Locality Sensitive Hashing (LSH) is a powerful technique for efficiently finding approximate nearest neighbors in high-dimensional spaces, with applications in computer science, search engines, and recommendation systems. This article explores the nuances, complexities, and current challenges of LSH, as well as recent research and practical applications.
LSH works by hashing data points into buckets so that similar points are more likely to map to the same buckets, while dissimilar points map to different ones. This allows for sub-linear query performance and theoretical guarantees on query accuracy. However, LSH faces challenges such as large index sizes, hash boundary problems, and sensitivity to data and query-dependent parameters.
Recent research in LSH has focused on addressing these challenges. For example, MP-RW-LSH is a multi-probe LSH solution for ANNS in L1 distance, which reduces the number of hash tables needed for high query accuracy. Another approach, Unfolded Self-Reconstruction LSH (USR-LSH), supports fast online data deletion and insertion without retraining, addressing the need for machine unlearning in retrieval problems.
Practical applications of LSH include:
1. Collaborative filtering for item recommendations, as demonstrated by Asymmetric LSH (ALSH) for sublinear time Maximum Inner Product Search (MIPS) on Netflix and Movielens datasets.
2. Large-scale similarity search in distributed frameworks, where Efficient Distributed LSH reduces network cost and improves runtime performance in real-world applications.
3. High-dimensional approximate nearest neighbor search, where Hybrid LSH combines LSH-based search and linear search to achieve better performance across various search radii and data distributions.
A company case study is Spotify, which uses LSH for music recommendation by finding similar songs in high-dimensional spaces based on audio features.
In conclusion, LSH is a versatile and powerful technique for finding approximate nearest neighbors in high-dimensional spaces. By addressing its challenges and incorporating recent research advancements, LSH can be effectively applied to a wide range of practical applications, connecting to broader theories in computer science and machine learning.
Locality Sensitive Hashing (LSH)
Locality Sensitive Hashing (LSH) Further Reading
1.MP-RW-LSH: An Efficient Multi-Probe LSH Solution to ANNS in $L_1$ Distance http://arxiv.org/abs/2103.05864v1 Huayi Wang, Jingfan Meng, Long Gong, Jun Xu, Mitsunori Ogihara2.A Survey on Locality Sensitive Hashing Algorithms and their Applications http://arxiv.org/abs/2102.08942v1 Omid Jafari, Preeti Maurya, Parth Nagarkar, Khandker Mushfiqul Islam, Chidambaram Crushev3.Lattice-based Locality Sensitive Hashing is Optimal http://arxiv.org/abs/1712.08558v1 Karthekeyan Chandrasekaran, Daniel Dadush, Venkata Gandikota, Elena Grigorescu4.Unfolded Self-Reconstruction LSH: Towards Machine Unlearning in Approximate Nearest Neighbour Search http://arxiv.org/abs/2304.02350v2 Kim Yong Tan, Yueming Lyu, Yew Soon Ong, Ivor W. Tsang5.Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS) http://arxiv.org/abs/1405.5869v1 Anshumali Shrivastava, Ping Li6.Efficient Distributed Locality Sensitive Hashing http://arxiv.org/abs/1210.7057v1 Bahman Bahmani, Ashish Goel, Rajendra Shinde7.DB-LSH: Locality-Sensitive Hashing with Query-based Dynamic Bucketing http://arxiv.org/abs/2207.07823v2 Yao Tian, Xi Zhao, Xiaofang Zhou8.Locality-Sensitive Hashing Scheme based on Longest Circular Co-Substring http://arxiv.org/abs/2004.05345v1 Yifan Lei, Qiang Huang, Mohan Kankanhalli, Anthony K. H. Tung9.Hybrid LSH: Faster Near Neighbors Reporting in High-dimensional Space http://arxiv.org/abs/1607.06179v3 Ninh Pham10.On Symmetric and Asymmetric LSHs for Inner Product Search http://arxiv.org/abs/1410.5518v3 Behnam Neyshabur, Nathan SrebroLocality Sensitive Hashing (LSH) Frequently Asked Questions
What is the difference between hashing and LSH?
Hashing is a general technique used to map data of arbitrary size to fixed-size values, called hash codes. It is widely used in computer science for various purposes, such as data storage, retrieval, and comparison. Traditional hashing functions aim to distribute data points uniformly across the hash space, minimizing the probability of collisions (i.e., different data points mapping to the same hash code). Locality Sensitive Hashing (LSH), on the other hand, is a specific type of hashing designed for high-dimensional data. The main goal of LSH is to map similar data points to the same or nearby hash codes, while dissimilar points map to different ones. This property allows for efficient approximate nearest neighbor search in high-dimensional spaces, as it reduces the search space and enables sub-linear query performance.
How to do locality sensitive hashing?
To perform Locality Sensitive Hashing, follow these steps: 1. Choose an appropriate LSH family for your data and distance metric. Common LSH families include Euclidean LSH, Cosine LSH, and MinHash. 2. Determine the number of hash tables and hash functions required for your desired trade-off between query time and accuracy. 3. For each hash table, generate a set of random hash functions from the chosen LSH family. 4. For each data point, compute its hash code using the hash functions and insert it into the corresponding hash table. 5. To query for approximate nearest neighbors, compute the query point's hash codes and search for similar points in the same or nearby buckets of the hash tables.
Where is locality sensitive hashing used?
Locality Sensitive Hashing is used in various applications, including: 1. Search engines: LSH can be used to find similar documents or web pages in high-dimensional spaces, such as text or image data. 2. Recommendation systems: LSH can be applied to collaborative filtering for item recommendations, as demonstrated by Asymmetric LSH (ALSH) for sublinear time Maximum Inner Product Search (MIPS) on Netflix and Movielens datasets. 3. Large-scale similarity search: LSH is used in distributed frameworks to reduce network cost and improve runtime performance in real-world applications, such as Efficient Distributed LSH. 4. High-dimensional approximate nearest neighbor search: Hybrid LSH combines LSH-based search and linear search to achieve better performance across various search radii and data distributions.
What is LSH for approximate near neighbor search?
LSH for approximate near neighbor search is a technique that uses Locality Sensitive Hashing to efficiently find points in high-dimensional spaces that are close to a given query point. By hashing data points into buckets so that similar points are more likely to map to the same buckets, LSH enables sub-linear query performance and provides theoretical guarantees on query accuracy. This makes it a powerful tool for finding approximate nearest neighbors in large-scale, high-dimensional datasets.
What are the challenges of LSH?
Some challenges of Locality Sensitive Hashing include: 1. Large index sizes: LSH often requires multiple hash tables to achieve high query accuracy, which can lead to large memory requirements. 2. Hash boundary problems: Points close to hash boundaries may be missed during the search process, leading to false negatives. 3. Sensitivity to data and query-dependent parameters: LSH performance can be affected by the choice of hash functions, number of hash tables, and other parameters, which may require tuning for specific datasets and query types.
What are some recent advancements in LSH research?
Recent research in LSH has focused on addressing its challenges and improving its performance. Some notable advancements include: 1. MP-RW-LSH: A multi-probe LSH solution for Approximate Nearest Neighbor Search (ANNS) in L1 distance, which reduces the number of hash tables needed for high query accuracy. 2. Unfolded Self-Reconstruction LSH (USR-LSH): An approach that supports fast online data deletion and insertion without retraining, addressing the need for machine unlearning in retrieval problems. 3. Hybrid LSH: A method that combines LSH-based search and linear search to achieve better performance across various search radii and data distributions.
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