https://www.youtube.com/watch?v=DRbjpuqOsjk
Like KNN but a lot faster.Blog post by creator of ANNOY : https://erikbern.com/2015/10/01/nearest-neighbors-and-vector-models-part-2-how-to-search-in-high-di

https://towardsdatascience.com/comprehensive-guide-to-approximate-nearest-neighbors-algorithms-8b94f057d6b6
The use cases for "Nearest Neighbor" are endless, and it is in use in many computer-science areas, such as image recognition, machine learning, and computational linguistics (1, 2 and more). Amongst the endless use-cases are Netflix's recommendation, Spotify's recommendation, Pinterest's visual search, and many more amazing products.

https://towardsdatascience.com/using-approximate-nearest-neighbor-search-in-real-world-applications-a75c351445d
The naive approach here is to use one of the ANN libraries mentioned above to perform a nearest neighbor search and then filter out the results. However, this is problematic. Imagine that 1000 documents are relevant to the query "approximate nearest neighbor", with 100 added each year over the past 10 years.

https://www.elastic.co/blog/understanding-ann
Approximate nearest neighbor (ANN) is an algorithm that finds a data point in a data set that's very close to the given query point, but not necessarily the absolute closest one. An NN algorithm searches exhaustively through all the data to find the perfect match, whereas an ANN algorithm will settle for a match that's close enough.. This might sound like a worse solution, but it's

https://medium.com/gsi-technology/a-data-scientists-guide-to-picking-an-optimal-approximate-nearest-neighbor-algorithm-6f91d3055115
Because we are finding the 10 nearest-neighbors of a selected point, the Recall score takes the distances of the 10 nearest-neighbors our algorithms computed and compares them to the distance of

https://www.graphext.com/glossary/approximate-nearest-neighbors-ann
Approximate Nearest Neighbors (ANN): ANN is an approximate algorithm that aims to find the nearest neighbors faster than KNN by trading off some accuracy. The algorithm uses various techniques, such as space partitioning, hashing, and tree-based data structures (e.g., k-d trees, ball trees, or locality-sensitive hashing) to speed up the search

https://link.springer.com/content/pdf/10.1007/978-3-030-11509-8_1
For all sufficiently small ε, computing an ε-approximate nearest neighbor in the Euclidean distance is roughly equivalent to computing an (ε/2)-approximate nearest neighbor in the squared Euclidean distance. Our objective is to compute an (ε/2)-approximation to the value of Fmin(q), where Fmin is the lower envelope of the functions fi.

https://www.cs.cmu.edu/~agray/approxnn.pdf
Here is one possible strategy for partitioning. We first project all the points down to the vector ~ u = v:rpv ~ v:lpv, ~ and then find the median point A along ~ u. Next, we assign all the points projected to the left of A to v:lc, and all the points projected to the right of A to v:rc.

https://www.theoryofcomputing.org/articles/v008a014/v008a014.pdf
Definition 1.2. The (c;r)-approximate near neighbor problem (or (c;r)-NN) with failure probability f is to construct a data structure over a set of points P in metric space (X;D) supporting the following query: given any fixed query point q 2 X, if DP(q) r, then report some p0 2 P \ B(q;cr), with probability. 1 f .

https://people.csail.mit.edu/gregory/annbook/introduction.pdf
Gregory Shakhnarovich, Piotr Indyk, and Trevor Darrell. The nearest-neighbor (NN) problem occurs in the literature under many names, including the best match or the post office problem. The problem is of significant importance to several areas of computer science, includ-ing pattern recognition, searching in multimedia data, vector compression

https://towardsdatascience.com/similarity-search-part-4-hierarchical-navigable-small-world-hnsw-2aad4fe87d37
Hierarchical Navigable Small World (HNSW) is a state-of-the-art algorithm used for an approximate search of nearest neighbours. Under the hood, HNSW constructs optimized graph structures making it very different from other approaches that were discussed in previous parts of this article series.

https://medium.com/@brijesh_soni/the-potential-of-approximate-nearest-neighbors-ann-in-high-dimensional-spaces-579567e4f1a7
Conclusion. Algorithms called approximate nearest neighbors provide a ground-breaking answer to the problems high-dimensional data presents. They enable applications across several industries by

https://medium.com/@abdullahsamilguser/approximate-nearest-neighbor-methods-713dcfa8518f
Approximate Nearest Neighbors Oh Yeah (ANNOY) ANNOY is a "Tree Based Method". Tree based methods (KD-Trees, Random Projection Trees etc.) works by building a tree structure from the dataset.

https://arxiv.org/pdf/2102.08942.pdf
The goal of the approximate version of the nearest neighbor problem, also called c-approximate Nearest Neighbor search, is to return objects that are within2 ×' distance from the query object (where 2 >1 is a user-defined approximation ratio and ' is the distance of the query object from its nearest neighbor). 1.1 Locality Sensitive Hashing

https://dspace.mit.edu/bitstream/handle/1721.1/129551/1806.09823.pdf?sequence=2
Approximate Nearest Neighbor Search in High Dimensions Alexandr Andoni Piotr Indyk Ilya Razenshteyn Abstract The nearest neighbor problem is defined as follows: Given a set Pof npoints in some metric space (X,D), build a data structure that, given any point q, returns a point in Pthat is closest to q(its "nearest neighbor" in P). The data

https://arxiv.org/abs/2403.13491
Approximate nearest neighbor search (ANNS) on high-dimensional vectors has become a fundamental and essential component in various machine learning tasks. Prior research has shown that the distance comparison operation is the bottleneck of ANNS, which determines the query and indexing performance. To overcome this challenge, some novel methods have been proposed recently. The basic idea is to

https://dl.acm.org/doi/10.1145/3589282
Approximate K nearest neighbor (AKNN) search in the high-dimensional Euclidean vector space is a fundamental and challenging problem. ... High-Dimensional Similarity Query Processing for Data Science. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining (Virtual Event, Singapore) (KDD '21). ACM, New York, NY

https://link.springer.com/chapter/10.1007/978-3-030-11509-8_1
Approximate nearest-neighbor searching is an important retrieval problem with numerous applications in science and engineering. This problem has been the subject of many research papers spanning decades of work. ... Delone sets, and how to apply these concepts to develop new data structures for approximate polytope membership queries and

https://arxiv.org/pdf/1704.01460v1.pdf
on the probability that the above approach fails to return the exact nearest neighbor of a given query. Expansion Conditions Finding the nearest neighbor for a query point qin a general metric space (X;d) can re-quire up to (n) comparisons in the worst case, using any data structure built on the given set S(Beygelzimer et al., 2006).

https://www.cs.cmu.edu/afs/cs/user/glmiller/public/computational-geometry/15-852-F12/Handouts/PointLocationConference.pdf
NEAREST NEIGHBOR SEARCHING by making use of the floor function to achieve efficient running times; however, it is not clear whether this observation can be applied to the approximate nearest neighbor problem. 2 The Data Structure. Recall that we are given a set of n data points S in Rd.

https://www.geeksforgeeks.org/k-nearest-neighbors-knn-regression-with-scikit-learn/
Finding K nearest neighbors: Identify the K points in the training set that are closest to the new data point. Predicting the target value : Compute the average of the target values of the K nearest neighbors and use this as the predicted value for the new data point.

https://arxiv.org/abs/1806.09823
The nearest neighbor problem is defined as follows: Given a set P of n points in some metric space (X, D), build a data structure that, given any point q, returns a point in P that is closest to q (its "nearest neighbor" in P ). The data structure stores additional information about the set P, which is then used to find the nearest neighbor

https://www.semanticscholar.org/paper/New-Directions-in-Approximate-Nearest-Neighbor-Mount/6ca36a9ba7b3c367cfda7ae57723208f73c88570
This paper discusses local convexification, Macbeath regions, Delone sets, and how to apply these concepts to develop new data structures for approximate polytope membership queries and approximate vertical ray-shooting queries. Approximate nearest-neighbor searching is an important retrieval problem with numerous applications in science and engineering. This problem has been the subject of

https://www.biorxiv.org/content/10.1101/2024.01.28.577627.full.pdf
4 70 a M-dimensional manifold of ℝ!, where M < N (Camastra and Staiano, 2016).For example, NN-Descent71 recall will be very low for dataset with large local intrinsic dimension (LID) such as LID > 72 20 because it produces large amount of incorrect K nearest neighbors when applied upon high- dimensional data (Dong, et al., 2011; Radovanovic, et73 al., 2010).