Computational Topology-based Analysis of Data Sets Correlation Function

Abstract

In this paper, relying on computational approaches based on topological data analysis, and applying the computational algorithm in order to derive topological invariants such as Betti numbers, we present a new method for computing scaling exponents of time series. Our results indicate that the maximum value of 0-Betti has scaling behavior with respect to Hurst exponent. In addition, the computed Hurst exponent using topological data analysis approach is independent to the size of corresponding data set.

Full text

Computational Topology-based analysis of data sets correlation function
Masoomy, Hosein1,2; Askari, Behrooz1,2 ; Movahed, Seyed Mohammad Sadegh1,2
1Department of Physics, Shahid Beheshti University, Velenjak, Tehran, IRAN
2Ibn-Sina Multidisciplinary Laboratory,Department of Physics, Shahid Beheshti University, Velenjak, Tehran, IRAN
Abstract
In this paper, relying on computational approaches based on topological data analysis, and applying the
computational algorithm in order to derive topological invariants such as Betti numbers, we present a new method
for computing scaling exponents of time series. Our results indicate that the maximum value of 0-Betti has scaling
behavior with respect to Hurst exponent. In addition, the computed Hurst exponent using topological data analysis
approach is independent to the size of corresponding data set.
Keywords: Topological Data Analysis, Scaling properties, correlation, Hurst exponent
PACS No.
1Complexity
2Effective Theory
][
3Measure-theoretic
4Probabilistic framework
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][
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5Weighted two-point correlation function
6Detrended Fluctuation Analysis
7Finite size effect
8Irregularity
9Hurst exponent
TDA
10 Topological Data Analysis (TDA)
11 Topological invariant
12 Topological space
13 Persistent Homology (PH)
14 Persistent Barcode (PB)
15 Persistent Diagram (PD)
16 Betti Curve
17 Simplex
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18 Chain
19 Cycle
20 Boundary
21 Betti number
22 Holes
0
0
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