Heat-driven framework for interpretation of data in networks

Yi Fang, Purdue University

Abstract

Researchers are regularly interested in interpreting the multipartite structure of data entities according to their functional relationships. However, the data is often heterogeneous with an intricately hidden inner structure. With limited prior knowledge, researchers are likely to confront the problem of transforming this data into knowledge. The focus of our work is to develop new methods to exploit intrinsic similarities behind noisy and incomplete raw data and to construct a meaningful map of the data in a robust data-driven manner. My work was initially inspired by the observation that heat is a global structure-aware message. The novelty of this thesis is derived from an analogy between the process of data interpretation and that of heat transfer, in which all data points contribute simultaneously and globally to reveal intrinsic similarities between regions of data, meaningful coordinates for embedding the data, and exemplar data points that lie at optimal positions for heat transfer. In this thesis, we aim to develop a general framework, named Heat-Driven Framework, that includes a set of newly defined heat-featured concepts and a set of newly developed algorithms for addressing the challenges by taking advantage of those concepts. We have introduced four heat featured concepts: Heat Affinity (HA), Heat Mean Signature (HMS), Heat Center (HC), and Heat Sink (HS) in this thesis for the Heat-Driven framework. HA is defined as the measure of heat transfer between a pair of nodes after a certain amount of time, which associates every pair of nodes to a real-valued function parameterized by the heat diffusion time. HMS is defined for quantitatively evaluating the temperature distribution resulting from the heat flow process, which associates every node to a real-valued function parameterized by the heat diffusion time. The appealing properties of those concepts are attributed to the fact that they are able to exploit the measures of the intrinsic structural connections among nodes in the network. HMS explores how a node intrinsically connects to the rest of the network at different scales and HA explores how a pair of nodes connects to each other at a different scale. As shown in the thesis, both concepts have demonstrated their efficiency in the assistance of network analysis. In addition, the other two concepts, HC and HS, are useful in the community structure discovery in the network as they naturally characterize the property of a cluster center and a cluster member. We have developed four algorithms: Intrinsic Geometric Structure (IGS), Temperature Distribution (TD) descriptor, Heat-Passing, and Heat-Mapping, based on the HA, HMS, HC, and HS or their combinations. Driven by the HA, the IGS is intended to improve the fidelity of interactions in the networks by exploring the implicit relationships among the nodes in the network. Driven by the HMS, the TD descriptor is developed to capture a structure invariant of a 3D shape, which is represented by a graph, for shape matching and retrieval. Driven by a combination of all of the concepts defined above, the Heat-Passing and Heat-Mapping are developed to find a robust graph clustering. We demonstrate the effectiveness of the Heat-Driven Framework with applications in a broad range of domains as diverse as social science, biology, and engineering. Initial results indicate that the methodology is able to reveal functionally consistent relationships in a robust fashion. The main aim of the thesis is to develop a general framework to facilitate the data interpretation for researchers across a variety of domains.

Degree

Ph.D.

Advisors

Ramani, Purdue University.

Subject Area

Mechanical engineering|Computer science

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