Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of permutation matrices, we relax the variable to be the more tractable doubly stochastic matrices and add an Lp-norm (0 < p < 1) regularization term to the objective fu...

The L-curve is often applied to determine a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side contaminated by errors of unknown norm. The location of the vertex of the L-curve typically yields a suitable value of the regularization parameter. However, the computation of the L-curve and of its curvature is quite costly ...

Class-instance label propagation algorithms have been successfully used to fuse information from multiple sources in order to enrich a set of unlabeled instances with class labels. Yet, nobody has explored the relationships between the instances themselves to enhance an initial set of class-instance pairs. We propose two graph-theoretic methods (centrality and regularization), which start with ...

In this paper we review the main techniques for volume reconstruction from a set of views using Shape from Silhouette techniques and we propose a new method that adapts the inconsistencies analysis shown in (Landabaso et al., 2008) to the graph cuts framework (Snow et al., 2000) which allows the introduction of spatial regularization. For this aim we use a new viewing line based inconsistency a...

Formulas for the most general case of the zeta function associated to a quadratic+linear+constant form (in Z) are given. As examples, the spectral zeta functions ζα(s) corresponding to bosonic (α = 2) and to fermionic (α = 3) quantum fields living on a noncommutative, partially toroidal spacetime are investigated. Simple poles show up at s = 0, as well as in other places (simple or double, depe...

In the classic theory of elastic rods, two non-adjacent points along the rod may upon contact occupy the same physical space. We develop an elastic rod model with a pairwise repulsive potential such that if two non-adjacent points along the rod are close in physical space, there is an energy barrier that prevents contact. For adjacent pairs, the repulsive potential is negligible and the elastic...

A variety of graph-based semi-supervised learning (SSL) algorithms and graph construction methods have been proposed in the last few years. Despite their apparent empirical success, the field of SSL lacks a detailed study that empirically evaluates the influence of graph construction on SSL. In this paper we provide such an experimental study. We combine a variety of graph construction methods ...

This paper studies learning node representations with graph neural networks (GNNs) for unsupervised scenario. Specifically, we derive a theoretical analysis and provide an empirical demonstration about the non-steady performance of GNNs over different datasets, when supervision signals are not appropriately defined. The depends on both feature smoothness locality structure. To smooth discrepanc...