Tuning the performance of a computational persistent homology package

Hylton, Alan; Henselman-Petrusek, Gregory; Sang, Janche; Short, R.T.

doi:10.1002/spe.2678

Cited by 12 publications

(7 citation statements)

References 36 publications

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“…The first part of our analysis was performed in Microsoft Excel 2016 (Microsoft Office 365, Version 2004, Microsoft Corp., Redmond, WA, USA) and the free statistics packages JASP (Version 0.12.0, Amsterdam, Netherlands [20]) and jamovi (Version 1.2.16 [21]). We descriptively compared individual mean HRex between recovered and strained states before comparing changes from Monday to Friday (ΔStrain) and changes from Friday to Monday (ΔRecovery).…”

Section: Discussionmentioning

confidence: 99%

Monitoring training and recovery responses with heart rate measures during standardized warm-up in elite badminton players

et al. 2020

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Purpose To investigate short-term training and recovery-related effects on heart rate during a standardized submaximal running test. Methods Ten elite badminton players (7 females and 3 males) were monitored during a 12-week training period in preparation for the World Championships. Exercise heart rate (HRex) and perceived exertion were measured in response to a 5-min submaximal shuttle-run test during the morning session warm-up. This test was repeatedly performed on Mondays after 1–2 days of pronounced recovery (‘recovered’ state; reference condition) and on Fridays following 4 consecutive days of training (‘strained’ state). In addition, the serum concentration of creatine kinase and urea, perceived recovery–stress states, and jump performance were assessed before warm-up. Results Creatine kinase increased in the strained compared to the recovered state and the perceived recovery–stress ratings decreased and increased, respectively (range of average effects sizes: |d| = 0.93–2.90). The overall HRex was 173 bpm and the observed within-player variability (i.e., standard deviation as a coefficient of variation [CV]) was 1.3% (90% confidence interval: 1.2% to 1.5%). A linear reduction of -1.4% (-3.0% to 0.3%) was observed in HRex over the 12-week observational period. HRex was -1.5% lower (-2.2% to -0.9%) in the strained compared to the recovered state, and the standard deviation (as a CV) representing interindividual variability in this response was 0.7% (-0.6% to 1.2%). Conclusions Our findings suggest that HRex measured during a standardized warm-up can be sensitive to short-term accumulation of training load, with HRex decreasing on average in response to consecutive days of training within repeated preparatory weekly microcycles. From a practical perspective, it seems advisable to determine intra-individual recovery–strain responses by repeated testing, as HRex responses may vary substantially between and within players.

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Section: Discussionmentioning

confidence: 99%

Monitoring training and recovery responses with heart rate measures during standardized warm-up in elite badminton players

et al. 2020

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“…In the end, we are left with 65053 edges, and a maximal filtration value of 1.427. First, note that some implementations (of which the first one is Eirene [19]) of Rips persistence first check at which filtration value the complex becomes a cone (here around 2) and ignore longer edges. In our algorithm, this check is performed implicitly and the long edges are dominated by the apex of the cone and thus get removed (we actually manage to go significantly lower than 2).…”

Section: Complete Graphmentioning

confidence: 99%

“…Traditionally, there are two complementary lines of research that have been explored to improve the computation of persistent homology. The first approach led to improvement of the persistence algorithm (the boundary matrix reduction algorithm) and of its analysis, to efficient implementations and optimizations, and to a new generation of software [17,4,3,19,23,28,1]. The second and complementary approach is to reduce (or simplify) the input filtration to a smaller filtration through various geometric or topological techniques in an exact or approximate way and then compute the persistent homology of the smaller reduced filtration.…”

Section: Introductionmentioning

confidence: 99%

Swap, Shift and Trim to Edge Collapse a Filtration

Glisse¹,

Pritam²

2022

Preprint

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Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag (or clique) complexes, which can in particular speed up the computation of its persistent homology [6]. They used so-called edge collapse to reduce the input flag filtration and their reduction method required only the 1skeleton of the filtration. In this paper we revisit the usage of edge collapse for efficient computation of persistent homology. We first give a simple and intuitive explanation of the principles underlying that algorithm. This in turn allows us to propose various extensions including a zigzag filtration simplification algorithm. We finally show some experiments to better understand how it behaves.

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“…We will focus primarily on sequential approaches to persistent homology computation. Other, non-sequential approaches include the chunk algorithm [3], spectral sequence procedures [46,22], Morse-theoretic batch reduction [32,33,58,6,29,34,48,59,21], distributed algorithms [4,53,44], GPU acceleration [63,38], streaming [41], and homotopy collapse [9,20,8]. There are closely related techniques in matrix factorization and zigzag persistence [50,11,10].…”

Section: Related Literaturementioning

confidence: 99%

U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology

Hang¹,

Giusti²,

Ziegelmeier³

et al. 2021

Preprint

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Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -and indeed, linear -algebra. However, matrices in this domain are typically large, with rows and columns numbered in billions. Low-rank approximation of such arrays typically destroys essential information; thus, new mathematical and computational paradigms are needed for very large, sparse matrices.We present the U-match matrix factorization scheme to address this challenge. U-match has two desirable features. First, it admits a compressed storage format that reduces the number of nonzero entries held in computer memory by one or more orders of magnitude over other common factorizations. Second, it permits direct solution of diverse problems in linear and homological algebra, without decompressing matrices stored in memory. These problems include look-up and retrieval of rows and columns; evaluation of birth/death times, and extraction of generators in persistent (co)homology; and, calculation of bases for boundary and cycle subspaces of filtered chain complexes. Such bases are key to unlocking a range of other topological techniques for use in TDA, and U-match factorization is designed to make such calculations broadly accessible to practitioners.As an application, we show that individual cycle representatives in persistent homology can be retrieved at time and memory costs orders of magnitude below current state of the art, via global duality. Moreover, the algebraic machinery needed to achieve this computation already exists in many modern solvers.

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Tuning the performance of a computational persistent homology package

Cited by 12 publications

References 36 publications

Monitoring training and recovery responses with heart rate measures during standardized warm-up in elite badminton players

Monitoring training and recovery responses with heart rate measures during standardized warm-up in elite badminton players

Swap, Shift and Trim to Edge Collapse a Filtration

U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology

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