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Machine Learning and Security
book

Machine Learning and Security

by Clarence Chio, David Freeman
February 2018
Intermediate to advanced
383 pages
11h 30m
English
O'Reilly Media, Inc.
Content preview from Machine Learning and Security

Appendix A. Supplemental Material for Chapter 2

More About Metrics

In our discussion of clustering, we primarily used the standard Euclidean distance between vectors in a vector space:

Euclidean distance is also known as the L2 norm. There are several other metrics that are commonly used in applications:

  • One variation of Euclidean distance is the L1 norm, also known as Manhattan distance (because it counts the number of “blocks” between two points on a grid):

    d left-parenthesis x comma y right-parenthesis equals sigma-summation Underscript i Endscripts bar left-parenthesis x Subscript i Baseline minus y Subscript i Baseline right-parenthesis bar
  • Another is the L∞ norm, defined as the following:

    d left-parenthesis x comma y right-parenthesis equals max Underscript i Endscripts bar left-parenthesis x Subscript i Baseline minus y Subscript i Baseline right-parenthesis bar
  • For vectors of binary values or bits, you can use Hamming distance, which is the number of bits in common between x and y. This can be computed as:

    d left-parenthesis x comma y right-parenthesis equals upper H left-parenthesis normal not-sign left-parenthesis x circled-plus y right-parenthesis right-parenthesis

    where H(v) is the Hamming weight; that is, the number of “1” bits in v. If the points you compare are of different bit length, the shorter one will need to be prepended with zeros.

  • For lists, you can use the Jaccard similarity:

    d left-parenthesis x comma y right-parenthesis equals StartFraction bar x intersection y bar Over bar x union y bar EndFraction

    The Jaccard similarity computes the number of elements in common between x and y, normalized ...

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Publisher Resources

ISBN: 9781491979891Errata Page