Name
Title | ||
|---|---|---|
Persistence Barcodes versus Kolmogorov Signatures: Detecting Modes of One-Dimensional Signals |
Abstract | ||
|---|---|---|
We investigate the problem of estimating the number of modes (i.e., local maxima)—a well-known question in statistical inference—and we show how to do so without presmoothing the data. To this end, we modify the ideas of persistence barcodes by first relating persistence values in dimension one to distances (with respect to the supremum norm) to the sets of functions with a given number of modes, and subsequently working with norms different from the supremum norm. As a particular case, we investigate the . We argue that this modification has certain statistical advantages. We offer confidence bands for the attendant , thereby allowing for the selection of relevant signatures with a statistically controllable error. As a result of independent interest, we show that minimize the number of critical points for a very general class of functions. We illustrate our results by several numerical examples. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s10208-015-9281-9 | Foundations of Computational Mathematics |
Keywords | Field | DocType |
Persistent homology,Mode hunting,Exponential deviation bound,Partial sum process,Taut strings,Primary 62G05,62G20,68U05,Secondary 62H12,57R70,58E05 | Mathematical optimization,Uniform norm,Mathematical analysis,Persistent homology,Maxima and minima,Kolmogorov structure function,Critical point (mathematics),Mathematics | Journal |
Volume | Issue | ISSN |
17 | 1 | 1615-3375 |
Citations | PageRank | References |
2 | 0.43 | 9 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrich Bauer | 1 | 102 | 10.84 |
| Axel Munk | 2 | 3 | 1.12 |
| Hannes Sieling | 3 | 3 | 0.78 |
| Max Wardetzky | 4 | 475 | 21.63 |