A Novel Preference-Oriented Navigation System for Optimal Routing

Applied Mathematical Sciences, Vol. 4, 2010, no. 29, 1437 - 1449

A Novel Preference-Oriented Navigation System for Optimal Routing Selection Nianlong Xu The Graduated School of Information, Production and Systems Waseda University 2-7 Hibikino, Wakamatsu-ku, Kitakyushu-shi, Fukuoka 808-0135, Japan [email protected], [email protected] Keiichi Koyanagi The Graduated School of Information, Production and Systems Waseda University 2-7 Hibikino, Wakamatsu-ku, Kitakyushu-shi, Fukuoka 808-0135, Japan

Abstract The conventional navigation retrieval generally matches according to keywords and recommends information for users without considering their preferences. The ever-increasing descriptions of POIs have made the preference-oriented retrieval difficult. Even if the users get the preferable points, they are still confused about the route plan in journeys. In our research, to filter out the non-preferable POIs, the novel preference-oriented navigation framework has been proposed. And then, to clarify the relationship among the preferable results for estimation, we have clustered POIs by their attributes of reviewing values and geographic approximations and evaluate them by the assigned clusters. Moreover, for purpose of recommending the route provides the most preferable points with the lowest cost to the user, the proposal of attribute-based routing algorithm that contains the Clustering-based Sorting Algorithm (CSA) for policy of region-based routing and Gradient-based Ordering Algorithm (GOA) for inner routing within each region was generated. The efficiency of proposed algorithms was verified through the simulation experiments. The superiority of xu-GSA on balancing the preferences between the shortest path and the point value has been sufficiently emerged through the comparison with the Gradient-based Nearest Neighbor Algorithm which had performed the decent class on routing selection. Keywords: Navigation; Filter; Multiple attributes; Clustering; Routing algorithm

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1 Introducction In the passt few years, a prior knowledge-b k based naviggation show wn in Figuree 1 haas become an importaant section of retrievall service. However, H it bases on the t asssumptions that most users like common po opularity off recommenndation rath her thhan the indiividual prefference andd the pre-pro oposed routte could sattisfy the mo ost peersons. Actuually, it com mplicated the process of compariison amongg the retriev val reesults and crreated an annnoying andd longsome experience for the userrs.

Figurre 1: prior knowledge-b k based naviggation Since thee expected points mayy not includ de the attribbute of onlly position or inntroduction. In the othher hand, a user’s querry interest is often foccused on one o paarticular paart of the points, p and it always relies r on thhe same cuustomer group w which is com mposed of a set of simiilar personss. Our researrch suggestts utilizing the t m multiple attriibutes of reesources too filter the non-preferaable points, such as the t reesources froom social neetworks, whhich can be used to desscribe and ddistinguish the t inneligible poiints more coonvenientlyy. For purpoose of relatiing the prefferable poin nts selected,, we have cclustered theem byy their multtiple attribuutes of geospatial featu ures and reeviewing vaalues. It sin nce thhe geospatiaal informatioon like posiition and co onnectivity we w could obbtain from the t G and GIS GPS S systems, meanwhile the review wing values could be ccollected fro om soocial netwoorks. Furtheermore, to recommend r d the optim mal routing,, the multip ple atttribute-baseed clusterinng mechanissms and thee clustering--based routting algorith hm w were designeed. In simullation experiment, thee proposed clustering-bbased sorting allgorithm (C CSA) has efffectually reeduced the traveler’s confusion c oon routing by coomparison of the oppportunity coost for each h cluster. The T other m major section naamely the gradient-bas g sed orderingg algorithm m (GOA) haas demonstrrated an inn ner roouting process within each clustter by balan ncing the value v of pooints and the t coorrespondinng path costt. As one of o the new routing alggorithms coonsidering the t m multiple attriibute of poiints as well as the oppo ortunity cosst for naviggation servicce, thhe combinattorial algoritthms were named n as xu u-GSA in our current rresearch. Referringg the relatedd works, thee GeoCLEF provided foor search tasks involvin ng

N Novel prefereence-orientted navigatiion system

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booth spatial and a multilinngual aspectts did not brreak away thhe restrictioon of encoding reesources. It ascribes onnly semanticc query can nnot be efficcient to graasp the trail of prreference. The T region--based K-m means clusteering algoritthms (S. Saakaida, 199 98) annd its evolving region segmentatio s on algorithm ms (Y. Chenn, 2009) didd not consid der thhe multiple attributes a off point and much less on o problem of the impaact balancin ng. Foor heuristic routing, suuch as the Nearest N Neig ghbor Algorrithm (W.K K. Tsai, 200 08) annd gradient projection method (A..v.Wangenh heimI, 20088) are all forr dealing wiith hiigher degreee of organiization in the t structurre of the sccene througgh search and a iddentificationn. Howeverr, the lackk of clusteer-based orrdering andd forwarding m mechanisms still exists. Thence, ouur current ressearch has reformed r alll the shortag ges m mentioned abbove and prroposed thee set of nov vel feasible solution appproaches for f reecommendinng the optim mal route in navigation service. The rest section of this paperr is organizzed as folllows: In Section 2, the t prroposed novvel navigatiion framewoork is preseented. In Seection 3, wee give out the t soolution approach for optimal rouuting selection. In Seection 4, thhe simulation exxperiments and result analysis arre implemented. Finallly, in Sectiion 5, a briief cooncluding reemark of this research is discussed d.

2 A novel preferenc p ce-orienteed navigattion frameworks The noveel preference-orientedd navigation n frameworkk is compoosed by thrree m modulees that are thhe Informattion Retriev main val module, Social netw works modu ule annd the Recoommendatioon modules shown in Fiigure 2.

Figure 2:: Preferencee-oriented navigation n frramework 2..1

Inform mation Retrrieval (IR) module m

The curreent IR moddule motivatted by a deesire to go beyond b keyywords whiich inncludes the semantic parser p and the locatio on based content c thatt is in actiive seervice of maaps navigatiion. 2..2

Social networks module m

As mentiioned abovee, the improovement off SNS has made m the feaatures mining from person’s individuall informatioon in the soccial-net posssible and prracticable.

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The Area-based Review is a middleware to support data structure from the current IR system (original retrieved results) and the mining results from Identity Database, such as similar persons with their result selections. It took an original role of filter and provided us a points-scores list as input data for next module 2.3

Recommendation module

2.3.1 Evaluation Switch Since the Area-based Review provided the preferable points without considering the scope, our research has proposed the similarity ratio to relate the result scope to the similarity degree between the user and similar persons. As informal contrast, the point marks in Figure 3 show the preferable results filtering via the Evaluation Switch. Obviously the deleted ones are non-preferable for user.

Figure 3: Original result without filtering 2.3.2 Geospatial Analyzer The second module Geospatial Analyzer could not only gather information of eligible points from the Evaluation Switch which is supported by the GPS, but also could receive vector data provided by the Geospatial Information System (GIS). As one sort of useful data in routing calculation, the connectivity of streets that would impact the calculating correctness might be verified by the GIS. With combination of the point scores and positions from pre-module, as well as connectivity of streets provided by external system like GIS, we could indicate that the target of Geospatial Analyzer is for clustering points by considering shortest distance and approximate values (scores) between each of two points. As a secondary practice in this paper, we have assumed that each point had connected directly with others in the simulation networks. The weighting α is defined to control the preference of point value or distance in clustering. 2.3.3 Routing Instructor The third module Routing Instructor is proposed for extending and generating a new sort of function in Maps Navigation Service. For purpose of routing recommendation to the user, it should be discussed that the acquisition from traveler’s perspective. The main expectance could be generalized as using fewer costs to obtain more valuable points of sightseeing. As mentioned above, we have obtained the attribute of the clusters number and position of cluster canters from the pre-module Geospatial Analyzer. The Routing Instructor should provide a sorting algorithm to decide the order of clusters by utilizing the attribute to recommend the optimal route that could obtain

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the most valuable points with disbursement of the least cost.

3 Solution approaches 3.1

Information Retrieval (IR) module

In this research, we have assumed that the smaller quantity of similar persons could bring about the smaller scope of preferred points. Therefore, we could control the quantity of non-preferred points by controlling the quantity of similar persons. It relies on the similarity ratio R given as follows:

R=

A∩ B A∪ B

× PB

(1)

Where A was the set of traveler’s feature and B was the set of similar person’s attributes. The intersection A ∩ B presented the number of approximate features and the union set A ∪ B gave out the combining number of both features on A and B. The PB was the proportion of matched attributes in all attributes of B. 3.2

Geospatial Analyzer

3.2.1 Attribute network clustering model Notations indices: i, j ∈ {1,2,…, n}, index of point; r {1, 2, ..., m}, index of cluster; Parameters: n: the number of points in network; m: the number of clusters; n’: the maximum number of points assigned in one cluster; hi: the centroid point in the rth cluster; P: position of point by coordinate; v: reviewing value of point; s(a, b): difference value between point a and b; l(a, b): the realistic distance between point a and b; α: preference weighting; d (i, j): degree of approximation between point i and j; Cr: the set of suffixes of all points in the rth cluster. Decision variables: ⎧1, the ith point is assigned into the rth cluster yir = ⎨ ⎩0, otherwise Degree of approximation: d (α , i, j ) = α × sij + (1 − α ) × lij

(2)

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Clustering obbject:

min F ( y ) =

1 m ∑ ∑ d ( j, hi) n i =1 j∈Ci

((3)

3..2.2 Prefereence-based K-means clustering c algorithm a Clustering algorithm: a b balance-bas sed K-mean ns Input: poiint data (n, P, P v), preeference weighting α Output: clustering result Cr, (r = 1, …, m) Begin Step 1: Calculate C diistance l (Pi, Pj), Pi, Pi ∈P. Step 2: Calculate C vaalue differeence s (vi, vj), ) vi ,vi ∈v. Step 3: Calculate C deegree of appproximation n d (α, s, l), α∈ (0,1). Step 4: Assign A ith point, p i = 1, 2, … , n, to o cluster Cr , min i d (α, s, l) > if d (α, sq, lq). q = 1, 2,..., m, annd q ≠ r

Step 5: recalculate r the m centrooids. Step 6: repeat r step 4 and 5 untiil the centro oid node no longer movve. End 3..2.3 Attribu ute network k clusteringg model

Figure 4: Illustrationn of clusterinng results by b different preference weighting α The weigghting α coontrols the impact on geographicc proximity or the vallue prroximity illuustrated in Figure 4, where w the in ndex v with the numbeer on the rig ght prresents the value v of thee point. Estim mation method to selecct α is givenn as followss:

1 n

α = 1 − α v − αd

(4) (

αd =

Δdlongest − Δdshhortest ∑ Δd

(5) (

αv =

Δvlargest − Δvsmmallest ∑ Δv

(6) (

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In our reesearch, we defined thhe weighting g α impacteed by two factors. Th hey reespectively based on the t distancee differencee α d and the value ddifference αv beetween prefferable poinnts, where α d takes meaning m of the t asymmeetry degree on geeographic distribution d and αv prresents the asymmetryy degree onn point vallue diistribution. It I is obviouus that if thee points takiing the sam me value located in a veery assymmetry scale of geography, α could c go sm mall. It meanns the impaact from vallue appproximatioon was weakken in clustering, which matched the t real situuation. 3..3

Routin ng Instructoor

It would be naturallly associateed to the TSP T problem ms when reefer to a map m rooute calculaation. Howeever, there are such differentia d t that we cann not convert w work into thhe classicall TSP probblem. It req quired us to t consider that how to baalance the traditional cost from distance as a well as the t opportuunity cost on seelecting thee value of points rathher than th hat of TSP.. Furthermoore, we haave stipulated thee centroid as a the Entraance and thee last point passed as tthe header for f eaach cluster shown s in Fiigure 5 since travelers generally g likke region-bbased routing.

Figure 5: Routingg forwardingg by estimatting and orddering the ddynamic •

Stepp 1: calculatting the verggence within the rth cluuster:

Gr =

∑ ∑ l (i, j)

(7) (

i∈Cr j ≠i ; j∈Cr

•

Stepp 2: calculatting the valuue of the rth h cluster:

Vr = •

∑v

i∈C r

i

Gr

(8) (

Stepp 3: convertting the oppportunity cost caused byy the value as well as the t verggence of cluuster into thhe path and d selecting the path takking the leaast costt as the Rouuting Enter, where lcr iss the distancce between tthe origin and a the Entrance off the rth clussterr: cos t =

Clustering-b based sortin ng algorith hm

lcr Vr

(9) (

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Nianlong N X and Keiiichi Koyana Xu agi

Begin Path; // a set store thhe selected path; Vr ; // vallue of the rtth cluster; lcq; // disttance betweeen current position and d the qth cluuster; for (r= =1, to m)

∑v = ; ∑ ∑ l (i, j) i

Vr

i∈Cr

/ value of th // he rth clusteer;

i∈Cr j ≠ i ; j∈Cr

⎧⎪ lcq ⎫⎪ ⎧l ⎫ Q = ⎨q < min ⎨ cr ⎬, r = 1,2, L m, annd r ≠ q ⎬; ⎪⎩ Vq ⎪⎭ ⎩ Vr ⎭

// select thhe entering cluster c by th he least cost; for (q =1, to m) Path ← Q; Q // put ordeering numb ber into the set s Path; End

Fiigure 6: graddient-based d inner routiing Moreoverr, it requireed us to clarrify that inn ner routing within each cluster. We W haave proposed the graadient-basedd ordering algorithm where the process was w deemonstratedd in Figure 6. The inneer path starttes at the ceentroid of clluster follow ws thhe gradient to t each otheer point witthin the clusster. When the t one takiing maximu um grradient was selected ass the forwarding object, the passedd points wass deleted fro om thhe forwardinng route annd the process was rep peated utilll the clusterr header. The T caalculation of o gradient was show wn as follo ows, wheree v is the value of the t foorwarding point p withinn the rth cluster and l is the disttance betweeen it and the t cuurrent point. maxx F (v, l ) =

v l

(10 0)

4 Experim ment and discussion d n First of all, a we connsidered othher possiblee mechanism ms for routte selection in Maps Navigaation Serviice. As the most popu M ular algorithhm for solvving the TS SP prroblem, thee Nearest Neighbor N A Algorithm was w taking some simiilar means to thhinking soluution of ourss. Thus, wee have propo osed the evvolving algoorithm nameely grradient-baseed Nearest Neighbor N allgorithm (G GNNA) as ann attempt inn experimen nt.

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Assum mption

The 50 points p of sigghtseeing loocated on th he map of the t Californnia state weere seelected and each of theem was assiigned an vaalue betweeen 0 to 5, w where point of vaalue 0 meanns un-review wed by persons beforee. The selectted points aand simulatiion off the realistiic road netw works was shhown in Fig gure 7.

Figure 7:: selected pooints and realistic road networks 4..2

Enviroonment Hardwaree: Inter Core Duo P86000 2.4GHz; RAM 2.0G GB; Software: Google Eaarth 5.1.35009.4636 (betta); MATLA AB R2008bb.

4..3

Simulaation experriments

4..3.1 Routin ng by Gradiient-based Nearest Neeighbor (GN NNA) The routing by GN NNA is the exploratio on of the maximum m ggradient-bassed N Neighbors deefined as folllows: maxx F (v, l ) =

v l′

(11 1)

Where v is the meann value of any two po oints and l ′ is the reallistic distan nce beetween the center of thhem and thee current po oint. The arrrows show wn in Figuree 8 haave indicateed the forwaarding direcction of the entire path.

F Figure 8: Enntire routing g by GNNA A

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The rightt section thaat we have inclosed on n map was like l a distinnct annotation onn the shortaage of the GNNA. G Thee enlarged segment s waas shown inn Figure 9. On O geeography, these t five points p weree located in n the samee area, how wever the tw wo arrrows enteriing have inddicated thatt circuitous route certaainly existedd, which haave giiven rise to excess or evven meaninngless path cost. c

Figure 9: 9 Enlarged segment off shortage onn GNNA 4..3.2 Routin ng by xu-GS SA We havee clustered the 50 poinnts into 7 clusters c beffore routingg by xu-GS SA shhown in Figgure 10. Thhe PID abbrreviated forr ID of poinnt and the ccorresponding poosition in Taable 1 weree given by thhe U.S. Cen nsus Bureauu. Table 1. Input daata form to Geospatial G A Analyzer

PID 8182618

Posiition X -1211.37557

Point Y Value 38.55945 52 3

Figure 10: Entire routing by xu-GS SA

Cluster Cluster ID Value 1 2.7

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Result analysis and discussion

The evaluation function for simulation experiment was given as follows, where g is the last point passed.

∑ E= ∑

g

i g i

v l

(12)

Figure 11: Estimation between GNNA and xu-GSA To think over the traveler might stop journey at any point, g could become anyone of the 50 points. The numerator presents the total value obtained and the denominator gives out the total distance till the gth point. The comparison result between the GNNA and xu-GSA in Figure 11 has indicated that the stability as well as the evaluation value of routing by xu-GSA is better than that of GNNA. Furthermore, contrasting with the routing by GNNA presented the circuitous route, the five areas-based routing by xu-GSA has prevented this excess cost as well as matched the real need of region-based selection for the traveler.

5 Conclusions In this paper, we have proposed a novel preference-oriented navigation framework by considering the social resources and multiple attribute of POIs that have improved the functional value of the Maps Navigation Service. Moreover, the effectiveness of the proposed new routing algorithm of the xu-GSA for route selection was verified by the simulation experiment. The stability as well as the real need-matched of region-based routing selection by the xu-GSA for optimal route have also been emerged via the comparison with GNNA. As a part of future research, the preference weighting α in the attribute clustering network should be provided with the self-adaptive modification through the control of fuzzy system or other intelligent machine learning methods. Additionally, it is expected for traveler that to modify the proposed xu-GSA to demonstrate a better stability of performance by preventing or reducing some

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other excess cost in journey.

Acknowledgement This work is supported by “Ambient SoC Global COE Program of Waseda University” of the Ministry of Education, Culture, Sports, Science and Technology, Japan and Toyota Motors. The authors are also deeply indebted to the U.S. Census Bureau for providing the digital road-map database

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[11] Chen, Y. et al, 2009. Coarse-to-fine moving region segmentation in compressed video. Image Analysis for Multimedia Interactive Services, International Workshop on. Los Alamitos, USA: IEEE Computer Society, pp. 45-48.

Received: December, 2009