Near Neighbor Distribution in Sets of Fractal Nature
نویسنده
چکیده
Distances of several nearest neighbors of a given point in a multidimensional space play an important role in some tasks of data mining. Here we analyze these distances as random variables defined to be functions of a given point and its k-th nearest neighbor. We prove that if there is a constant q such that the mean k-th neighbor distance to this constant power is proportional to the near neighbor index k then its distance to this constant power converges to the Erlang distribution of order k. We also show that constant q is the scaling exponent known from the theory of multifractals.
منابع مشابه
Application of Power-Law Frequency Fractal Model for Recognition of Vertical Cu Distribution in Milloieh Porphyry Deposit, SE Iran
Identification of the vertical and horizontal distributions for elemental grades is of an important sign in different mineral exploration stages. The main aim of this work is to determine the vertical distribution directional properties of Cu values in the Milloieh Cu porphyry deposit, Kerman (SE Iran) using the power-law frequency fractal model. This work is carried out based on four mineraliz...
متن کاملEvaluating the performance of concentration-number (C-N) fractal model for separation of soil horizon regarding vertical distribution and 3D models
This study aims to evaluate the efficiency of the concentration-number (C-N) fractal model for discrimination of soil horizon regarding the depth distribution profile. In this regard, soil parameters such as pH, organic carbon content, calcareous mineral content, electrical conductivity and available phosphorus of Ziarat forestland in Golestan Province, north of Iran, has been investigated. The...
متن کاملImproving Energy-Efficient Target Coverage in Visual Sensor Networks
Target coverage is one of the important problems in visual sensor networks. The coverage should be accompanied with an efficient use of energy in order to increase the network lifetime. In this paper, we address the maximum lifetime for visual sensor networks (MLV) problem by maximizing the network lifetime while covering all the targets. For this purpose, we develop a simulated annealing (SA) ...
متن کاملبعد فراکتالی وابسته به انرژی در توزیع سطحی الکترونهای بهمنهای گستره هوایی
Secondary electrons at ground level of simulated extensive air showers have been analyzed using a wavelet transform based technique, in order to investigate the variation of fractal dimensions of the lateral distribution of the electrons with shower energy and primary particle mass number. The fractal dimension is shown to increase with shower energy and seems to saturate to constant values n...
متن کاملOperads of higher transformations for globular sets and for higher magmas
In this article we discuss examples of fractal $omega$-operads. Thus we show that there is an $omega$-operadic approach to explain existence of the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}, the reflexive globular set of reflexive globular sets, the $omega$-magma of $omega$-magmas, and also the reflexive $omega$-magma ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012