منابع مشابه
Zigzag Persistence
We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop ...
متن کاملZigzag Persistence via Reflections and Transpositions
We introduce a new algorithm for computing zigzag persistence, designed in the same spirit as the standard persistence algorithm. Our algorithm reduces a single matrix, maintains an explicit set of chains encoding the persistent homology of the current zigzag, and updates it under simplex insertions and removals. The total worst-case running time matches the usual cubic bound. A noticeable diff...
متن کاملAlgebraic Stability of Zigzag Persistence Modules
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of R-valued functions, the result was later cast in a more general algebraic form, in the language of persistence modules and interleavings. In this paper, we establish an analogue of this algebraic stability theorem for z...
متن کاملApplications of Zigzag Persistence to Topological Data Analysis
The theory of zigzag persistence is a substantial extension of persistent homology, and its development has enabled the investigation of several unexplored avenues in the area of topological data analysis. In this paper, we discuss three applications of zigzag persistence: topological bootstrapping, parameter thresholding, and the comparison of witness complexes.
متن کاملZigzag codes and concatenated zigzag codes
This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-APP (MLA) formulation, which requires a total of only 20 addition-equivalent operations...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2010
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-010-9066-0