Indicator vector

In mathematics, the indicator vector or characteristic vector or incidence vector of a subset T of a set S is the vector such that if and if

If S is countable and its elements are numbered so that , then where if and if

To put it more simply, the indicator vector of T is a vector with one element for each element in S, with that element being one if the corresponding element of S is in T, and zero if it is not.[1][2][3]

An indicator vector is a special (countable) case of an indicator function.

ExampleEdit

If S is the set of natural numbers  , and T is some subset of the natural numbers, then the indicator vector is naturally a single point in the Cantor space: that is, an infinite sequence of 1's and 0's, indicating membership, or lack thereof, in T. Such vectors commonly occur in the study of arithmetical hierarchy.

NotesEdit

  1. ^ Mirkin, Boris Grigorʹevich (1996). Mathematical Classification and Clustering. p. 112. ISBN 0-7923-4159-7. Retrieved 10 February 2014.
  2. ^ von Luxburg, Ulrike (2007). "A Tutorial on Spectral Clustering" (PDF). Statistics and Computing. 17 (4): 2. Archived from the original (PDF) on 6 February 2011. Retrieved 10 February 2014.
  3. ^ Taghavi, Mohammad H. (2008). Decoding Linear Codes Via Optimization and Graph-based Techniques. ProQuest. p. 21. Retrieved 10 February 2014.