相关论文: Efficient Point-to-Subspace Query in $\ell^1$: The…
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image),…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…
Randomized dimensionality reduction has been recognized as one of the fundamental techniques in handling high-dimensional data. Starting with the celebrated Johnson-Lindenstrauss Lemma, such reductions have been studied in depth for the…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
We study the Approximate Nearest Neighbor problem for metric spaces where the query points are constrained to lie on a subspace of low doubling dimension, while the data is high-dimensional. We show that this problem can be solved…
We describe a new method called t-ETE for finding a low-dimensional embedding of a set of objects in Euclidean space. We formulate the embedding problem as a joint ranking problem over a set of triplets, where each triplet captures the…
Efficient indexing and searching of high dimensional data has been an area of active research due to the growing exploitation of high dimensional data and the vulnerability of traditional search methods to the curse of dimensionality. This…
Personalized text-to-image generation has attracted unprecedented attention in the recent few years due to its unique capability of generating highly-personalized images via using the input concept dataset and novel textual prompt. However,…
Linear subspace representations of appearance variation are pervasive in computer vision. This paper addresses the problem of robustly matching such subspaces (computing the similarity between them) when they are used to describe the scope…
We demonstrate that frequently appearing objects can be discovered by training randomly sampled patches from a small number of images (100 to 200) by self-supervision. Key to this approach is the pattern space, a latent space of patterns…
Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…
Conceptual spaces are geometric representations of conceptual knowledge, in which entities correspond to points, natural properties correspond to convex regions, and the dimensions of the space correspond to salient features. While…
We study the design of efficient approximation algorithms for the $\ell$-center clustering and minimum-diameter $\ell$-clustering problems in high dimensional Euclidean and Hamming spaces. Our main tool is randomized dimension reduction.…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…