CN103034678A - RkNN (reverse k nearest neighbor) inquiring method based on Voronoi diagram - Google Patents
RkNN (reverse k nearest neighbor) inquiring method based on Voronoi diagram Download PDFInfo
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Abstract
The invention discloses an RkNN (reverse k nearest neighbor) inquiring method based on a Voronoi diagram, and belongs to the technical field of space data inquiring. The method comprises the following steps of step1, according to an inquiring site set, generating the corresponding Voronoi diagram with an m order; step 2, importing a dataset of an inquiring object; step 3, inputting the k value and the coordinates of an inquiring site q, so as to obtain the RkNN inquiring results; and step 4, finishing. The method has the advantages that the double-color RkNN inquiring in the dataset with frequency change is realized, and the results of R(k-1)NN, RkNN and R(k+1)NN can be inquired on the Voronoi diagram with the m order; the pre-calculation amount is reduced; compared with the prior art, the inquiring efficiency is greatly improved; and the advantages are more obvious along with the increase of the quantity of inquiring object sets, and the application performance of the Voronoi diagram is improved.
Description
Technical field
The invention belongs to spatial data inquiring technology field, particularly a kind of anti-k arest neighbors querying method based on Voronoi figure.
Background technology
The mobile object inquiring technology can be applied to urban transportation, Aero-Space, communication network etc. and exists in the network of mobile object in the spatial database, thereby it can come according to a large amount of space-time datas mined information to offer the relevant consulting of client.Typical space querying is arest neighbors (nearest neighbors, NN) inquiry and k arest neighbors (k nearest neighbors, kNN) inquiry.For example: the passenger can ask which hotel is nearest apart from the station; The driver can inquire about 2 nearest refuelling stations somewhere.Anti-k arest neighbors (reverse k nearest neighbors, RkNN) inquiry is the mutation of kNN inquiry, whom it answers query object is regarded as nearest-neighbors, a series of chain stores such as certain city issue some advertisements to the client possibly, the customers of each chain store's sending advertisement are different, these clients' scope can define becomes the customers that are subject to certain chain store's impact, just can determine these colonies with the RkNN inquiry; Each mobile object tends to sharing some information etc. recently or in oppositely to the object that advances in mobile database system in addition.In addition, in field of play, the spatial database query technology also has certain development prospect, in the massively multiplayer game World of Warcraft by the exploitation of the Blizzard company of the U.S., the game player finds the enemy or seeks the operations such as buildings in the map detecting be exactly the embodiment of kNN and RNN.
RkNN inquiry then is replenishing of kNN inquiry and development, is divided into monochromatic RkNN inquiry and double-colored RkNN(BRkNN by the difference of data set) inquire about.F.korn and S.Muthukrishnan have proposed the concept of RNN inquiry, and have provided the querying method of finding the solution RNN.With two R set to inquire about, insertion, deletion action.Yang and Lin have improved above method, have introduced the Rdnn tree, inquire about and become possibility so that carry out RNN inquiry and NN with single tree.Stanoi has proposed a kind of method SAE, and the method is not calculate in the situation of prediction, and SAE is divided into 6 sectors that size is identical with the peripheral extent of query point.SAE at first finds the candidate target of RNN in sector separately; Secondly, for each candidate target finished one independently NN inquire about to judge that this candidate target is last result.The people such as Maheshwari have proposed the RNN inquiry of main memory data structure.Put its structure for each and keeping it to the distance of arest neighbors.
The method of Stanoi is in higher dimensional space, and along with the increase of dimension, the candidate value of RNN presents exponential increase.Efficient significantly reduces.In order to address this problem, the people such as Singh have proposed to find out the RkNN candidate value by carrying out conventional kNN inquiry.But the shortcoming of the method is not to be to find all RkNN points.The method of Tao is similar to Stanoi, is called TPL.TPL is divided into two stages---screening and refining, and a given query point q, the method recurrence is got back to the unallocated space of q point, until there is not candidate target remaining.When the step of filtering, removed some and be defined as the candidate target of error result.
At the RNN query aspects based on Voronoi figure, come lookup result with the Range-k proof method among the Voronoi figure in the Euclid plane that Li Song, Hao Zhongxiao propose.Namely by put concentrate a bit centered by, point is that radius generates one and judges that circle is next and find out RNN with this to the distance of query point.The method is only applicable to the inquiry to monochromatic RkNN, has a large amount of unnecessary I/O operations when double-colored RkNN inquiry.Maytham Safar has then proposed to carry out in the space of network Voronoi figure the RNN inquiry.Method is applicable to the aspects such as transportation network, and efficient is very low when the query object frequent.
Voronoi figure is the spatial decomposition, particularly point set p={p1 of determining with the distance of given object discrete set (such as point set), p2 ..., the Voronoi figure of pn} is defined as the cell collection.Here each cell, V (pi) is an area of space, by distance pi than forming apart from the nearer whole spatial data points of other points among the p.Voronoi figure can be generalized to m rank Voronoi figure (MVD).Query object in MVD in each zone is exactly the RkNN value of the generator of current region according to the definition of BRkNN as can be known.As shown in Figure 1, search the R3NN value of website 3: at first locate the Voronoi zone of the contained website 3 of those generators, four of V (1,3,5), V (1,3,4), V (1,3,6), V (1,2,3) are arranged.Therefore, the query object that comprises in these four Voronoi zones all is the R3NN Query Result of website 3.
But existing use MVD carries out the BRkNN querying method and has obvious shortcoming:
(1) precomputation of high cost.The cell that MVD needs all MVD of precomputation and all information relevant with cell such as generator, Voronoi limit, Voronoi summit etc.
(2) do not support the dynamically k value of change.MVD only can adapt to the RkNN inquiry with clear and definite k value, and MVD adapts to the RkNN inquiry that the k value is not more than the exponent number of figure.Therefore, this technology is not suitable for the situation of not knowing in advance the k value or may dynamically change the k value.
(3) renewal of inefficiency operation.For each insert or delete operation, cell has to recomputate.
Summary of the invention
The present invention is directed to the problems referred to above and shortcoming, in order to be implemented in the BRkNN result of a plurality of k values of inquiry on the Voronoi figure of individual m rank, a kind of anti-k arest neighbors querying method based on Voronoi figure is provided, realize changing the double-colored RkNN inquiry under the data set frequently, namely on the Voronoi figure of a certain m rank, can inquire the result of R (k-1) NN, RkNN, R (k+1) NN.
The objective of the invention is to be achieved through the following technical solutions: a kind of anti-k arest neighbors querying method based on Voronoi figure is to adopt the frame model that filters-refine.At filtration stage, call needed m rank Voronoi figure by the k value, and take the inquiry website as according to determining which Voronoi polygon to form query context by at m rank Voronoi figure, then all query objects in the query context are decided to be Candidate Set.In the refinement stage, take the k value as standard, if the k value is identical with the exponent number of the m rank Voronoi figure that calls, all query objects are the result in the Candidate Set so; If different, query object identical in all Candidate Sets is screened be defined as the result so first, then use the remaining candidate target of Range-k verification method checking, thereby obtain final Query Result, specifically comprise the steps:
Step 1: according to the inquiry station point set, generate corresponding m rank Voronoi figure, method is: existing m rank Voronoi drawing generating method;
Step 2: the importing enquire object data set, method is: the data file is read, and show data;
Step 3: the coordinate of input k value and query point q obtains the RkNN Query Result; Wherein:
When k=m, all interior query objects of polygon that comprise website q are the result,
When k＜m, check so that all comprise query object in the polygon of website q, if the position of query object (during as k=3, checks the single order Voronoi polygon of q) within comprising the k-3 rank Voronoi polygon of website q, be so the result; If do not exist, determine the result with the Range-k proof method so.Namely take query object as the center of circle, be that radius is done circle to the distance of website q, if in the circle and the website number that comprises on the circle
K is so the result, otherwise then is not,
As k〉during m, all query objects that comprise in the Voronoi polygon of website q are the result; And checking respectively these polygonal query objects in polygon, take query object as the center of circle, is that radius is done circle to the distance of website q, if in the circle and the website number that comprises on the circle
K+1 is so the result, otherwise then is not;
Step 4: finish.
The described m rank Voronoi figure that generates according to step 1 of step 3 can inquire the result of R (k-1) NN, RkNN, R (k+1) NN.
The present invention compared with prior art has the following advantages effect: realized the BRkNN result in a plurality of k values of individual m rank Voronoi figure inquiry.According to the character of Voronoi figure as can be known R (k-1) NN be the subset of RkNN, so in like manner can release R (k-2) NN, R (k-3) NN etc. also is the subset of RkNN, and RkNN is the subset of R (k+1) NN, R (k+2) NN etc. equally.Character can extend too so, inquires the result of R (k+2) NN or R (k-3) NN etc. at a m rank Voronoi figure.But it is to be noted, when only having exponent number as k value and Voronoi identical, could directly obtain the result.When two values not simultaneously, the just query context that dwindles that in fact obtains is a Candidate Set as a result in other words conj.or perhaps, and correct result also will just can obtain through calculating again.If the query context that obtains at m rank Voronoi figure is very large, such as R (k+2) NN, R (k-3) NN.This just means that the Candidate Set that obtains is also very large so, and namely the number of query object can increase in the Candidate Set.Bring very large calculated amount will for so ensuing work.Therefore be not that the k value that can inquire about on a m rank Voronoi figure is The more the better on.The present invention is in order to take into account inquiry velocity and disk storage amount, and the method that proposes has only realized inquiring about R (k-1) NN, three results of RkNN, R (k+1) NN at a m rank Voronoi figure.
The RkNN querying method is the Finch method that proposes in the document 1 preferably at present, and BRMVD method and Finch method that the present invention is designed compare, and test access index node number of times in two kinds of method query scripts (I/O number).The main relatively number of times of method access index node in two kinds of situations of the identical k value with different websites of same site different value of K.Test result shows that the present invention has reduced the precomputation amount, and search efficiency compares with existing method and improve a lot, and along with the increase of query object collection quantity, this advantage is also more obvious, has strengthened the application of Voronoi figure.
Description of drawings
Fig. 1 is a kind of anti-k arest neighbors querying method three rank Voronoi pictorial diagram based on Voronoi figure of the present invention;
Fig. 2 is a kind of anti-k arest neighbors querying method second order three rank mixing Voronoi pictorial diagram based on Voronoi figure of the present invention;
Fig. 3 is a kind of anti-k arest neighbors querying method places of cultural interest station data collection based on Voronoi figure of the present invention;
Fig. 4 is that a kind of anti-k arest neighbors querying method based on Voronoi figure of the present invention generates Voronoi diagram data document;
Fig. 5 is a kind of query object that imports based on the anti-k arest neighbors querying method of Voronoi figure of the present invention;
Fig. 6 is a kind of anti-k arest neighbors querying method input message interface based on Voronoi figure of the present invention;
Fig. 7 is a kind of anti-k arest neighbors querying method Query Result based on Voronoi figure of the present invention;
Fig. 8 is a kind of fixing inquiry of anti-k arest neighbors querying method website different value of K test based on Voronoi figure of the present invention;
Fig. 9 is a kind of different inquiry of anti-k arest neighbors querying method fixed k website test based on Voronoi figure of the present invention;
Figure 10 is a kind of anti-k arest neighbors querying method general flow chart based on Voronoi figure of the present invention.
Embodiment
Below in conjunction with specific embodiment the present invention is further elaborated, but protection scope of the present invention is not limited by specific embodiment, is as the criterion with claims.In addition, with under the prerequisite of technical solution of the present invention, any change or change that those of ordinary skills that the present invention is done realize easily all will fall within the claim scope of the present invention.
A kind of anti-k arest neighbors querying method based on Voronoi figure comprises the steps:
Step 1: according to the inquiry station point set, generate corresponding m rank Voronoi figure, method is: existing m rank Voronoi drawing generating method; Because every m rank Voronoi figure among the present invention can inquire about the result of R (k-1) NN, RkNN and R (k+1) NN, so generate 1,3,6,9 according to the needs of inquiry ... rank Voronoi figure.To generate 1,3,6,9 according to the needs of inquiry ... rank Voronoi figure.
Step 2: the importing enquire object data set, method is: the data file is read, and show data;
Step 3: the coordinate of input k value and query point q obtains the RkNN Query Result; Wherein:
When k=m, all interior query objects of polygon that comprise website q are the result,
When k＜m, check so that all comprise query object in the polygon of website q, if the position of query object (during as k=3, checks the single order Voronoi polygon of q) within comprising the k-3 rank Voronoi polygon of website q, be so the result; If do not exist, determine the result with the Range-k proof method so.Namely take query object as the center of circle, be that radius is done circle to the distance of website q, if in the circle and the website number that comprises on the circle
K is so the result, otherwise then is not,
As k〉during m, all query objects that comprise in the Voronoi polygon of website q are the result; And checking respectively these polygonal query objects in polygon, take query object as the center of circle, is that radius is done circle to the distance of website q, if in the circle and the website number that comprises on the circle
K+1 is so the result, otherwise then is not;
The described m rank Voronoi figure that generates according to step 1 can inquire the result of R (k-1) NN, RkNN, R (k+1) NN.
Step 4: finish.
With a real places of cultural interest landmark data collection CD, further specify the anti-k arest neighbors querying method based on Voronoi figure that the present invention proposes as shown in Figure 3.May further comprise the steps:
Step 1: according to CD places of cultural interest set of sites, generate the Voronoi graph data, and preserve document.
Generate the document of figure module preservation as shown in Figure 4, data are the data of 3 rank Voronoi figure among the figure.Every data line may be described a Voronoi polygon.Data in every row are divided into three parts, are respectively generators, the polygonal summit of Voronoi and MBR.Separate with ": " between every partial data.Our the first row data, first ": " 6 groups of numerals before are polygonal generator.Per two groups of a pair of coordinates of numeral, because be 3 rank polygons, 3 pairs of coordinates just in time represent 3 generators.The polygonal summit of second ": " data representation before equally also is per two groups of a pair of coordinates of numeral.4 groups of remaining polygonal MBR of data representation, front two groups of upper left corner coordinates that represent MBR, rear two groups of lower right corner coordinates that represent MBR.
Step 2: importing enquire object.Red part is the query object collection among Fig. 5, and black part is divided into set of sites.
Step 3: input message is inquired about, and obtains Query Result.As shown in Figure 6, input respectively the k value that will inquire about, and the x of inquiry website, the y coordinate gets final product.Provided among Fig. 7 and be the R6NN result of point (8770438,2050064).
Step 4: finish
Present embodiment adopts VC++ to realize, experiment is P4 2.4GHz at processor, and main memory is 1GB, and operating system is to carry out on the microcomputer of WindowsXP, and the present embodiment data set has adopted the partial data of real cultural terrestrial reference and residential area accumulation.The website number of CD data set is 2099, and the query object number is 4994, is characterized in the even at home whole area of dividing of set of sites, and during its central and north is relatively poly-, and the query object collection concentrates on the north relatively.This example compares the present invention and Finch method, tests access index node number of times in two kinds of method query scripts (I/O number), and experimental result is shown in Fig. 8-9.
In Fig. 8, point 1, point 2, point 3 are the relative situations concentrated with the website distribution of query object distribution, and needed I/O number is equally matched in this case can to find out two kinds of methods, all maintains on the lower data.Point 4, point 5, point 7, point 8 are that query object distributes and the website relative uniform situation that distributes, and two kinds of I/O time required numbers of method also are more or less the same in this case, all maintain on the higher numerical value.Point 6 and 9 of points are the query object situations that relative concentrated website is evenly distributed that distributes, and at this moment required I/O the number of Finch method is higher, and required I/O the number of BRMVD method is relatively low.Therefore, when treatment station was evenly distributed the data set of the relatively concentrated distribution of query object, the BRMVD method was better than the Finch method on the whole.
In Fig. 9, point 1, point 3, point 7 are positioned at the place that website and query object are all concentrated.Point 2, point 6 are positioned at the website place that query object distribute to concentrate that is evenly distributed.Point 4, point 5 are positioned at uniformly place of website distribution Integrated query object distribution.As can be seen from Figure 9 put 1, during the situation of point 3, point 7, the BRMVD method is because I/O the number that affect that website and query object distribute had obvious fluctuating.But numerical value maintains lower position and is more or less the same with I/O number of Finch method, and slightly is better than the latter.When the situation of point 2, point 6, find out that the Finch method is owing to I/O the number that affect that is subject to the query object distribution increases fast.Then I/O number is low is better than the former for the BRMVD method.When the situation of point 4, point 5, the impact that the BRMVD method is distributed by website and query object is little, and I/O time number is lower.The impact that the Finch method is distributed by query object is larger, and I/O number had significantly than the BRMVD method and rise.See that on the whole Fig. 9 shows that the BRMVD method is better than the Finch method.
Claims (2)
1. the anti-k arest neighbors querying method based on Voronoi figure is characterized in that: comprise the steps:
Step 1: according to the inquiry station point set, generate corresponding m rank Voronoi figure, method is: existing m rank Voronoi drawing generating method;
Step 2: the importing enquire object data set, method is: the data file is read, and show data;
Step 3: the coordinate of input k value and query point q obtains the RkNN Query Result; Wherein:
When k=m, all interior query objects of polygon that comprise website q are the result,
When k＜m, check so that all comprise query object in the polygon of website q, if the position of query object (during as k=3, checks the single order Voronoi polygon of q) within comprising the k-3 rank Voronoi polygon of website q, be so the result; If do not exist, determine the result with the Range-k proof method so, namely take query object as the center of circle, be that radius is done circle to the distance of website q, if in the circle and the website number that comprises on the circle
K is so the result, otherwise then is not,
As k〉during m, all query objects that comprise in the Voronoi polygon of website q are the result; And checking respectively these polygonal query objects in polygon, take query object as the center of circle, is that radius is done circle to the distance of website q, if in the circle and the website number that comprises on the circle
K+1 is so the result, otherwise then is not;
Step 4: finish.
2. a kind of anti-k arest neighbors querying method based on Voronoi figure according to claim 1 is characterized in that: the described m rank Voronoi figure that generates according to step 1 of step 3 can inquire the result of R (k-1) NN, RkNN, R (k+1) NN.
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| CN103559209A (en) * | 2013-10-10 | 2014-02-05 | 河南大学 | Method for querying nearest neighbor of efficient space combined by Voronoi Diagram and virtual grids |
| CN105912574A (en) * | 2016-03-30 | 2016-08-31 | 电子科技大学 | Multi-user decided spatial data query and verification method |
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| CN103544291B (en) * | 2013-10-29 | 2016-05-18 | 东北林业大学 | Mobile object CKNN querying method based on RRN-Tree in road network |
| CN107958087A (en) * | 2017-10-19 | 2018-04-24 | 大连大学 | The representative point acquisition methods of the distributed temporal index of the row's of falling Thiessen polygon of portable medical |
| CN107766495A (en) * | 2017-10-19 | 2018-03-06 | 大连大学 | Distributed temporal index method based on Voronoi diagram |
| CN109597866B (en) * | 2018-11-22 | 2020-05-19 | 成都理工大学 | Traffic rule-based continuous nearest neighbor monitoring method for moving object in road network |
| CN109741362B (en) * | 2018-12-29 | 2019-09-03 | 牡丹江师范学院 | Modeling method based on Voronoi and in big data security application |
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| CN102043857B (en) * | 2010-12-27 | 2012-06-20 | 中国科学院计算技术研究所 | All-nearest-neighbor query method and system |
| US10311105B2 (en) * | 2010-12-28 | 2019-06-04 | Microsoft Technology Licensing, Llc | Filtering queried data on data stores |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103559209A (en) * | 2013-10-10 | 2014-02-05 | 河南大学 | Method for querying nearest neighbor of efficient space combined by Voronoi Diagram and virtual grids |
| CN103559209B (en) * | 2013-10-10 | 2016-08-17 | 河南大学 | A kind of efficient spatial K-NN search method that Voronoi Diagram is combined with virtual grid |
| CN105912574A (en) * | 2016-03-30 | 2016-08-31 | 电子科技大学 | Multi-user decided spatial data query and verification method |
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Application publication date: 20130410 |