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Two Algorithms for NearestNeighbor Search in High Dimensions
, 1997
"... Representing data as points in a highdimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems aris ..."
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Representing data as points in a highdimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems arising in these applications can involve several hundred or several thousand dimensions. We consider the nearestneighbor problem for ddimensional Euclidean space: we wish to preprocess a database of n points so that given a query point, one can efficiently determine its nearest neighbors in the database. There is a large literature on algorithms for this problem, in both the exact and approximate cases. The more sophisticated algorithms typically achieve a query time that is logarithmic in n at the expense of an exponential dependence on the dimension d; indeed, even the averagecase analysis of heuristics such as kd trees reveals an exponential dependence on d in the query time. In this wor...
Contentbased query of image databases, inspirations from text retrieval: inverted files, frequencybased weights and relevance feedback
, 1998
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Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality
, 1999
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Fast Nonparametric Machine Learning Algorithms for Highdimensional Massive Data and Applications a Thesis
, 2005
"... Abstract Nonparametric methods have become increasingly popular in the statistics communities and probabilistic AI communities. A nonparametric model is a set that cannot be parameterized by a finite number of parameters. These models are extremely useful when the underlying distribution of the data ..."
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Abstract Nonparametric methods have become increasingly popular in the statistics communities and probabilistic AI communities. A nonparametric model is a set that cannot be parameterized by a finite number of parameters. These models are extremely useful when the underlying distribution of the data is unknown except that which can be inferred from samples. One simple and wellknown nonparametric method is called &quot;nearestneighbor classification&quot;. The nearestneighbor method uses those observations in the training set T closest in input space to a query q to form the prediction of q. Specifically, when k of those observations in T are considered, it is called knearestneighbor.