Related papers: A Facet Enumeration Algorithm for Convex Polytopes

Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…

State-of-the-art face recognition algorithms are able to achieve good performance when sufficient training images are provided. Unfortunately, the number of facial images is limited in some real face recognition applications. In this paper,…

Detect facial keypoints is a critical element in face recognition. However, there is difficulty to catch keypoints on the face due to complex influences from original images, and there is no guidance to suitable algorithms. In this paper,…

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but…

The convex hulls of face-vertex incident vectors of 3-face-colorable convex polytopes are computed. It is found that every such convex hull is a $d$-polytope with $d+2$ or $d+3$ vertices. Utilizing Gale transform and Gale diagram, we…

We study the fundamental problem of polytope membership aiming at large convex polytopes, i.e. in high dimension and with many facets, given as an intersection of halfspaces. Standard data-structures as well as brute force methods cannot…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

We consider the problem of computing a sequence of rankings that maximizes consumer-side utility while minimizing producer-side individual unfairness of exposure. While prior work has addressed this problem using linear or quadratic…

The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…

This paper presents an alternate choice of computing the convex hulls (CHs) for planar point sets. We firstly discard the interior points and then sort the remaining vertices by x- / y- coordinates separately, and later create a group…

Frequent itemsets form a polytope and can be found and analyzed with Linear Programming.

We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex…

In the field of face recognition, a model learns to distinguish millions of face images with fewer dimensional embedding features, and such vast information may not be properly encoded in the conventional model with a single branch. We…

We tackle the problem of efficiently approximating the volume of convex polytopes, when these are given in three different representations: H-polytopes, which have been studied extensively, V-polytopes, and zonotopes (Z-polytopes). We…

In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to…

The volume is an important attribute of a convex body. In general, it is quite difficult to calculate the exact volume. But in many cases, it suffices to have an approximate value. Volume estimation methods for convex bodies have been…

In this paper we consider the problem of multi-view face detection. While there has been significant research on this problem, current state-of-the-art approaches for this task require annotation of facial landmarks, e.g. TSM [25], or…

Face recognition has been studied extensively for more than 20 years now. Since the beginning of 90s the subject has became a major issue. This technology is used in many important real-world applications, such as video surveillance, smart…

Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…

Recently, we have seen an increase in the global facial recognition market size. Despite significant advances in face recognition technology with the adoption of convolutional neural networks, there are still open challenges, such as when…