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The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG has a vertex for each point, and a directed edge from p to q whenever q is a nearest neighbor of p , a point whose distance from p is minimum among all the given points other than p itself.
k-nearest neighbor search identifies the top k nearest neighbors to the query. This technique is commonly used in predictive analytics to estimate or classify a point based on the consensus of its neighbors. k-nearest neighbor graphs are graphs in which every point is connected to its k nearest neighbors.
An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small). If k = 1, then the object is simply assigned to the class of that single nearest neighbor. The k-NN algorithm can also be generalized for regression.
Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...
A point location data structure can be built on top of the Voronoi diagram in order to answer nearest neighbor queries, where one wants to find the object that is closest to a given query point. Nearest neighbor queries have numerous applications. For example, one might want to find the nearest hospital or the most similar object in a database.
Proximity problems is a class of problems in computational geometry which involve estimation of distances between geometric objects. A subset of these problems stated in terms of points only are sometimes referred to as closest point problems , [ 1 ] although the term "closest point problem" is also used synonymously to the nearest neighbor ...
Nearest neighbor decoding in coding theory; The k-nearest neighbor algorithm in machine learning, an application of generalized forms of nearest neighbor search and interpolation; The nearest neighbour algorithm for approximately solving the travelling salesman problem; The nearest-neighbor thermodynamic parameters for determining the ...
The problem was formulated by Lozovanu & Zelikovsky (1993) [1] and by Ravi et al. (1996). Ravi et al. also considered a geometric version of the problem, which can be seen as a special case of the graph problem. In the geometric k-minimum spanning tree problem, the input is a set