Learning to Hash for Maximum Inner Product Search

## Project description

SITQ is a fast algorithm for approximate Maximum Inner Product Search (MIPS). It can find items which are likely to maximize inner product against a query in sublinear time.

## Benchemark

Recommendation is one of fields where SITQ can be used. Experiments were conducted with MovieLens 100K Dataset and MovieLens 20M Dataset.

ALS in benfred/implicit is used to learn vectors of items and users, where the score of (user, item) pair is computed through inner product of those vectors. Precision@10 is the ratio of correct recommendations against test dataset. Fetched items are items against which inner product are computed. Hashing algorithms are more preferable as average and standard deviation of fetched items are smaller.

### ml-100k

Signature length: 4, Minimum fetched items: 20

Name

Precision@10

Fetched items. Avg

Fetched items. Std

SITQ

0.202

105.2

76.6

Simple-LSH

0.182

496.2

441.2

ITQ

0.199

131.3

93.7

LSH

0.156

161.9

94.4

brute force

0.242

(1680)

### ml-20m

Signature length: 8, Minimum fetched items: 20

Name

Precision@10

Fetched items. Avg

Fetched items. Std

SITQ

0.112

96.1

151.1

Simple-LSH

0.122

2158.2

5246.6

ITQ

0.090

111.0

332.9

LSH

0.069

531.3

912.2

brute force

0.151

(26671)

## Algorithm

SITQ is an algorithm which combines Simple-LSH [1] and ITQ [2].

Simple-LSH utilizes ordinary LSH which is for cosine similarity. In order to use LSH for MIPS, it converts a vector before computing its signature.

LSH computes signatures through transformation matrix which is fixed. ITQ learns transformation matrix from item vectors for better hashing.

SITQ converts vectors by means of Simple-LSH, and learns transformation matrix through ITQ.

## Example

### Install

pip install sitq

### Get Signature

import numpy as np

from sitq import Sitq

# Create sample dataset
items = np.random.rand(10000, 50)
query = np.random.rand(50)

sitq = Sitq(signature_size=8)

# Learn transformation matrix
sitq.fit(items)

# Get signatures for items
item_sigs = sitq.get_item_signatures(items)

# Get signature for query
query_sig = sitq.get_query_signatures([query])[0]

### Retrieve items

import numpy as np

from sitq import Mips

# Create sample dataset
items = np.random.rand(10000, 50)
query = np.random.rand(50)

mips = Mips(signature_size=8)

# Learn lookup table and parameters for search
mips.fit(items)

# Find items which are likely to maximize inner product against query
item_indexes, scores = mips.search(query, limit=10, distance=1)

## Project details

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