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6791 results in Communications and signal processing

Page 18 of 340

  • 10 - Matrix Completion and Recommender Systems

  • Jeffrey A. Fessler, University of Michigan, Ann Arbor, Raj Rao Nadakuditi, University of Michigan, Ann Arbor
  • Book:
    Linear Algebra for Data Science, Machine Learning, and Signal Processing
    Published online:
    01 November 2024
    Print publication:
    16 May 2024, pp 365-380

  • Summary

    This chapter discusses the important problem of matrix completion, where we know some, but not all, elements of a matrix and want to “complete” the matrix by filling in the missing entries. This problem is ill posed in general because one could assign arbitrary values to the missing entries, unless one assumes some model for the matrix elements. The most common model is that the matrix is low rank, an assumption that is reasonable in many applications. The chapter defines the problem and describes an alternating projection approach for noiseless data. It discusses algorithms for the practical case of missing and noisy data. It extends the methods to consider the effects of outliers with the robust principal component method, and applies this to video foreground/background separation. It describes nonnegative matrix factorization, including the case of missing data. A particularly famous application of low-rank matrix completion is the “Netflix problem”; this topic is also relevant to dynamic magnetic resonance image reconstruction, and numerous other applications with missing data (incomplete observations).

  • 6 - Norms and Procrustes Problems

  • Jeffrey A. Fessler, University of Michigan, Ann Arbor, Raj Rao Nadakuditi, University of Michigan, Ann Arbor
  • Book:
    Linear Algebra for Data Science, Machine Learning, and Signal Processing
    Published online:
    01 November 2024
    Print publication:
    16 May 2024, pp 197-237

  • Summary

    Previous chapters considered the Euclidean norm, the spectral norm, and the Frobenius norm. These three norms are particularly important, but there are many other important norms for applications. This chapter discusses vector norms, matrix norms, and operator norms, and uses these norms to analyze the convergence of sequences. It revisits the Moore–Penrose pseudoinverse from a norm-minimizing perspective. It applies norms to the orthogonal Procrustes problem and its extensions.

Wireless Communications
  • Principles and Practice
  • 2nd edition
  • Theodore S. Rappaport
  • Published online:
    22 March 2024
    Print publication:
    08 February 2024
  • Now reissued by Cambridge University Press, the updated second edition of this definitive textbook provides an unrivaled introduction to the theoretical and practical fundamentals of wireless communications. Key technical concepts are developed from first principles, and demonstrated to students using over 50 carefully curated worked examples. Over 200 end-of-chapter problems, based on real-world industry scenarios, help cement student understanding. The book provides a thorough coverage of foundational wireless technologies, including wireless local area networks (WLAN), 3G systems, and Bluetooth along with refreshed summaries of recent cellular standards leading to 4G and 5G, insights into the new areas of mobile satellite communications and fixed wireless access, and extra homework problems. Supported online by a solutions manual and lecture slides for instructors, this is the ideal foundation for senior undergraduate and graduate courses in wireless communications.

Page 18 of 340