Related papers: Face numbers of down-sets
Many practical applications in topological data analysis arise from data in the form of point clouds, which then yield simplicial complexes. The combinatorial structure of simplicial complexes captures the topological relationships between…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials.
Face clustering plays an essential role in exploiting massive unlabeled face data. Recently, graph-based face clustering methods are getting popular for their satisfying performances. However, they usually suffer from excessive memory…
Neighborly cubical polytopes are known as the cubical analogues of the cyclic polytopes. Using the short cubical $h$-vectors of cubical polytopes (introduced by Adin), we derive an explicit formula for the face numbers of the neighborly…
Feature selection has drawn much attention over the last decades in machine learning because it can reduce data dimensionality while maintaining the original physical meaning of features, which enables better interpretability than feature…
In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a 'minimal' set of coarse nodes (sometimes called corners) which assures…
In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…
In contrast to comparing faces via single exemplars, matching sets of face images increases robustness and discrimination performance. Recent image set matching approaches typically measure similarities between subspaces or manifolds, while…
Face recognition has already been well studied under the visible light and the infrared,in both intra-spectral and cross-spectral cases. However, how to fuse different light bands, i.e., hyperspectral face recognition, is still an open…
We provide a new combinatorial approach to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals. With this method we can recover most of the known results on resolutions of edge ideals with…
Generic face detection algorithms do not perform very well in the mobile domain due to significant presence of occluded and partially visible faces. One promising technique to handle the challenge of partial faces is to design face…
We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities…
Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via…
The perception of facial beauty is a complex phenomenon depending on many, detailed and global facial features influencing each other. In the machine learning community this problem is typically tackled as a problem of supervised inference.…
Face detection is a long-standing challenge in the field of computer vision, with the ultimate goal being to accurately localize human faces in an unconstrained environment. There are significant technical hurdles in making these systems…
This work presents an analysis of the efficiency of image augmentations for the face recognition problem from limited data. We considered basic manipulations, generative methods, and their combinations for augmentations. Our results show…
Face recognition has been an active research area in the past few decades. In general, face recognition can be very challenging due to variations in viewpoint, illumination, facial expression, etc. Therefore it is essential to extract…
We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and…
One form of the inclusion-exclusion principle asserts that if A and B are functions of finite sets then A(S) is the sum of B(T) over all subsets T of S if and only if B(S) is the sum of (-1)^|S-T| A(T) over all subsets T of S. If we replace…