Related papers: Minimum-Distortion Embedding

One of the most well-known and simplest models for diversity maximization is the Max-Min Diversification (MMD) model, which has been extensively studied in the data mining and database literature. In this paper, we initiate the study of the…

We propose two practical non-convex approaches for learning near-isometric, linear embeddings of finite sets of data points. Given a set of training points $\mathcal{X}$, we consider the secant set $S(\mathcal{X})$ that consists of all…

This paper introduces the Pareto Data Framework, an approach for identifying and selecting the Minimum Viable Data (MVD) required for enabling machine learning applications on constrained platforms such as embedded systems, mobile devices,…

Many real-world problems require reasoning across multiple scales, demanding models which operate not on single data points, but on entire distributions. We introduce generative distribution embeddings (GDE), a framework that lifts…

Distortion is widely existed in the images captured by popular wide-angle cameras and fisheye cameras. Despite the long history of distortion rectification, accurately estimating the distortion parameters from a single distorted image is…

The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…

Recent token reduction methods for Vision Transformers (ViTs) incorporate token merging, which measures the similarities between token embeddings and combines the most similar pairs. However, their merging policies are directly dependent on…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

Concepts are used to solve the term-mismatch problem. However, we need an effective similarity measure between concepts. Word embedding presents a promising solution. We present in this study three approaches to build concepts vectors based…

In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse…

We consider estimating a random vector from its noisy projections onto low dimensional subspaces constituting a fusion frame. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is…

Segmentation of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data. Although deep neural networks provide flexible nonparametric estimators, unconstrained…

Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…

Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…

Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…

Multiview network embedding aims at projecting nodes in the network to low-dimensional vectors, while preserving their multiple relations and attribute information. Contrastive learning approaches have shown promising performance in this…

Traditional monocular Visual-Inertial Odometry (VIO) systems struggle in low-texture environments where sparse visual features are insufficient for accurate pose estimation. To address this, dense Monocular Depth Estimation (MDE) has been…

Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular, they can spuriously separate connected components of the…

In the metric distortion problem there is a set of candidates $C$ and voters $V$ in the same metric space. The goal is to select a candidate minimizing the social cost: the sum of distances of the selected candidate from all the voters, and…

Deep metric learning aims to transform input data into an embedding space, where similar samples are close while dissimilar samples are far apart from each other. In practice, samples of new categories arrive incrementally, which requires…