MinHash LSH Forest¶
MinHash LSH is useful for radius (or threshold) queries. However, top-k queries are often more useful in some cases. LSH Forest by Bawa et al. is a general LSH data structure that makes top-k query possible for many different types of LSH indexes, which include MinHash LSH. I implemented the MinHash LSH Forest, which takes a MinHash data sketch of the query set, and returns the top-k matching sets that have the highest Jaccard similarities with the query set.
The interface of datasketch.MinHashLSHForest
is similar to
datasketch.MinHashLSH
,
however, it is very important to call index
method after adding the
keys. Without calling the index
method, the keys won’t be
searchable.
from datasketch import MinHashLSHForest, MinHash
data1 = ['minhash', 'is', 'a', 'probabilistic', 'data', 'structure', 'for',
'estimating', 'the', 'similarity', 'between', 'datasets']
data2 = ['minhash', 'is', 'a', 'probability', 'data', 'structure', 'for',
'estimating', 'the', 'similarity', 'between', 'documents']
data3 = ['minhash', 'is', 'probability', 'data', 'structure', 'for',
'estimating', 'the', 'similarity', 'between', 'documents']
# Create MinHash objects
m1 = MinHash(num_perm=128)
m2 = MinHash(num_perm=128)
m3 = MinHash(num_perm=128)
for d in data1:
m1.update(d.encode('utf8'))
for d in data2:
m2.update(d.encode('utf8'))
for d in data3:
m3.update(d.encode('utf8'))
# Create a MinHash LSH Forest with the same num_perm parameter
forest = MinHashLSHForest(num_perm=128)
# Add m2 and m3 into the index
forest.add("m2", m2)
forest.add("m3", m3)
# IMPORTANT: must call index() otherwise the keys won't be searchable
forest.index()
# Check for membership using the key
print("m2" in forest)
print("m3" in forest)
# Using m1 as the query, retrieve top 2 keys that have the higest Jaccard
result = forest.query(m1, 2)
print("Top 2 candidates", result)
The plot below shows the mean average precision (MAP) of linear scan with MinHash and MinHash LSH Forest. Synthetic data was used. See benchmark for details.

(Optional) If you have read the LSH Forest
paper, and
understand the data structure, you may want to customize another
parameter for datasketch.MinHashLSHForest
– l
, the number of prefix trees
(or “LSH Trees” as in the paper) in the LSH Forest index. Different from
the paper, this implementation fixes the number of LSH functions, in
this case num_perm
, and makes the maximum depth of every prefix tree
dependent on num_perm
and l
:
# The maximum depth of a prefix tree depends on num_perm and l
k = int(num_perm / l)
This way the interface of the datasketch.MinHashLSHForest
is in coherence with
the interface of MinHash
.
# There is another optional parameter l (default l=8).
forest = MinHashLSHForest(num_perm=250, l=10)