On interpoint distances for planar Poisson cluster processes

1983 ◽  
Vol 20 (3) ◽  
pp. 513-528 ◽  
Author(s):  
Richard J. Kryscio ◽  
Roy Saunders
Keyword(s):  
Lebesgue Measure ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Indicator Function ◽  
Poisson Processes ◽  
Interpoint Distance ◽  
Poisson Cluster ◽  
Cluster Processes

For stationary Poisson or Poisson cluster processes ξ on R2 we study the distribution of the interpoint distances using the interpoint distance function and the nearest-neighbor indicator function . Here Sr (x) is the interior of a circle of radius r having center x, I(t) is that subset of D which has x ∊ D and St(x) ⊂ D and χ is the usual indicator function. We show that if the region D ⊂ R2 is large, then these functions are approximately distributed as Poisson processes indexed by and , where µ(D) is the Lebesgue measure of D.

On interpoint distances for planar Poisson cluster processes

1983 ◽  
Vol 20 (03) ◽  
pp. 513-528
Author(s):  
Richard J. Kryscio ◽  
Roy Saunders
Keyword(s):  
Lebesgue Measure ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Indicator Function ◽  
Poisson Processes ◽  
Interpoint Distance ◽  
Poisson Cluster ◽  
Cluster Processes

For stationary Poisson or Poisson cluster processes ξ on R2 we study the distribution of the interpoint distances using the interpoint distance function and the nearest-neighbor indicator function . Here Sr (x) is the interior of a circle of radius r having center x, I(t) is that subset of D which has x ∊ D and St (x) ⊂ D and χ is the usual indicator function. We show that if the region D ⊂ R2 is large, then these functions are approximately distributed as Poisson processes indexed by and , where µ(D) is the Lebesgue measure of D.

A cluster process representation of a self-exciting process

1974 ◽  
Vol 11 (3) ◽  
pp. 493-503 ◽  
Author(s):  
Alan G. Hawkes ◽  
David Oakes
Keyword(s):  
Point Processes ◽  
Generating Functional ◽  
Cluster Process ◽  
Process Representation ◽  
Age Dependent ◽  
Birth Processes ◽  
Poisson Cluster ◽  
Cluster Processes

It is shown that all stationary self-exciting point processes with finite intensity may be represented as Poisson cluster processes which are age-dependent immigration-birth processes, and their existence is established. This result is used to derive some counting and interval properties of these processes using the probability generating functional.

A novel algorithm for community detection based on resistance distance and similarity

2021 ◽  
pp. 2150164
Author(s):  
Pengli Lu ◽  
Zhou Yu ◽  
Yuhong Guo
Keyword(s):  
Community Detection ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Detection Algorithm ◽  
Structure And Function ◽  
Resistance Distance ◽  
Node Similarity ◽  
The Common ◽  
Community Detection Algorithm ◽  
And Function

Community detection is important for understanding the structure and function of networks. Resistance distance is a kind of distance function inherent in the network itself, which has important applications in many fields. In this paper, we propose a novel community detection algorithm based on resistance distance and similarity. First, we propose the node similarity, which is based on the common nodes and resistance distance. Then, we define the distance function between nodes by similarity. Furthermore, we calculate the distance between communities by using the distance between nodes. Finally, we detect the community structure in the network according to the nearest-neighbor nodes being in the same community. Experimental results on artificial networks and real-world networks show that the proposed algorithm can effectively detect the community structures in complex networks.

Setting Attribute Weights for Nearest Neighbor Learning Algorithms Using C4.5

1997 ◽  
Vol 11 (03) ◽  
pp. 405-415 ◽  
Author(s):  
Charles X. Ling ◽  
John J. Parry ◽  
Handong Wang
Keyword(s):  
Machine Learning ◽  
Decision Trees ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Learning Algorithms ◽  
Simple Approach ◽  
Nearest Neighbour ◽  
Attribute Weights ◽  
New Methods

Nearest Neighbour (NN) learning algorithms utilize a distance function to determine the classification of testing examples. The attribute weights in the distance function should be set appropriately. We study situations where a simple approach of setting attribute weights using decision trees does not work well, and design three improvements. We test these new methods thoroughly using artificially generated datasets and datasets from the machine learning repository.

Count distributions, orderliness and invariance of Poisson cluster processes

1979 ◽  
Vol 16 (02) ◽  
pp. 261-273 ◽  
Author(s):  
Larry P. Ammann ◽  
Peter F. Thall
Keyword(s):  
Present Article ◽  
Generating Functional ◽  
Cluster Process ◽  
Multiple Events ◽  
Poisson Cluster Process ◽  
Finite Dimensional ◽  
The Family ◽  
Moment Measures ◽  
Poisson Cluster ◽  
Cluster Processes

The probability generating functional (p.g.fl.) of a non-homogeneous Poisson cluster process is characterized in Ammann and Thall (1977) via a decomposition of the KLM measure of the process. This p.g.fl. representation is utilized in the present article to show that the family 𝒟 of Poisson cluster processes with a.s. finite clusters is invariant under a class of cluster transformations. Explicit expressions for the finite-dimensional count distributions, product moment measures, and the distribution of clusters are derived in terms of the KLM measure. It is also shown that an element of 𝒟 has no multiple events iff the points of each cluster are a.s. distinct.

scholarly journals Unified Analysis of HetNets Using Poisson Cluster Processes Under Max-Power Association

2019 ◽  
Vol 18 (8) ◽  
pp. 3797-3812 ◽  
Author(s):  
Chiranjib Saha ◽  
Harpreet S. Dhillon ◽  
Naoto Miyoshi ◽  
Jeffrey G. Andrews
Keyword(s):  
Poisson Cluster ◽  
Cluster Processes
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