Related papers: Efficient Point-to-Subspace Query in $\ell^1$: The…

Finding the nearest subspace is a fundamental problem and influential to many applications. In particular, a scalable solution that is fast and accurate for a large problem has a great impact. The existing methods for the problem are,…

Enlarging input images is a straightforward and effective approach to promote small object detection. However, simple image enlargement is significantly expensive on both computations and GPU memory. In fact, small objects are usually…

While the problem of approximate nearest neighbor search has been well-studied for Euclidean space and $\ell_1$, few non-trivial algorithms are known for $\ell_p$ when ($2 < p < \infty$). In this paper, we revisit this fundamental problem…

Visual data, such as an image or a sequence of video frames, is often naturally represented as a point set. In this paper, we consider the fundamental problem of finding a nearest set from a collection of sets, to a query set. This problem…

We consider a fundamental problem in unsupervised learning called \emph{subspace recovery}: given a collection of $m$ points in $\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$…

Learning robust representations that allow to reliably establish relations between images is of paramount importance for virtually all of computer vision. Annotating the quadratic number of pairwise relations between training images is…

This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of…

We discuss the application of random projections to the fundamental problem of deciding whether a given point in a Euclidean space belongs to a given set. We show that, under a number of different assumptions, the feasibility and…

Many emerging use cases of data mining and machine learning operate on large datasets with data from heterogeneous sources, specifically with both sparse and dense components. For example, dense deep neural network embedding vectors are…

The overarching goals in image-based localization are scale, robustness and speed. In recent years, approaches based on local features and sparse 3D point-cloud models have both dominated the benchmarks and seen successful realworld…

A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…

The approximate nearest neighbor problem ($\epsilon$-ANN) in high dimensional Euclidean space has been mainly addressed by Locality Sensitive Hashing (LSH), which has polynomial dependence in the dimension, sublinear query time, but…

There is a growing interest in computer science, engineering, and mathematics for modeling signals in terms of union of subspaces and manifolds. Subspace segmentation and clustering of high dimensional data drawn from a union of subspaces…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. Most existing methods suffer from two critical issues.…

Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…

The anchor words algorithm performs provably efficient topic model inference by finding an approximate convex hull in a high-dimensional word co-occurrence space. However, the existing greedy algorithm often selects poor anchor words,…

State-of-the-art detection systems are generally evaluated on their ability to exhaustively retrieve objects densely distributed in the image, across a wide variety of appearances and semantic categories. Orthogonal to this, many real-life…

The softmax-based loss functions and its variants (e.g., cosface, sphereface, and arcface) significantly improve the face recognition performance in wild unconstrained scenes. A common practice of these algorithms is to perform…

In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\subset \mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n…