Related papers: Distributed computation of persistent homology
The Distributed Bloom Filter is a space-efficient, probabilistic data structure designed to perform more efficient set reconciliations in distributed systems. It guarantees eventual consistency of states between nodes in a system, while…
The discrete distribution clustering algorithm, namely D2-clustering, has demonstrated its usefulness in image classification and annotation where each object is represented by a bag of weighed vectors. The high computational complexity of…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
As computer clusters become more common and the size of the problems encountered in the field of AI grows, there is an increasing demand for efficient parallel inference algorithms. We consider the problem of parallel inference on large…
Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric…
Widely employed in cognitive psychology, Gestalt theory elucidates basic principles in visual perception. However, the Gestalt principles are validated mainly by psychological experiments, lacking quantitative research supports and…
We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using…
As the data size in Machine Learning fields grows exponentially, it is inevitable to accelerate the computation by utilizing the ever-growing large number of available cores provided by high-performance computing hardware. However, existing…
This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…
To analyze the topological properties of the given discrete data, one needs to consider a continuous transform called filtration. Persistent homology serves as a tool to track changes of homology in the filtration. The outcome of the…
Distributed training of deep neural networks has received significant research interest, and its major approaches include implementations on multiple GPUs and clusters. Parallelization can dramatically improve the efficiency of training…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…
Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Ripser. The cup product operation which is available at…
Force-directed layouts belong to a popular class of methods used to position nodes in a node-link diagram. However, they typically lack direct consideration of global structures, which can result in visual clutter and the overlap of…
The persistent homology pipeline includes the reduction of a, so-called, boundary matrix. We extend the work of Bauer et al. (2014) and Chen et al. (2011) where they show how to use dependencies in the boundary matrix to adapt the reduction…
Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…
Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…
This study details an approach for the analysis of social media collected political data through the lens of Topological Data Analysis, with a specific focus on Persistent Homology and the political processes they represent by proposing a…