Related papers: Convex hull algorithms based on some variational m…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
We consider the following problem in computational geometry: given, in the d-dimensional real space, a set of points marked as positive and a set of points marked as negative, such that the convex hull of the positive set does not intersect…
This paper investigates the transformation of a convex hull, derived from a d-dimensional point cloud, into a concave surface. Our primary focus is on the development of a methodology that ensures all points in the point cloud are…
Recently, motivated by the rapid increase of the data size in various applications, Monemizadeh [APPROX'23] and Driemel, Monemizadeh, Oh, Staals, and Woodruff [SoCG'25] studied geometric problems in the setting where the only access to the…
Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many…
When faced with multiple minima of an "inner-level" convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary "outer-level" convex objective of interest. Bilevel…
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
Salient object detection plays an important part in a vision system to detect important regions. Convolutional neural network (CNN) based methods directly train their models with large-scale datasets, but what is the crucial feature for…
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are…
3D object recognition accuracy can be improved by learning the multi-scale spatial features from 3D spatial geometric representations of objects such as point clouds, 3D models, surfaces, and RGB-D data. Current deep learning approaches…
Outlier Detection is a critical and cardinal research task due its array of applications in variety of domains ranging from data mining, clustering, statistical analysis, fraud detection, network intrusion detection and diagnosis of…
We study the polyhedral convex hull structure of a mixed-integer set which arises in a class of cardinality-constrained concave submodular minimization problems. This class of problems has an objective function in the form of $f(a^\top x)$,…
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…
It has been a long time, since data mining technologies have made their ways to the field of data management. Classification is one of the most important data mining tasks for label prediction, categorization of objects into groups,…
Computing the convex hull of a planar $n$-point set $P$ is one of the most fundamental problems in computational geometry. It has an $\Omega(n \log n)$ lower bound in the algebraic computation tree model, and many convex hull algorithms…
Vector-based algorithms are novel algorithms in optimal any-angle path planning that are motivated by bug algorithms, bypassing free space by directly conducting line-of-sight checks between two queried points, and searching along obstacle…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sublinear…
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…