  Recent technological advancements have led to the generation of huge amounts
of data over the web, such as text, image, audio and video. Most of this data
is high dimensional and sparse, for e.g., the bag-of-words representation used
for representing text. Often, an efficient search for similar data points needs
to be performed in many applications like clustering, nearest neighbour search,
ranking and indexing. Even though there have been significant increases in
computational power, a simple brute-force similarity-search on such datasets is
inefficient and at times impossible. Thus, it is desirable to get a compressed
representation which preserves the similarity between data points. In this
work, we consider the data points as sets and use Jaccard similarity as the
similarity measure. Compression techniques are generally evaluated on the
following parameters --1) Randomness required for compression, 2) Time required
for compression, 3) Dimension of the data after compression, and 4) Space
required to store the compressed data. Ideally, the compressed representation
of the data should be such, that the similarity between each pair of data
points is preserved, while keeping the time and the randomness required for
compression as low as possible.
  We show that the compression technique suggested by Pratap and Kulkarni also
works well for Jaccard similarity. We present a theoretical proof of the same
and complement it with rigorous experimentations on synthetic as well as
real-world datasets. We also compare our results with the state-of-the-art
"min-wise independent permutation", and show that our compression algorithm
achieves almost equal accuracy while significantly reducing the compression
time and the randomness.
