A SIMPLE ON-LINE RANDOMIZED INCREMENTAL ALGORITHM FOR COMPUTING HIGHER ORDER VORONOI DIAGRAMS

1992 ◽  
Vol 02 (04) ◽  
pp. 363-381 ◽  
Author(s):  
FRANZ AURENHAMMER ◽  
OTFRIED SCHWARZKOPF
Keyword(s):  
Voronoi Diagram ◽  
Structural Changes ◽  
Nearest Neighbor ◽  
Voronoi Diagrams ◽  
Simple Algorithm ◽  
Incremental Algorithm ◽  
K Nearest Neighbor ◽  
On Line ◽  
Incremental Construction ◽  
Primal Space

We present a simple algorithm for maintaining order-k Voronoi diagrams in the plane. By using a duality transform that is of interest in its own right, we show that the insertion or deletion of a site involves little more than the construction of a single convex hull in three-space. In particular, the order-k Voronoi diagram for n sites can be computed in time [Formula: see text] and optimal space [Formula: see text] by an on-line randomized incremental algorithm. The time bound can be improved by a logarithmic factor without losing much simplicity. For k≥ log 2 n, this is optimal for a randomized incremental construction; we show that the expected number of structural changes during the construction is ⊝(nk2). Finally, by going back to primal space, we obtain a dynamic data structure that supports k-nearest neighbor queries, insertions, and deletions in a planar set of sites. The structure promises easy implementation, exhibits a satisfactory expected performance, and occupies no more storage than the current order-k Voronoi diagram.

Outlier Detection for Soft-Sensor Modeling Data Based on k-Nearest Neighbor

2012 ◽  
Vol 468-471 ◽  
pp. 2504-2509
Author(s):  
Qiang Da Yang ◽  
Zhen Quan Liu
Keyword(s):  
Outlier Detection ◽  
Nearest Neighbor ◽  
Detection Method ◽  
Soft Sensor ◽  
K Nearest Neighbor ◽  
Sensor Model ◽  
Sensor Technique ◽  
On Line ◽  
Modeling Data ◽  
Sensor Modeling

The on-line estimation of some key hard-to-measure process variables by using soft-sensor technique has received extensive concern in industrial production process. The precision of on-line estimation is closely related to the accuracy of soft-sensor model, while the accuracy of soft-sensor model depends strongly on the accuracy of modeling data. Aiming at the special character of the definition for outliers in soft-sensor modeling process, an outlier detection method based on k-nearest neighbor (k-NN) is proposed in this paper. The proposed method can be realized conveniently from data without priori knowledge and assumption of the process. The simulation result and practical application show that the proposed outlier detection method based on k-NN has good detection effect and high application value.

Parallel kNN Queries for Big Data Based on Voronoi Diagram Using MapReduce

2015 ◽  
pp. 392-414
Author(s):  
Wei Yan
Keyword(s):  
Big Data ◽  
Voronoi Diagram ◽  
Spatial Databases ◽  
Nearest Neighbor ◽  
Programming Model ◽  
Dimensional Space ◽  
Data Sets ◽  
Two Dimensional ◽  
K Nearest Neighbor ◽  
K Nearest Neighbors

In cloud computing environments parallel kNN queries for big data is an important issue. The k nearest neighbor queries (kNN queries), designed to find k nearest neighbors from a dataset S for every object in another dataset R, is a primitive operator widely adopted by many applications including knowledge discovery, data mining, and spatial databases. This chapter proposes a parallel method of kNN queries for big data using MapReduce programming model. Firstly, this chapter proposes an approximate algorithm that is based on mapping multi-dimensional data sets into two-dimensional data sets, and transforming kNN queries into a sequence of two-dimensional point searches. Then, in two-dimensional space this chapter proposes a partitioning method using Voronoi diagram, which incorporates the Voronoi diagram into R-tree. Furthermore, this chapter proposes an efficient algorithm for processing kNN queries based on R-tree using MapReduce programming model. Finally, this chapter presents the results of extensive experimental evaluations which indicate efficiency of the proposed approach.

A proposition of querying scheme with network Voronoi diagram in bichromatic reverse k-nearest neighbor

2017 ◽  
Vol 13 (1) ◽  
pp. 62-75 ◽  
Author(s):  
Yusuke Gotoh ◽  
Chiori Okubo
Keyword(s):  
Voronoi Diagram ◽  
Design Methodology ◽  
Processing Time ◽  
Nearest Neighbor ◽  
Spatial Networks ◽  
K Nearest Neighbor ◽  
Influence Zone ◽  
Content Type ◽  
Future Direction ◽  
Practical Implications

Purpose This study aims to propose and evaluate a searching scheme for a bichromatic reverse k-nearest neighbor (BRkNN) that has objects and queries in spatial networks. In this proposed scheme, the author’s search for the BRkNN of the query using an influence zone for each object with a network Voronoi diagram (NVD). Design/methodology/approach The author’s analyze and evaluate the performance of the proposed searching scheme. Findings The contribution of this paper is that it confirmed that the proposed searching scheme gives shorter processing time than the conventional linear search. Research limitations/implications A future direction of this study will involve making a searching scheme that reduces the processing time when objects move automatically on spatial networks. Practical implications In BRkNN, consider two groups in a convenience store, where several convenience stores, which are constructed in Groups A and B, operate in a given region. The author’s can use RNN is RkNN when k = 1 (RNN) effectively to set a new store considering the Euclidean and road distances among stores and the location relationship between Groups A and B. Originality/value In the proposed searching scheme, the author’s search for the BRkNN of the query for each object with an NVD using the influence zone, which is the region where an object in the spatial network recognizes the nearest neighbor for the query.

scholarly journals Detect Frauds in Credit Card using Data Mining Techniques

2019 ◽  
Vol 9 (2) ◽  
pp. 4891-4895
Keyword(s):  
Data Mining ◽  
Credit Card ◽  
Nearest Neighbor ◽  
Hidden Markov ◽  
K Nearest Neighbor ◽  
Detection Systems ◽  
Important Concern ◽  
On Line ◽  
Using Data ◽  
The Individual

In today era credit card are extensively used for day to day business as well as other transactions. Ascent within the variety of transactions through master card has junction rectifier to rise in the dishonest activities. In trendy day's fraud is one in every of the most important concern within the monetary loses not solely to the merchants however additionally to the individual purchasers. Data processing had competed a commanding role within the detection of credit card in on-line group action. Our aim is to first of all establish the categories of the fraud secondly, the techniques like K-nearest neighbor, Hidden Markov model, SVM, logistic regression, decision tree and neural network. So fraud detection systems became essential for the banks to attenuate their loses. In this paper we have research about the various detecting techniques to identify and detect the fraud through varied techniques of data mining

A ROBUST TOPOLOGY-ORIENTED INCREMENTAL ALGORITHM FOR VORONOI DIAGRAMS

1994 ◽  
Vol 04 (02) ◽  
pp. 179-228 ◽  
Author(s):  
KOKICHI SUGIHARA ◽  
MASAO IRI
Keyword(s):  
Numerical Computation ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
The Other ◽  
Geometric Algorithms ◽  
Incremental Algorithm ◽  
Single Precision ◽  
Careful Choice ◽  
Numerical Errors ◽  
Incremental Method

The paper presents a robust algorithm for constructing Voronoi diagrams in the plane. The algorithm is based on an incremental method, but is quite new in that it is robust against numerical errors. Conventionally, geometric algorithms have been designed on the assumption that numerical errors do not take place, and hence they are not necessarily valid for real computers where numerical errors are inevitable. The algorithm to be proposed in this paper, on the other hand, is designed with the recognition that numerical errors are inevitable in real computation; i.e., in the proposed algorithm higher priority is placed on topological structures than on numerical values. As a result, the algorithm is "completely" robust in the sense that it always gives some output however poor the precision of numerical computation may be. In general, the output cannot be more than an approximation to the true Voronoi diagram which we should have got by infinite-precision computation. However, the algorithm is asymptotically correct in the sense that the output converges to the true diagram as the precision becomes higher. Moreover, careful choice of the way of numerical computation makes the algorithm stable enough; indeed the present version of the algorithm can construct in single-precision arithmetic a correct Voronoi diagram for one million generators randomly placed in the unit square in the plane.

Processing Continuous k Nearest Neighbor Queries in Obstructed Space with Voronoi Diagrams

2020 ◽  
Vol 7 (2) ◽  
pp. 1-27
Author(s):  
Huaijie Zhu ◽  
Xiaochun Yang ◽  
Bin Wang ◽  
Wang-Chien Lee ◽  
Jian Yin ◽  
...  
Keyword(s):  
Nearest Neighbor ◽  
Voronoi Diagrams ◽  
K Nearest Neighbor ◽  
Nearest Neighbor Queries
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