Abstract
Distances of the nearest neighbor or several nearest neighbors are essential in probability density estimate by the method of k nearest neighbors or in problems of searching in large databases. A typical task of the probability density estimate using several nearest neighbors is the Bayes’s classifier. The task of searching in large databases is looking for other nearest neighbor queries. In this paper it is shown that for a uniform distribution of points in an n-dimensional Euclidean space the distribution of the distance of the i-th nearest neighbor to the n-power has Erlang distribution. The power approximation of the newly introduced probability distribution mapping function of distances of nearest neighbors in the form of suitable power of the distance is presented. A way to state distribution mapping exponent q for a probability density estimation including boundary effect in high dimensions is shown.
This work was supported by the Ministry of Education of the Czech Republic under project No. LN00B096.
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© 2004 Springer-Verlag Berlin Heidelberg
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Jirina, M., Jirina, M. (2004). Features of Neighbors Spaces. In: Van Emde Boas, P., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2004: Theory and Practice of Computer Science. SOFSEM 2004. Lecture Notes in Computer Science, vol 2932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24618-3_20
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DOI: https://doi.org/10.1007/978-3-540-24618-3_20
Publisher Name: Springer, Berlin, Heidelberg
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