# Proximity in the Age of Distraction: Robust Approximate Nearest Neighbor Search

@inproceedings{HarPeled2017ProximityIT, title={Proximity in the Age of Distraction: Robust Approximate Nearest Neighbor Search}, author={Sariel Har-Peled and Sepideh Mahabadi}, booktitle={SODA}, year={2017} }

We introduce a new variant of the nearest neighbor search problem, which allows for some coordinates of the dataset to be arbitrarily corrupted or unknown. Formally, given a dataset of $n$ points $P=\{ x_1,\ldots, x_n\}$ in high-dimensions, and a parameter $k$, the goal is to preprocess the dataset, such that given a query point $q$, one can compute quickly a point $x \in P$, such that the distance of the query to the point $x$ is minimized, when ignoring the "optimal" $k$ coordinates. Note…

## 8 Citations

### LSH on the Hypercube Revisited

- Computer ScienceArXiv
- 2017

The most basic settings are revisited, where $P$ is a set of points in the binary hypercube under the $L_1/Hamming metric, and a short description of the LSH scheme is presented, which is inspired by the authors recent work.

### Sampling a Near Neighbor in High Dimensions — Who is the Fairest of Them All?

- Computer ScienceACM Trans. Database Syst.
- 2022

This work shows that LSH based algorithms can be made fair, without a significant loss in efficiency, and develops a data structure for fair similarity search under inner product that requires nearly-linear space and exploits locality sensitive filters.

### Parameter-free Locality Sensitive Hashing for Spherical Range Reporting

- Computer ScienceSODA
- 2017

A parameter-free way of using multi-probing, for LSH families that support it, and it is shown that for many such families this approach allows us to get expected query time close to $O(n^\rho+t)$, which is the best the authors can hope to achieve using LSH.

### High-dimensional Spherical Range Reporting by Output-Sensitive Multi-Probing LSH

- Computer ScienceArXiv
- 2016

This work presents a parameter free way of using multi-probing, for LSH families that support it, and shows that for many such families this approach allows us to get query time close to O(n^\rho+t)$, which is the best the authors can hope to achieve using LSH.

### C G ] 9 A pr 2 01 7 LSH on the Hypercube Revisited

- Mathematics, Computer Science
- 2021

This note revisits the most basic settings, where P is a set of points in the binary hypercube {0, 1} d , under the L1/Hamming metric, and presents a short description of the LSH scheme in this case.

### Sublinear algorithms for massive data problems

- Computer Science
- 2017

This thesis presents algorithms and proves lower bounds for fundamental computational problems in the models that address massive data sets, and introduces theoretical problems and concepts that model computational issues arising in databases, computer vision and other areas.

### Analysis of the Period Recovery Error Bound

- Computer ScienceESA
- 2020

This paper provides the first analysis of the relationship between the error bound and the number of candidates, as well as identification of the error parameters that still guarantee recovery, and provides a hierarchy of more restrictive upper error bounds that asymptotically reduces the size of the potential period candidate set.

### Index Structures for Fast Similarity Search for Binary Vectors

- Computer Science
- 2017

Index structures are presented that are based on hash tables and similarity-preserving hashing and also on tree structures, neighborhood graphs, and distributed neural autoassociation memory for fast similarity search for objects represented by binary vectors.

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