Related papers: Compression with wildcards: Abstract simplicial co…
Given are the facets of an abstract (finite) simplicial complex SC. We show how to partition SC into few pieces, each one compactly encoded by the use of wildcards. Such a representation is useful for the optimization of a target function…
Like any simplicial complex the simplicial complex of all frequent sets can be compressed with wildcards once the maximal frequent sets (=facets) are known. Namely, the task (a particular kind of ALLSAT problem) is achieved by the author's…
The model set of a general Boolean function in CNF is calculated in a compressed format, using novel wildcards. This method can be explained in very visual ways. Preliminary comparison with existing methods (BDD's and Mathematica's ESOP…
With the ever-increasing volume of visual data, the efficient and lossless transmission, along with its subsequent interpretation and understanding, has become a critical bottleneck in modern information systems. The emerged codebook-based…
Our main objective is the COMPRESSED enumeration (based on wildcards) of all minimal hitting sets of general hypergraphs. To the author's best knowledge the only previous attempt towards compression, due to Toda, is based on BDD's and much…
Let $W$ be a finite set which simultaneously serves as the universe of any poset $(W,\preceq)$ and as the vertex set of any graph $G$. Our algorithm, abbreviated A-I-I, enumerates (in a compressed format using don't-care symbols) all…
In this paper, we propose a novel end-to-end feature compression scheme by leveraging the representation and learning capability of deep neural networks, towards intelligent front-end equipped analysis with promising accuracy and…
We compare various viewpoints on down-sets (simplicial complexes), illustrating how the combinatorial inclusion-exclusion principle may serve as an alternative to more advanced methods of studying their face numbers.
It plays a fundamental role to compactly represent the visual information towards the optimization of the ultimate utility in myriad visual data centered applications. With numerous approaches proposed to efficiently compress the texture…
As the latest video coding standard, versatile video coding (VVC) has shown its ability in retaining pixel quality. To excavate more compression potential for video conference scenarios under ultra-low bitrate, this paper proposes a bitrate…
In this paper, we propose a scalable image compression scheme, including the base layer for feature representation and enhancement layer for texture representation. More specifically, the base layer is designed as the deep learning feature…
We develop a new method called affine facial reduction (FR) for recovering Slater's condition for semidefinite programming (SDP) relaxations of combinatorial optimization (CO) problems. Affine FR is a user-friendly method, as it is fully…
An algorithm is developed to compute the complete CS decomposition (CSD) of a partitioned unitary matrix. Although the existence of the CSD has been recognized since 1977, prior algorithms compute only a reduced version (the 2-by-1 CSD)…
We present a novel technique for converting a Boolean CNF into an orthogonal DNF, aka exclusive sum of products. Our method (which will be pitted against a hardwired command from Mathematica) zooms in on the models of the CNF by imposing…
In semidefinite programming (SDP), a number of pre-processing techniques have been developed including chordal-completion procedures, which reduce the dimension of individual constraints by exploiting sparsity therein, and facial reduction,…
Current methods which compress multisets at an optimal rate have computational complexity that scales linearly with alphabet size, making them too slow to be practical in many real-world settings. We show how to convert a compression…
We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible…
AI systems rely on extensive training on large datasets to address various tasks. However, image-based systems, particularly those used for demographic attribute prediction, face significant challenges. Many current face image datasets…
Recent deep learning-based methods for lossy image compression achieve competitive rate-distortion performance through extensive end-to-end training and advanced architectures. However, emerging applications increasingly prioritize semantic…
Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…