• Login
    View Item 
    •   Home
    • Theses and Dissertations
    • Theses and Dissertations
    • View Item
    •   Home
    • Theses and Dissertations
    • Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of TUScholarShareCommunitiesDateAuthorsTitlesSubjectsGenresThis CollectionDateAuthorsTitlesSubjectsGenres

    My Account

    LoginRegister

    Help

    AboutPoliciesHelp for DepositorsData DepositFAQs

    Statistics

    Display statistics

    Topics in Harmonic Analysis on Combinatorial Graphs

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    TETDEDXGidelew-temple-0225E-11 ...
    Size:
    1.134Mb
    Format:
    PDF
    Download
    Genre
    Thesis/Dissertation
    Date
    2014
    Author
    Gidelew, Getnet Abebe
    Advisor
    Pesenson, I. Z. (Isaak Zalmanovich)
    Committee member
    Berhanu, Shiferaw
    Mendoza, Gerardo A.
    Nowak, Krzysztof G.
    Department
    Mathematics
    Subject
    Mathematics
    Average Sampling On Graphs
    Harmonic Analysis On Graphs
    Multi-resolution On Graphs
    Quadratures On Graphs
    Sampling On Graphs
    Signal Approximation On Graphs
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/2914
    
    Metadata
    Show full item record
    DOI
    http://dx.doi.org/10.34944/dspace/2896
    Abstract
    In recent years harmonic analysis on combinatorial graphs has attracted considerable attention. The interest is stimulated in part by multiple existing and potential applications of analysis on graphs to information theory, signal analysis, image processing, computer sciences, learning theory, and astronomy. My thesis is devoted to sampling, interpolation, approximation, and multi-resolution on graphs. The results in the existing literature concern mainly with these theories on unweighted graphs. My main objective is to extend existing theories and obtain new results about sampling, interpolation, approximation, and multi-resolution on general combinatorial graphs such as directed, undirected and weighted.
    ADA compliance
    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    Collections
    Theses and Dissertations

    entitlement

     

    Related items

    Showing items related by title, author, creator and subject.

    • Thumbnail

      Explicit Bounds from the Alon–Boppana Theorem

      Richey, J; Shutty, N; Stover, M (2018-10-02)
      © 2018, © 2018 Taylor & Francis. The purpose of this article is to give explicit methods for bounding the number of vertices of finite k-regular graphs with given second eigenvalue. Let X be a finite k-regular graph and μ1(X) the second largest eigenvalue of its adjacency matrix. It follows from the well-known Alon–Boppana theorem that for any ε > 0 there are only finitely many such X with μ1(X) < (2 − ϵ)√k − 1, and we effectively implement Serre's quantitative version of this result. For any k and ε, this gives an explicit upper bound on the number of vertices in a k-regular graph with μ1(X) < (2 − ϵ)√k − 1).
    • Thumbnail

      A graph convolutional network-based deep reinforcement learning approach for resource allocation in a cognitive radio network

      Zhao, D; Qin, H; Song, B; Han, B; Du, X; Guizani, M; Du, Xiaojiang|0000-0003-4235-9671 (2020-09-02)
      © 2020 by the authors. Licensee MDPI, Basel, Switzerland. Cognitive radio (CR) is a critical technique to solve the conflict between the explosive growth of traffic and severe spectrum scarcity. Reasonable radio resource allocation with CR can effectively achieve spectrum sharing and co-channel interference (CCI) mitigation. In this paper, we propose a joint channel selection and power adaptation scheme for the underlay cognitive radio network (CRN), maximizing the data rate of all secondary users (SUs) while guaranteeing the quality of service (QoS) of primary users (PUs). To exploit the underlying topology of CRNs, we model the communication network as dynamic graphs, and the random walk is used to imitate the users’ movements. Considering the lack of accurate channel state information (CSI), we use the user distance distribution contained in the graph to estimate CSI. Moreover, the graph convolutional network (GCN) is employed to extract the crucial interference features. Further, an end-to-end learning model is designed to implement the following resource allocation task to avoid the split with mismatched features and tasks. Finally, the deep reinforcement learning (DRL) framework is adopted for model learning, to explore the optimal resource allocation strategy. The simulation results verify the feasibility and convergence of the proposed scheme, and prove that its performance is significantly improved.
    • Thumbnail

      Graph-based Modern Nonparametrics For High-dimensional Data

      Mukhopadhyay, Subhadeep; Dong, Yuexiao; Lee, Kuang-Yao; Chervoneva, Inna (Temple University. Libraries, 2019)
      Developing nonparametric statistical methods and inference procedures for high-dimensional large data have been a challenging frontier problem of statistics. To attack this problem, in recent years, a clear rising trend has been observed with a radically different viewpoint--``Graph-based Nonparametrics," which is the main research focus of this dissertation. The basic idea consists of two steps: (i) representation step: code the given data using graphs, (ii) analysis step: apply statistical methods on the graph-transformed problem to systematically tackle various types of data structures. Under this general framework, this dissertation develops two major research directions. Chapter 2—based on Mukhopadhyay and Wang (2019a)—introduces a new nonparametric method for high-dimensional k-sample comparison problem that is distribution-free, robust, and continues to work even when the dimension of the data is larger than the sample size. The proposed theory is based on modern LP-nonparametrics tools and unexplored connections with spectral graph theory. The key is to construct a specially-designed weighted graph from the data and to reformulate the k-sample problem into a community detection problem. The procedure is shown to possess various desirable properties along with a characteristic exploratory flavor that has practical consequences. The numerical examples show surprisingly well performance of our method under a broad range of realistic situations. Chapter 3—based on Mukhopadhyay and Wang (2019b)—revisits some foundational questions about network modeling that are still unsolved. In particular, we present unified statistical theory of the fundamental spectral graph methods (e.g., Laplacian, Modularity, Diffusion map, regularized Laplacian, Google PageRank model), which are often viewed as spectral heuristic-based empirical mystery facts. Despite half a century of research, this question has been one of the most formidable open issues, if not the core problem in modern network science. Our approach integrates modern nonparametric statistics, mathematical approximation theory (of integral equations), and computational harmonic analysis in a novel way to develop a theory that unifies and generalizes the existing paradigm. From a practical standpoint, it is shown that this perspective can provide adequate guidance for designing next-generation computational tools for large-scale problems. As an example, we have described the high-dimensional change-point detection problem. Chapter 4 discusses some further extensions and application of our methodologies to regularized spectral clustering and spatial graph regression problems. The dissertation concludes with the a discussion of two important areas of future studies.
    DSpace software (copyright © 2002 - 2021)  DuraSpace
    Temple University Libraries | 1900 N. 13th Street | Philadelphia, PA 19122
    (215) 204-8212 | scholarshare@temple.edu
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.