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A graph-based classification method is proposed for semi-supervised learning in the case of Euclidean data and for classification in the case of graph data. Our manifold learning technique is based on a convex optimization problem involving…

We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…

The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used.…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

We study the two dimensional least gradient problem in a convex polygonal set in the plane. We show existence of solutions when the boundary data are attained in the trace sense. Due to the lack of strict convexity, the classical results…

A novel 3D shape classification scheme, based on collaborative representation learning, is investigated in this work. A data-driven feature-extraction procedure, taking the form of a simple projection operator, is in the core of our…

The efficient computation of viewpoints under consideration of various system and process constraints is a common challenge that any robot vision system is confronted with when trying to execute a vision task. Although fundamental research…

Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…

Traditional deep learning models rely on methods such as softmax cross-entropy and ArcFace loss for tasks like classification and face recognition. These methods mainly explore angular features in a hyperspherical space, often resulting in…

We investigate degree bounds for fields of rational invariants of representations of finite groups. We prove many cases of a bound for $\mathbb{Z}/p\mathbb{Z}$ conjectured by Blum-Smith, Garcia, Hidalgo, and Rodriguez. For arbitrary groups,…

We prove that a classifier with a Barron-regular decision boundary can be approximated with a rate of high polynomial degree by ReLU neural networks with three hidden layers when a margin condition is assumed. In particular, for strong…

Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…

This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…

Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…

We show that a closed piecewise-linear hypersurface immersed in $R^n$ ($n\ge 3$) is the boundary of a convex body if and only if every point in the interior of each $(n-3)$-face has a neighborhood that lies on the boundary of some convex…

We study geometric characterizations of unbounded integer polynomial optimization problems. While unboundedness along a ray fully characterizes unbounded integer linear and quadratic optimization problems, we show that this is not the case…

We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak in the case of quadratic map. We…

Regression via classification (RvC) is a common method used for regression problems in deep learning, where the target variable belongs to a set of continuous values. By discretizing the target into a set of non-overlapping classes, it has…