Related papers: Minimum-Distortion Embedding
With the development of feature extraction technique, one sample always can be represented by multiple features which locate in high-dimensional space. Multiple features can re ect various perspectives of one same sample, so there must be…
We initiate the study of metric embeddings with \emph{outliers}. Given some metric space $(X,\rho)$ we wish to find a small set of outlier points $K \subset X$ and either an isometric or a low-distortion embedding of $(X\setminus K,\rho)$…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
Large-scale multimodal contrastive learning has recently achieved impressive success in learning rich and transferable representations, yet it remains fundamentally limited by the uniform treatment of feature dimensions and the neglect of…
We state an open problem in the theory of diversities: what is the worst case minimal distortion embedding of a diversity on $n$ points in $\ell_1$. This problem is the diversity analogue of a famous problem in metric geometry: what is the…
Depth position highly affects lens distortion, especially in close-range photography, which limits the measurement accuracy of existing stereo vision systems. Moreover, traditional depth-dependent distortion models and their calibration…
Construction of optimal deformations is one of the long standing problems of computational mathematics. We consider the problem of computing quasi-isometric deformations with minimal possible quasi-isometry constant (global estimate for…
Similarity query is the family of queries based on some similarity metrics. Unlike the traditional database queries which are mostly based on value equality, similarity queries aim to find targets "similar enough to" the given data objects,…
Deep metric learning (DML) is a cornerstone of many computer vision applications. It aims at learning a mapping from the input domain to an embedding space, where semantically similar objects are located nearby and dissimilar objects far…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
Monocular Depth Estimation (MDE) enables spatial understanding, 3D reconstruction, and autonomous navigation, yet deep learning approaches often predict only relative depth without a consistent metric scale. This limitation reduces…
Constructing latent vector representation for nodes in a network through embedding models has shown its practicality in many graph analysis applications, such as node classification, clustering, and link prediction. However, despite the…
Low isometric distortion is often required for mesh parameterizations. A configuration of some vertices, where the distortion is concentrated, provides a way to mitigate isometric distortion, but determining the number and placement of…
In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), or on a distance matrix denoting original space distances, is mapped to (projected onto) one point in a low dimensional space…
In this paper, we investigate the approximability of two node deletion problems. Given a vertex weighted graph $G=(V,E)$ and a specified, or "distinguished" vertex $p \in V$, MDD(min) is the problem of finding a minimum weight vertex set $S…
Monocular Depth Estimation (MDE) is a fundamental computer vision task with important applications in 3D vision. The current mainstream MDE methods employ an encoder-decoder architecture with multi-level/scale feature processing. However,…
Although Vision Transformers (ViTs) have recently advanced computer vision tasks significantly, an important real-world problem was overlooked: adapting to variable input resolutions. Typically, images are resized to a fixed resolution,…
Motivated by the need for communication-efficient distributed learning, we investigate the method for compressing a unit norm vector into the minimum number of bits, while still allowing for some acceptable level of distortion in recovery.…
Networks have been widely used as the data structure for abstracting real-world systems as well as organizing the relations among entities. Network embedding models are powerful tools in mapping nodes in a network into continuous…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…