Related papers: Survey: Geometric Foundations of Data Reduction

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…

We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…

Non-linear dimensionality reduction (NLDR) methods such as t-distributed stochastic neighbour embedding (t-SNE) are ubiquitous in the natural sciences, however, the appropriate use of these methods is difficult because of their complex…

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

Existing methods have demonstrated effective performance on a single degradation type. In practical applications, however, the degradation is often unknown, and the mismatch between the model and the degradation will result in a severe…

This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Exploratory data analysis is a fundamental aspect of knowledge discovery that aims to find the main characteristics of a dataset. Dimensionality reduction, such as manifold learning, is often used to reduce the number of features in a…

Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…

Reward maximization, safe exploration, and intrinsic motivation are often studied as separate objectives in reinforcement learning (RL). We present a unified geometric framework, that views these goals as instances of a single optimization…

Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…

Current hyperspectral anomaly detection (HAD) benchmark datasets suffer from low resolution, simple background, and small size of the detection data. These factors also limit the performance of the well-known low-rank representation (LRR)…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality…

In the recent past, nested structures in Riemannian manifolds has been studied in the context of dimensionality reduction as an alternative to the popular principal geodesic analysis (PGA) technique, for example, the principal nested…

Implicit Neural Representations (INRs) have emerged as a powerful tool for geometric representation, yet their suitability for physics-based simulation remains underexplored. While metrics like Hausdorff distance quantify surface…

This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data…

\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating…