An Algorithmic Way to Generate Simplexes for Topological Data Analysis
نویسندگان
چکیده
In this article we present a new algorithm for creating simplicial Vietoris-Rips complexes that is easily parallelizable using computation models like MapReduce and Apache Spark. The algorithm does not involve any computation in homology spaces.
منابع مشابه
TOPOLOGICAL SIMILARITY OF L-RELATIONS
$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...
متن کاملUnderstanding Latent Semantic Indexing: A Topological Structure Analysis Using Q-Analysis Method
The method of latent semantic indexing (LSI) is well known for tackling the synonymy and polysemy problems in information retrieval. However, its performance can be very different for various datasets and the questions of what characteristics of a dataset and why these characteristics contribute to this difference have not been fully understood. In this paper, we propose that the mathematical s...
متن کاملA scalable data structure for three-dimensional non-manifold objects
In this paper, we address the problem of representing and manipulating non-manifold, mixed-dimensional objects described by three-dimensional simplicial complexes embedded in the 3D Euclidean space. We describe the design and the implementation of a new data structure, that we call the non-manifold indexed data structure with adjacencies (NMIA), which can represent any three-dimensional Euclide...
متن کاملSuper- and sub-additive transformations of aggregation functions from the point of view of approximation
The way super- and sub-additive transformations of aggregation functions are introduced involve suprema and infima taken over simplexes whose dimensions may grow arbitrarily. Exact values of such transformations may thus be hard to determine in general. In this note we discuss methods of algorithmic approximation of such transformations.
متن کاملAlgebraic Topology for Knowledge Representation in Analogy Solving
We propose a computational model for analogy solving based on a topological formalism of representation. The source and the target analogs are represented as simplexes and the analogy solving is modeled as a topological deformation of these simplexes along a polygonal chain and according to some constraints. We apply this framework to the resolution of IQ-tests typically presented as “given A, ...
متن کامل