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A NEW STATISTIC FOR ASSESSING GROSS STRUCTURE OF MULTIDIMENSIONAL PATTERNS

IP.com Disclosure Number: IPCOM000148968D
Original Publication Date: 1899-Dec-30
Included in the Prior Art Database: 2007-Apr-12
Document File: 70 page(s) / 3M

Publishing Venue

Software Patent Institute

Related People

Panayirci, Erdal: AUTHOR [+3]

Abstract

A NEW S T A T I S T I C FOR ASSESSIRC GROSS STRUCTURE OF MULTIDIMENSIONAL PATTERNS f r d a l Panayirci and Richard C* Dubes

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A NEW S T A T I S T I C FOR ASSESSIRC GROSS STRUCTURE OF MULTIDIMENSIONAL PATTERNS

f r d a l Panayirci and Richard C* Dubes

Computer Science Deoart men*

Michlgan State University

East Lansing, Michigan 48824

ABSTRACT

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     This paper examines a d-dimensional extension of the Cox-Lewis s t a t i s t i c and investigates i t s power as a function o f dimensionality in discriminating among random* aggregated, and regular arrangements o f points i n d-dimensions. This discrimination problem i s c a l i e d the c l u s t e r i n g tendency problem i n Pattern Recognition. Tests f o r c l u s t e r i n q tendency based on c l u s t e r size, quadrats* and distances are reviewed with special a t t e n t i o n t o distance-based t e s t s t h a t use
sampling oriqins. The d-dimensional Cox-Lewis s t a t i s t i c i s defined and a new derivation of i t s d i s t r j b u t i o n under a randomness hypothesis o f a Poisson s p a t i a l p o i n t process i s given. Analyticat expressions for the densities o f the Cox-Lewis s t a t i s t i c u n @ ~ r l a t t i c e r e g u l a r i t y and under extreme clustering are also provided* The powers o f Meyman-Pearson t e s t s o f hyootheses based on t h e Cox-Lewis s t a t i s t i c are derived and compared* Power i s a uniqodat functfon o f dimensionality in the t e s t o f l a t t i c e r e g u l a r i t y w i t h the minimum occurr5nq a t 12 dimensionsb.

     The power of the Cox-Lewis s t a t f s t i c i s also examined under hard-core r e g u l a r i t y and under Neyman-Scott c l u s t e r i n g with Yontc Carlo sSrnulations* The Cox-Lewls s t a t i s t i c Leads t o one-sided t e s t s for r e g u l a r i t y which are as powerful as any t e s t s reported i n t h e Literature* The choice o f sampling w'indow can be d i f f i c u l t w i t 4 r e a l data but the Cox-Lenis s t a t i s t i c shows qreat promSse f o r assessinq clustering tendency.

Research supported i n Dart by NSF Grant ECS-8017106.

E o Panayirci 4s on leave from the Technjcal University o f Tstanbul under t h e FuLbriqht-Hays and NATO S c i e n t i f i c Programs*

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I. Introduction

2. Background
2.1 Soatial Point Processes
2.2 Categories of
Tests for Clustering Tendency
2.3 Distance-Based Methods
2.4 Tests Using Sampling Ortgins

3. Proposed Test
3.1 Oefinitlon of Stattstfc
3.2 O f s t rlbut ion Under Randomness
3.3 Distribution Under
Lattice Regularity
3.4 Gistribut ion Under Extreme Clustering

4. Simulated Power Studfes
4.1 Hard Core Regularity 4*2 Neyman-Scott Clustering

5. Summary and Oiscussfon

REFERENCES

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E x ~ t o r a t o r y
data analysis i s a generic term f o r a body of

mathematical, s t a t i s...