Related papers: Projection pursuit for discrete data
We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a…
Tomographic investigations are a central tool in medical applications, allowing doctors to image the interior of patients. The corresponding measurement process is commonly modeled by the Radon transform. In practice, the solution of the…
Moving objects leave extended tracks in optical images acquired with a telescope that is tracking stars or other targets. By searching images for these tracks, one can obtain statistics on populations of space debris in Earth orbit. The…
Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…
Projection Pursuit is a classic exploratory technique for finding interesting projections of a dataset. We propose a method for recovering projections containing either Imbalanced Clusters or a Bernoulli-Rademacher distribution using a…
We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…
This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large…
There has been recently a lot of research on sparse variants of random projections, faster adaptations of the state-of-the-art dimensionality reduction technique originally due to Johsnon and Lindenstrauss. Although the construction is very…
Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an…
We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label…
Communication of dense information between humans and machines is relatively low bandwidth. Many modern search and recommender systems operate as machine learning black boxes, giving little insight as to how they represent information or…
We consider the reconstruction of a two-dimensional discrete image from a set of tomographic measurements corresponding to the Radon projection. Assuming that the image has a structure where neighbouring pixels have a larger probability to…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Multi-Object Tracking (MOT) aims to maintain stable and uninterrupted trajectories for each target. Most state-of-the-art approaches first detect objects in each frame and then implement data association between new detections and existing…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
The accurate visual tracking of a moving object is a human fundamental skill that allows to reduce the relative slip and instability of the object's image on the retina, thus granting a stable, high-quality vision. In order to optimize…
We propose learning discrete structured representations from unlabeled data by maximizing the mutual information between a structured latent variable and a target variable. Calculating mutual information is intractable in this setting. Our…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…
The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos…