4

I need to generate random index vectors (with large number of dimensions of about 1000), which would by mostly sparse(mostly zero values). The vectors can contain values of either 1(positive dimension), -1(negative dimension) and 0.These vectors are being generated for every word in corpus of text. What could be the best way to achieve this in Java, while ensuring the randomness of the resulting vectors?

Thank you

rmenon
  • 55
  • 4

2 Answers2

1

To store a vector, keep a list of its non-zero positions and +1/-1 bits. You would need a Byte for the +1/-1 bit.

If you really wanted to save as much memory as possible, you could keep a long BitSet containing the +1/-1 information for all the vectors together, and each vector would remember its starting index in the BitSet.

To generate vectors orthogonal to the others, you can do:

 [0 1 0 0 -1 ...]
 [1 0 1 0 0 ...]  // zeros where the first vector is non-zero
 ...

Keep a linked list of all the available 1000 indices. When generating a vector, pick a small random number of random indices, generate a vector with these indices non-zero, and remove the indices from the list of available indices. However this way you quickly run out of available indices. But in 1000-dimensional space there are only 1000 mutually orthogonal vectors, so you could create vectors for at most 1000 words anyway.

Also, the fact that the vectors have to be orthogonal means that they can't be completely random, because truly random vectors could happen to be non-orthogonal.

Martin Konicek
  • 39,126
  • 20
  • 90
  • 98
0

If you want to try a low-cost approach (programming-wise), then a HashMap<Integer, Byte> or something close could make a decent sparse vector.

Rom1
  • 3,167
  • 2
  • 22
  • 39
  • Could there be a better way to do this? Actually I have an additional requirement that, each vector generated should be orthogonal to other vectors? – rmenon Apr 24 '11 at 00:02
  • For a better sparse vector, you could have a look at [this question](http://stackoverflow.com/questions/1934254/which-is-the-best-way-to-implement-a-sparse-vector-in-java). – Rom1 Apr 24 '11 at 09:43