Related papers: Compression for 2-Parameter Persistent Homology
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
Network compression has been widely studied since it is able to reduce the memory and computation cost during inference. However, previous methods seldom deal with complicated structures like residual connections, group/depth-wise…
Recent advancements in deep learning-based image compression are notable. However, prevalent schemes that employ a serial context-adaptive entropy model to enhance rate-distortion (R-D) performance are markedly slow. Furthermore, the…
In recent years, great progress has been made in a variety of application domains thanks to the development of increasingly deeper neural networks. Unfortunately, the huge number of units of these networks makes them expensive both…
Recurrent neural networks have a strong inductive bias towards learning temporally compressed representations, as the entire history of a sequence is represented by a single vector. By contrast, Transformers have little inductive bias…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
Visual analytics have played an increasingly critical role in the Internet of Things, where massive visual signals have to be compressed and fed into machines. But facing such big data and constrained bandwidth capacity, existing…
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…
We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…
With the increasing demand for video content at higher resolutions, it is evermore critical to find ways to limit the complexity of video encoding tasks in order to reduce costs, power consumption and environmental impact of video services.…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
This article describes a lightweight additive homomorphic algorithm with the same encryption and decryption keys. Compared to standard additive homomorphic algorithms like Paillier, this algorithm reduces the computational cost of…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
The task of finding the optimal compression of a polyline with straight-line segments and arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. Optimal compression algorithms find…
The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…
Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation…
Data deduplication saves storage space by identifying and removing repeats in the data stream. Compared with traditional compression methods, data deduplication schemes are more time efficient and are thus widely used in large scale storage…
We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal…
In this article, we introduce a new parameterized family of topological descriptors, taking the form of candidate decompositions, for multi-parameter persistence modules, and we identify a subfamily of these descriptors, that we call…