smile.neighbor.package-info Maven / Gradle / Ivy
/*
* Copyright (c) 2010-2021 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Smile is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Smile. If not, see
* The simplest solution to the NNS problem is to compute the distance from
* the query point to every other point in the database, keeping track of
* the "best so far". This algorithm, sometimes referred to as the naive
* approach, has a running time of O(Nd) where N is the cardinality of S
* and d is the dimensionality of M. There are no search data structures
* to maintain, so linear search has no space complexity beyond the storage
* of the database. Surprisingly, naive search outperforms space partitioning
* approaches on higher dimensional spaces.
*
* Space partitioning, a branch and bound methodology, has been applied to the
* problem. The simplest is the k-d tree, which iteratively bisects the search
* space into two regions containing half of the points of the parent region.
* Queries are performed via traversal of the tree from the root to a leaf by
* evaluating the query point at each split. Depending on the distance
* specified in the query, neighboring branches that might contain hits
* may also need to be evaluated. For constant dimension query time,
* average complexity is O(log N) in the case of randomly distributed points.
* Alternatively the R-tree data structure was designed to support nearest
* neighbor search in dynamic context, as it has efficient algorithms for
* insertions and deletions.
*
* In case of general metric space branch and bound approach is known under
* the name of metric trees. Particular examples include vp-tree and BK-tree.
*
* Locality sensitive hashing (LSH) is a technique for grouping points in space
* into 'buckets' based on some distance metric operating on the points.
* Points that are close to each other under the chosen metric are mapped
* to the same bucket with high probability.
*
* The cover tree has a theoretical bound that is based on the dataset's
* doubling constant. The bound on search time is O(c12 log n) where c is
* the expansion constant of the dataset.
*
* @author Haifeng Li
*/
package smile.neighbor;