable machine learning models has become an increasingly important issue. One way in which data scientists have been able to develop interpretable models has been to use dimension reduction techniques. In this paper, we…

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…

Machine Learning facilitates building a large variety of models, starting from elementary linear regression models to very complex neural networks. Neural networks are currently limited by the size of data provided and the huge…

We investigate metric learning in the context of dynamic time warping (DTW), the by far most popular dissimilarity measure used for the comparison and analysis of motion capture data. While metric learning enables a problem-adapted…

The modern image search system requires semantic understanding of image, and a key yet under-addressed problem is to learn a good metric for measuring the similarity between images. While deep metric learning has yielded impressive…

When visualizing a high-dimensional dataset, dimension reduction techniques are commonly employed which provide a single 2-dimensional view of the data. We describe ENS-t-SNE: an algorithm for Embedding Neighborhoods Simultaneously that…

In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases…

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…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of quality assessment measures, in order to evaluate the resulting low-dimensional representation independently…

Ultrasound elasticity images which enable the visualization of quantitative maps of tissue stiffness can be reconstructed by solving an inverse problem. Classical model-based approaches for ultrasound elastography use deterministic finite…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

A fundamental task in machine learning involves visualizing high-dimensional data sets that arise in high-impact application domains. When considering the context of large imbalanced data, this problem becomes much more challenging. In this…

It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…

Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…

In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It…

In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…