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Clustering by Finding Average Density

Proceedings of the 2nd International Conference on Artificial Intelligence and Advanced Manufacture, 2020
Density Peak Clustering (DPC) algorithm can get better clustering results of data sets with lower dimensions. However, for the high-dimensional data sets, there are many nodes in the clustering center area; their densities are relatively high and close to each other, so that it is hard to identify the centering node accurately.
Wenkang Huang   +4 more
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Equivalence of Surface Density and Average Directional Density

Mathematics of Operations Research, 1984
The average directional density criteria for evaluating tilings is shown to be equivalent to surface density and valid for random broken paths just as for straight paths.
B. Curtis Eaves, James A. Yorke
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Average Intersection and Pivoting Densities

SIAM Journal on Numerical Analysis, 1987
To follow a path in \({\mathbb{R}}^ N\), defined by N-1 (nonlinear) equations \(f(x)=0\), an attractive approach is to decompose \({\mathbb{R}}^ N\) into simplices and to approximate f by a piecewise linear function \(\hat f\) for which this path becomes a broken line.
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THE AVERAGE DENSITY OF SELF-CONFORMAL MEASURES

Journal of the London Mathematical Society, 2001
The paper calculates the average density of the normalized Hausdorff measure on the fractal set generated by a conformal iterated function system. It equals almost everywhere a positive constant given by a truncated generalized s-energy integral, where s is the corresponding Hausdorff dimension.
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Average Densities, Tangent Measures and Rectifiability

Periodica Mathematica Hungarica, 1998
The author gives upper and lower estimates for average \(\alpha\)-densities in the sense of \textit{T. Bedford} and \textit{A. M. Fisher} [Proc. Lond. Math. Soc., III. Ser. 64, No. 1, 95-124 (1992; Zbl 0741.28004)] and connections with flatness and rectifiability conditions.
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On the Average Sensitivity and Density of k-CNF Formulas

2013
We study the relationship between the average sensitivity and density of k-CNF formulas via the isoperimetric function \(\varphi:[0,1]\to{I\!\!R}\),
Dominik Scheder, Li-Yang Tan
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Density-induced ordered weighted averaging operators

International Journal of Intelligent Systems, 2011
We provide a special type of induced ordered weighted averaging (OWA) operator called density-induced OWA (DIOWA) operator, which takes the density around the arguments as the inducing variables to reorder the arguments. The density around the argument, which can measure the degree of similarity between the argument and its nearest neighbors, is ...
Feng-Mei Ma, Ya-Jun Guo
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