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2275 results in Pattern Recognition and Machine Learning

Page 64 of 114

Foundations of Data Science
  • Avrim Blum, John Hopcroft, Ravindran Kannan
  • Published online:
    17 January 2020
    Print publication:
    23 January 2020
  • This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

  • 5 - Link Analysis

  • Jure Leskovec, Stanford University, California, Anand Rajaraman, Jeffrey David Ullman, Stanford University, California
  • Book:
    Mining of Massive Datasets
    Published online:
    16 April 2020
    Print publication:
    09 January 2020, pp 169-205

  • Summary

    We shall begin the chapter by explaining what PageRank is and how it is computed efficiently. Yet the war between those who want to make the Web useful and those who would exploit it for their own purposes is never over. When PageRank was established as an essential technique for a search engine, spammers invented ways to manipulate the PageRank of a Web page, often called link spam. That development led to the response of TrustRank and other techniques for preventing spammers from attacking PageRank. We shall discuss TrustRank and other approaches to detecting link spam. Finally, this chapter also covers some variations on PageRank. These techniques include topic-sensitive PageRank (which can also be adapted for combating link spam) and the HITS, or “hubs and authorities” approach to evaluating pages on the Web.

  • 2 - MapReduce and the New Software Stack

  • Jure Leskovec, Stanford University, California, Anand Rajaraman, Jeffrey David Ullman, Stanford University, California
  • Book:
    Mining of Massive Datasets
    Published online:
    16 April 2020
    Print publication:
    09 January 2020, pp 20-77

  • Summary

    We include in this chapter a discussion of generalizations of MapReduce, first to systems that support acyclic workflows and then to systems that implement recursive algorithms. Our last topic for this chapter is the design of good MapReduce algorithms, a subject that often differs significantly from the matter of designing good parallel algorithms to be run on a supercomputer. When designing MapReduce algorithms, we often find that the greatest cost is in the communication. We thus investigate communication cost and what it tells us about the most efficient MapReduce algorithms. For several common applications of MapReduce we are able to give families of algorithms that optimally trade the communication cost against the degree of parallelism.

  • 3 - Finding Similar Items

  • Jure Leskovec, Stanford University, California, Anand Rajaraman, Jeffrey David Ullman, Stanford University, California
  • Book:
    Mining of Massive Datasets
    Published online:
    16 April 2020
    Print publication:
    09 January 2020, pp 78-137

  • Summary

    We begin our discussion of locality-sensitive hashing (LSH) with an examination of the problem of finding similar documents – those that share a lot of common text. We first show how to convert documents into sets in a way that lets us view textual similarity of documents as sets having a large overlap. A second key trick we need is minhashing, which is a way to convert large sets into much smaller representations, called signatures, that still enable us to estimate closely the Jaccard similarity of the represented sets. Finally, we see how to apply the bucketing idea inherent in LSH to the signatures. In Section 3.5 we begin our study of how to apply LSH to items other than sets. We consider the general notion of a distance measure that tells to what degree items are similar. Then, we consider the general idea of locality-sensitive hashing, and we see how to do LSH for some data types other than sets. We examine in detail several applications of the LSH idea. Finally, we consider some techniques for finding similar sets that can be more efficient than LSH when the degree of similarity we want is very high.

Page 64 of 114