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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.
The kNN query is one of the hardest problems on multi-dimensional data, especially when the dimensionality of the data is high. The iDistance is designed to process kNN queries in high-dimensional spaces efficiently and it is especially good for skewed data distributions, which usually occur in real-life data sets. The iDistance can be ...
In k-nearest neighbor models, a high value of k leads to high bias and low variance (see below). In instance-based learning, regularization can be achieved varying the mixture of prototypes and exemplars. [13] In decision trees, the depth of the tree determines the variance. Decision trees are commonly pruned to control variance. [7]: 307
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 ...
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 ...
The HNSW graph offers an approximate k-nearest neighbor search which scales logarithmically even in high-dimensional data. It is an extension of the earlier work on navigable small world graphs presented at the Similarity Search and Applications (SISAP) conference in 2012 with an additional hierarchical navigation to find entry points to the ...