Computational Topology Techniques for Characterizing Time-Series Data

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and holes - could be useful for real-world data, TDA lets us compare different systems, and even do membership testing or change-point detection. However, TDA is computationally expensive and involves a number of free parameters. This complexity can be obviated by coarse-graining, using a construct called the witness complex. The parametric dependence gives rise to the concept of persistent homology: how shape changes with scale. Its results allow us to distinguish time-series data from different systems - e.g., the same note played on different musical instruments.Comment: 12 pages, 6 Figures, 1 Table, The Sixteenth International Symposium on Intelligent Data Analysis (IDA 2017

Marine Target Detection from Nonstationary Sea-Clutter Based On Topological Data Analysis

AbstractDue to the instinct complexity and the large scale non-stationary of so-called sea-clutter, radar backscatters from ocean surface, it is always challenging to detect the weak marine target. In classical statistical approaches, the seaclutter is modeled as several kinds of stochastic processes, which are found inadequate, especially in high sea-state circumstances. Therefore it is reasonable to discover the underlying dynamics that is responsible for generating the time series of sea-clutter. In this work, we take into account of the marine target detection from the X-Band seaclutter datasets with low Signal-Clutter-Ratio, and propose adequate methods to process these non-stationary data, including Empirical Mode Decomposition and Topological Data Analysis. Both theoretical simulation and experimental results indicate the proposed method's usefulness of for marine target detection, which is implemented by extract different structural features from measured sea-clutter data

Topology and intelligent data analysis

Abstract. A broad range of mathematical techniques, ranging from statistics to fuzzy logic, have been used to great advantage in intelligent data analysis. Topology—the fundamental mathematics of shape—has to date been conspicuously absent from this repertoire. This paper shows how topology, properly reformulated for a finite-precision world, can be useful in intelligent data analysis tasks.