Harish Chintakunta

Distributed Localization of Coverage Holes Using Topological Persistence

We develop distributed algorithms to detect and localize coverage holes in sensor networks. We neither assume coordinate information of the nodes, neither any distances between the nodes. We use algebraic topological methods to define a coverage hole, and develop provably correct algorithm to detect a hole. We then partition the network into smaller subnetworks, while ensuring that the holes are preserved, and checking for holes in each. We show that repeating this process leads to localizing the coverage holes. We demonstrate the improved complexity of our algorithm using simulations.

Discovering the Whole by the Coarse: A topological paradigm for data analysis

The increasing interest in big data applications is ushering in a large effort in seeking new, efficient, and adapted data models to reduce complexity, while preserving maximal intrinsic information. Graph-based models have recently been getting a lot of attention on account of their intuitive and direct connection to the data [43]. The cost of these models, however, is to some extent giving up geometric insight as well as algebraic flexibility.

REAL TIME DETECTION OF HARMONIC STRUCTURE: A CASE FOR TOPOLOGICAL SIGNAL ANALYSIS

The goal of this study is to find evidence of cyclicity or periodicity in data with low computational complexity and high accuracy. Using delay embeddings, we transform the timedomain signal into a point cloud, whose topology reflects the periodic behavior of the signal. Persistent homology is employed to determine the underlying manifold of the point cloud, and the Euler characteristic provides for a fast computation of topology of the resulting manifold. We apply the introduced approach to breathing sound signals for wheeze detection. Our experiments substantiate the capabilities of the proposed method.

Applied topology in static and dynamic sensor networks

In the study of sensor networks, many applications require topological analysis, and for some problems topological information is even sufficient. Here, we review how algebraic topology (and specifically simplicial homology theory) can be used as a general framework for detection of coverage holes in a coordinate-free sensor network. Extensions to distributed processing and localization algorithms are also reviewed, before progressing into discussion of a new way to apply algebraic topological methods to the analysis of coverage properties in dynamic sensor networks. Zigzag persistent homology is a recently developed method to track homological features (such as holes) over a sequence of spaces. This paper demonstrates the promise of this method for the identification of coverage holes in a time-varying coordinate-free sensor network, as well as the designation of coverage holes as significant or not, based on the length of time they are present in the sequence.

Node Dominance: Revealing Community and Core-Periphery Structure in Social Networks

This study relates the local property of node dominance to local and global properties of a network. Iterative removal of dominated nodes yields a distributed algorithm for computing a core-periphery decomposition of a social network, where nodes in the network core are seen to be essential in terms of network flow and global structure. Additionally, the connected components in the periphery give information about the community structure of the network, aiding in community detection. A number of explicit results are derived, relating the core and periphery to network flow, community structure, and global network structure, which are corroborated by observational results. The method is illustrated using a real world network (DBLP co-authorship network), with ground-truth communities.

Computing persistent features in big data: A distributed dimension reduction approach

Persistent homology has become one of the most popular tools used in topological data analysis for analyzing big data sets. In an effort to minimize the computational complexity of finding the persistent homology of a data set, we develop a simplicial collapse algorithm called the selective collapse. This algorithm works by representing the previously developed strong collapse as a forest and uses that forest data to improve the speed of both the strong collapse and of persistent homology. Finally, we demonstrate the savings in computational complexity using geometric random graphs.

A distributed collapse of a network's dimensionality

Algebraic topology has been successfully applied to detect and localize sensor network coverage holes with minimal assumptions on sensor locations. These methods all use a computation of topological invariants called homology spaces. We develop a distributed algorithm for collapsing a sensor network, hence simplifying its analysis. We prove that the collapse is equivalent to a previously developed strong collapse in that it preserves coverage hole locations. In this way, the collapse simplifies the network without losing crucial information about the coverage region. We show that the algorithm requires only one-hop information in a communication network, making it faster than clique-finding algorithms that increase the number of computations necessary for hole localization. This makes it an effective pre-processing step to finding network coverage holes.

Detection and tracking of systematic time-evolving failures in sensor networks

Sensor networks are often deployed to monitor hazardous environments. Several events/phenomenon in such environments may cause spatially and temporally correlated failures in the network. We present here, a low complexity distributed algorithm for detecting and tracking such failures. We assume that nodes inside the failure region are either destroyed or unable to communicate with any other node. The algorithm presented here does not assume any co-ordinate information for the nodes. We evaluate the algorithm using simulations.

Introduction to the special session on Topological Data Analysis, ICASSP 2016

Topological Data Analysis (TDA) is a topic which has recently seen many applications. The goal of this special session is to highlight the bridge between signal processing, machine learning and techniques in topological data analysis. In this way, we hope to encourage more engineers to start exploring TDA and its applications. This paper briefly introduces the standard techniques used in this area, delineates the common theme connecting the works presented in this session, and concludes with a brief summary of each of the papers presented.