Persistent homology in graph power filtrations.

The persistence of homological features in simplicial complex representations of big datasets in R n resulting from Vietoris-Rips or Cech filtrations is commonly used to probe the topological structure of such datasets. In this paper, the notion of homological persistence in simplicial complexes obtained from power filtrations of graphs is introduced. Specifically, the rth complex, r ≥ 1, in such a power filtration is the clique complex of the rth power Gr of a simple graph G. Because the graph distance in G is the relevant proximity parameter, unlike a Euclidean filtration of a dataset where regional scale differences can be an issue, persistence in power filtrations provides a scale-free insight into the topology of G. It is shown that for a power filtration of G, the girth of G defines an r range over which the homology of the complexes in the filtration are guaranteed to persist in all dimensions. The role of chordal graphs as trivial homology delimiters in power filtrations is also discussed and the related notions of 'persistent triviality', 'transient noise' and 'persistent periodicity' in power filtrations are introduced.

Application of integrated sensing and processing decision trees for target detection and localization on digital mirror array imagery.

We demonstrate the applicability of integrated sensing and processing decision trees (ISPDTs) methodology to a set of digital mirror array (DMA) hyperspectral imagery. In particular, we demonstrate that ISPDTs can be used to detect and localize targets by using just a few DMA Hadamard frames, so that an entire hyperspectral data cube need not be collected to successfully perform the given task. This suggests that such an integrated sensing-processing suite may be appropriate for extremely time-sensitive pattern-recognition applications.

Integrated sensing and processing decision trees.

We introduce a methodology for adaptive sequential sensing and processing in a classification setting. Our objective for sensor optimization is the back-end performance metric--in this case, misclassification rate. Our methodology, which we dub Integrated Sensing and Processing Decision Trees (ISPDT), optimizes adaptive sequential sensing for scenarios in which sensor and/or throughput constraints dictate that only a small subset of all measurable attributes can be measured at any one time. Our decision trees optimize misclassification rate by invoking a local dimensionality reduction-based partitioning metric in the early stages, focusing on classification only in the leaves of the tree. We present the ISPDT methodology and illustrative theoretical, simulation, and experimental results.