Individualized Pedestrian Navigation Using Fuzzy ... - Semantic Scholar
2005 IEEE International Conference on Systems, Man and Cybernetics Waikoloa, Hawaii October 10-12, 2005
Individualized Pedestrian Navigation Using Fuzzy Measures and Integrals Takehisa Onisawa Graduate School of Systems and Information Engineering, University of Tsukuba, Japan [email protected]
Yuta Akasaka Onisawa Lab., Graduate School of Systems and Information Engineering, University of Tsukuba, Japan [email protected] Abstract – This paper proposes the pedestrian navigation system selecting a route based on users’ own preference for routes. The present system consists of a route selection part and a route guidance part. The route selection part selects the route with the highest subjective satisfaction degree which are estimated by a road evaluation model (REM). The REM applies fuzzy measures and integrals to calculate the subjective satisfaction degrees of a road. The route guidance part gives users instructions with linguistic expressions fitting to users’ own sensuous feeling of distance (SFD). Experimental results show that the route selected by the present system is preferable to other routes and the REM appropriately reflects users’ own preference. Keywords: route selection, linguistic expressions, subjective information, individualization.
1 Introduction Navigation systems for car drivers or pedestrians have come into wide use recently. The navigation systems usually show the shortest route from an origin to a destination. If users consider only time it takes to reach the destination, they may be satisfied with the shortest route presented by the navigation systems. The shortest route, however, does not make users satisfied in every situation. For example, in the situation of going for a stroll for recreation, users may not be satisfied with the shortest route if they would like to go through streets with beautiful roadside trees. Even if the presented route is a little longer than the shortest one, users find satisfaction in the route selected based on their own preference for routes [1]. We have already proposed the pedestrian navigation system that selects routes based on users’ own preference [2] [3]. In our previous studies, road attributes such as road pleasantness, road crowdedness, are assigned to a road, and the system selects routes that users would like to walk along in a situation, which is dependent on users’ companion, the weather and so on. For example, they would like to take a walk with their friend or they would like to walk in a
0-7803-9298-1/05/$20.00©2005 IEEE
calm spring day. In the route selection, fuzzy measures and integrals are applied to express the importance of each road attribute on the evaluation of a road and estimate the satisfaction degree of a road in a given situation, respectively. The fuzzy measures are obtained by questionnaire data of each user, so that the obtained fuzzy measures reflect users’ own preference for routes. Furthermore, the proposed system leads users to their destination along the selected route with linguistic expressions fitting their own SFD [4]. The road attributes, however, are fixed in the previous studies, and the same road attributes are used for the evaluation of a road among all users. In order to reflect users’ own preference for the route selection more than the previous system, this paper aims at not only obtaining the users’ own fuzzy measures but also choosing the road attributes based on users’ subjectivity. Chapter 2 defines fuzzy measures and integrals used for the evaluation on a road. Chapter 3 shows the system structure and also explains the route selection part including a road evaluation model(REM), and the route guidance part, which both are components of the proposed system. The REM and its construction method are described in Chapter 4. Subject experiments to confirm the validity of the present system are performed in Chapter 5. Conclusions are described in the final chapter. In this paper, a road means a line segment connecting two intersections, and a route means a path with an origin and a destination, which is composed of roads.
2
Fuzzy Measures and Integrals
2.1 Definition Let P(X) be a power set of a finite set X = {x1 , . . . , xn }, i.e., the set of all subsets in a set X. And let us consider a real function as a set function on a set X. Definition1: Fuzzy measures g on set X are defined [5] as set function g : P(X) → [0, ∞] satisfying Eqs.(1) and (2). g(∅) = 0, (1) A ⊂ B ⊂ X ⇒ g(A) ≤ g(B). (2)
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Figure 2: Evaluation model with fuzzy measures and integrals Figure 1: Choquet integral
Table 1: Example of fuzzy measure g(∅) g({x1 }) g({x2 }) g({x3 })
In this paper, fuzzy measures are considered as g : P(X) → [0, 1], g(X) = 1 for simplicity. Although various types of integrals are proposed as fuzzy integrals with respect to fuzzy measures, Choquet integrals are considered in this paper. Definition2: Choquet integrals of a measurable function f with respect to fuzzy measures g are defined by Eq.(3) [5]. ∞ (C) f (x)dg = g {x | f (x) > t} dt, (3) 0
where f is set function f : X → [0, ∞]. When function f is a simple function defined by Eq.(4), n (ακ − ακ−1 ) · χAκ (x), (4) f (x) = κ=1
(0 = α0 ≤ α1 ≤ · · · ≤ αn , X = A1 ⊃ A2 ⊃ · · · ⊃ An ) Choquet integrals of function f are obtained by Eq.(5). n (ακ − ακ−1 ) · g(Aκ ), (5) (C) f (x)dg = κ=1
where χAκ (x) denotes characteristic functions of sets Aκ (κ = 1, 2, . . . , n). Fig.1 illustrates Choquet integrals defined by Eq.(5). The horizontal axis shows the values of fuzzy measures g and the vertical axis shows the values of function f . The area of the shaded part in Fig.1 is the value of Choquet integrals.
2.2 Evaluation Model with Fuzzy Measures and Integrals Multiattribute evaluation models [6] are one of the main field that fuzzy measures and integrals are applied to. Fuzzy measures and integrals are interpreted as below when they are employed for the evaluation model of an object with some attributes. Let O be an evaluation object with n attributes included in attribute set X = {x1 , . . . , xn }. Attribute values f (xi ) (i = 1, . . . , n) are the evaluation values of object O from the viewpoint of each attribute xi (i = 1, . . . , n). Furthermore, fuzzy measures g(A) (A ⊂ X) defined on set X mean the importance of attribute sets A at the evaluation of object O. The value of Choquet integrals is considered as the total evaluation value of object O, which have attribute values f (xi ) (i = 1, . . . , n), based on fuzzy measures g expressing the importance of attributes. Fig.2 shows the evaluation model with fuzzy measures and integrals.
= = = =
0.0 0.3 0.3 0.3
g({x1 , x2 }) g({x1 , x3 }) g({x2 , x3 }) g({x1 , x2 , x3 })
= = = =
0.6 0.4 0.8 1.0
2.3 Shapley Index The Shapley index is introduced in order to estimate the importance of attribute xi ∈ X. Let A \ B be a difference set of sets A, B ⊂ X, i.e., x ∈ A \ B ⇔ x ∈ A and x B. The importance of attribute xi is not determined only by g({xi }). Considering fuzzy measures g defined on set X = {x1 , x2 , x3 } as shown in Table1, the importance of attribute x3 are not necessarily assessed at 0.3, despite g({x3 }) = 0.3. The incremental importance should be also taken into consideration. For example, the incremental importance degrees by adding {x3 } to {x1 } and {x3 } to {x1 , x2 } are 0.1 and 0.4, respectively. It is necessary to consider relation between attribute x3 and all of attribute sets D ⊂ X \ {x3 } at the estimation of the importance of attribute x3 . In this study, the Shapley index [7] is used for estimating the importance of attributes. Definition3: Let g be fuzzy measures on attribute set X = {x1 , . . . , xn }. The Shapley index ϕ(g)(xi ) for every attribute xi ∈ X with respect to g is defined by Eqs.(6) and (7) [7]. ϕ(g)(xi ) = γX (D) · [g(D ∪ {xi }) − g(D)],
(i = 1, . . . , n) (6)
D⊂X\{xi }
(|X| − |D| − 1)! · |D|! , |X|! where |X| denotes the number of elements of set X. γX (D) =
(7)
The Shapley index ϕ(g)(xi ) implies the weighted average of the importance of attribute xi since g(D ∪ {xi }) − g(D) (xi D) represents the incremental importance when {xi } is added to D. That is, the larger the Shapley index value ϕ(g)(xi ), the more attribute xi possesses the importance on the evaluation.
3
System Structure
3.1 Overview of System The present system consists of two main parts, the route selection part and the route guidance part, as shown in Fig.3. The route selection part has information on users’ own preference for routes, called preference database. The database has road attribute values, i.e., users’ subjective evaluations of each road from the viewpoints of road attributes such as road pleasantness, road quietness, and fuzzy measures expressing
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Eq.(8), among all routes from the origin to the destination.
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where the route consists of q roads, (Road point) p is Road point of the p-th road and (Road length) p is the distance of the p-th road.
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Figure 3: System structure
(a)Traveling map
(b)Interface for traveling
3.4 Route Guidance Part
(c)Picture of landmark
Figure 4: Example of user interface
the importance of each road attribute on the evaluation of a road. Given an origin, a destination and a situation in which users walk, the route selection part selects the route from the origin to the destination reflecting users’ own preference for routes. The route guidance part has information on users’ own sensuous feeling of distance, called SFD database. The database has fuzzy sets expressing users’ cognitive distance of each road and fuzzy sets expressing the meaning of linguistic terms expressing users’ cognitive distance. The route guidance part presents the route selected by the route selection part with linguistic expressions, e.g., go straight for a while. Users are given instructions repeatedly until they reach their destination.
3.2 User Interface for Traveling Users move on the map shown in Fig.4(a) with the user interface for traveling shown in Fig.4(b). Each road has landmarks or views as shown by dots in Fig.4(a), and the photo of a landmark or a view is presented to users when they move there. Fig.4(c) shows an example of the landmark photo when users move in front of CAFE shown in Fig.4(b). Users feel impressions of the road by the photos.
The route guidance part gives users the instructions of the route selected by the route selection part. The instructions are expressed in the form of (the distance to the intersection users turn next, the direction users go to after passing the intersection), e.g., go straight for a while and turn to the right. The given instructions reflect users’ own SFD. Information on users’ SFD is expressed by two kinds of fuzzy sets which are preserved in the SFD database. One is the fuzzy set expressing users’ cognitive distance of each road and the other is the one that expresses the meaning of linguistic terms expressing users’ cognitive distance. These fuzzy sets are obtained by the Sketch Map method [8] mentioned in 5.3. In order to express the route with linguistic expressions that reflect users’ own SFD, the route guidance part calculates the fitness value of two fuzzy sets defined by Eq.(9). 1 [sup{μA˜ (x) ∧ μB˜ (x)} + inf{μA˜ (x) ∨ μB˜ (x)}], (9) 2 where μA˜ (x) and μB˜ (x) are membership functions of fuzzy ˜ respectively, B˜ denotes the complement of sets A˜ and B, ˜ fuzzy set B, ∧ and ∨ stand for the minimum and the maximum operations, respectively, and sup and inf are the supremum and the infimum operations, respectively. In this study fuzzy set A˜ expresses users’ own cognitive distance of each road and fuzzy set B˜ expresses the meaning of linguistic terms expressing users’ cognitive distance. The route guidance part calculates the fitness value and gives linguistic terms expressing the distance to the next intersection and the direction of which fitness value is the largest. This procedure is repeated every time users turn each intersection until users reach the destination. If users are out of the selected route, this part gives users the instruction to go back and shows the route from the losing point to the destination with linguistic expressions. fitness =
4
Road Evaluation Model (REM)
4.1 Overview of REM
3.3 Route Selection Part Given an origin, a destination and a situation in which users move on a map, the route selection part selects the route out of many ones from the origin to the destination based on users’ own preference for route selection. The route selection part consists of the REM and the preference database. The REM calculates Road point, which users’ own satisfaction degree of a road, by using fuzzy measures and integrals. The route selection part selects the route with the highest Route point, i.e., the satisfaction degree of a route defined by
Given the situation in which users have a walk, the REM estimates the satisfaction degree of a road, i.e., Road point. The REM makes use of the evaluation model with fuzzy measures and integrals described in 2.2 for the evaluation on the satisfaction degree of a road. The evaluation model with fuzzy measures and integrals is applied as follows. • object O : a road • attribute xi : a word expressing the attribute of the road (road attribute)
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• attribute value f (xi ) : the evaluation value of the road from the viewpoint of road attribute xi (road attribute value) • fuzzy measures g : the importance degrees of each attribute set on the evaluation of the satisfaction degree of the road • Choquet integral (C) f (x)dg : the satisfaction degree of the road (Road point)
Table 2: Example of constructing REM temp
X1 = X init x1 , 0.08 x2 , 0.30 x3 , 0.13 x4 , 0.23 x5 , 0.26 0.2 0.085
xi , ϕ(g)(xi ) temp
1 / |Xm | identifying error
Let X = {x1 , . . . , xn } indicate the road attribute set of a road, and g be fuzzy measures defined on set X. Given the situation, the REM obtains Choquet integrals with road attribute values f (xi ) and fuzzy measures g preserved in the preference database. The REM assesses the result of Choquet integrals at Road point, i.e., the satisfaction degree of the present road.
temp
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X3
x2 , 0.26 x4 , 0.26 x5 , 0.48 0.3 0.083
x5 , 1.00 1.0 0.11
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4.2 Construction Method of REM
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The REM is composed of road attribute set X and fuzzy measures g on set X. The individual road attribute sets and the individual fuzzy measures are obtained as follows so that users’ own preference is reflected directly in the REM. Let X init = {x1init , . . . , xinit N } denote the initial road attribute set, and temp Xm (m = 1, 2, . . . ) indicate the subset of set X init satisfying temp temp temp X1 = X init and Xm ⊇ Xm+1 . step1: Identifying fuzzy measures of N road attributes in set temp Xm (m = 1), i.e., set X init . step2: Choosing the road attribute(s) with large Shapley intemp dex values from set Xm , and eliminating not chosen road attribute(s). Adding 1 to m. temp step3: Composing set Xm of the road attribute(s) chosen in step2. step4: Identifying fuzzy measures of the road attribute(s) in temp set Xm . temp step5: Repeating step2, step3 and step4 until set Xm becomes an empty set. temp step6: Determining that set Xm making the identifying ertemp ror smallest among all sets Xm (m = 1, 2, . . . , m) is final final final set X = {x1 , . . . , xn } (⊆ X init ), i.e., the individual road attribute set. step7: Constructing the REM with individual road attribute set X final and individual fuzzy measures g defined on set X final . Fuzzy measures are identified in step1 and step4 by HLMS (Heuristic Least Mean Squares) [9]. The HLMS obtains fuzzy measures so that the mean square error between the satisfaction degrees of roads obtained by Eq.(5) and those evaluated by users themselves on questionnaire is minimized. The road attributes with the Shapley index values satisfying Eq.(10) are chosen in step2. 1 temp ϕ(g)(xi ) > temp (i = 1, . . . , |Xm |), (10) |Xm | temp temp where |Xm | is the number of elements of set Xm . If all road attributes xi (i = 1, . . . , |X|) in a set X have the equivalent importance degrees on the evaluation of a road, all the
Figure 5: Prepared map in experiments Shapley index values ϕ(g)(xi ) (i = 1, . . . , |X|) are obtained by Eq.(11), ϕ(g)(xi ) =
g(X) 1 = |X| |X|
(i = 1, . . . , |X|),
(11)
since the Shapley index has a property Eq.(12) [7]. |X|
ϕ(g)(xi ) = g(X) = 1.
(12)
i=1
In this study, the road attribute xi with the Shapley index values satisfying Eq.(10) is regarded as important on the evaluation of a road and chosen in step2. Table2 shows the example of constructing the REM by the proposed method. temp Set X2 with the smallest identifying error among all sets temp Xm (m = 1, 2, 3) is considered to be users’ own road attribute set X final .
5
Experiments
The experiments are performed in order to confirm the validity of the present system. There are 11 subjects and three situations S j ( j = 1, 2, 3). S1 : They would like to take a walk alone, S2 : They would like to take a walk with their parents, S3 : They would like to pass the time until an appointment. Subjects’ own REMs, preference databases and SFD databases are constructed. The subjects walk along the routes selected by their own REMs according to instructions given by the route guidance part, and evaluate the satisfaction degrees of the selected routes. Fig.5 shows the traveling map prepared for the experiments.
5.1 Construction of REM The subjects’ own REMs are obtained in situations S j ( j = 1, 2, 3) by the method described in 4.2. Thirty roads with some landmarks or views are prepared in order to obtain
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the REMs. These roads are not included in the traveling map as shown in Fig.5. After the subjects walk along each road, they evaluate the satisfaction degrees of the roads in each situation with a 5-point scale, 1 : dissatisfied, 2 : a little dissatisfied, 3 : neutral, 4 : a little satisfied, 5 : satis fied. Let zkj ( j = 1, 2, 3; k = 1, . . . , 30) be the satisfaction degree of the k -th road in situation S j . They also evaluate the road from the viewpoints of 8 road attributes, x1init : lively, x2init : sophisticated, x3init : solitary, x4init : fancy, x5init : crowded, x6init : calm, x7init : pleasant, x8init : refreshing with a 5-point scale, 1 : they don’t think so at all, 2 : they don’t think so very much, 3 : neutral, 4 : they think so a little, 5 : they think so. Let X init = {x1init , . . . , x8init } denote the ini tial road attribute set. Let f1k , . . . , and f8k (k = 1, . . . , 30) be the road attribute values of the k -th road. The individual REMs in situations S j ( j = 1, 2, 3), which are composed of individual road attribute set X final ⊆ X init and individual fuzzy measures g defined on set X final , are obtained with the set of 30 data ( f1k , . . . , f8k , zkj ; j = 1, 2, 3, k = 1, . . . , 30) under the following quantifications of questionnaire results; 1 → 0.0, 2 → 0.25, 3 → 0.5, 4 → 0.75, 5 → 1.0.
5.2
Construction of Preference Database
The subjects walk along 84 roads which are included in the traveling map as shown in Fig5, and evaluate each road from the viewpoints of x1init , . . . , and x8init . Let f1k , . . . , and f8k (k = 1, . . . , 84) be the road attribute values of the k-th road with respect to road attributes x1init , . . . , and x8init , respectively. Fuzzy measures g in situation S j ( j = 1, 2, 3) obtained in 5.1 and road attributes values f1k , . . . and f8k (k = 1, . . . , 84) of the roads shown in Fig.5 are preserved in subjects’ own preference databases.
5.3
Construction of SFD Database
The Sketch Map method [8], which is used in the field of spatial cognition research, is applied to the acquisition of subjects’ own quantitative sensuous feeling of distance. In this method, the subjects move along given routes and keeps them in mind. And then the subjects sketch surroundings, landmarks and so on from memory. In this study, only the user interface as shown in Fig.4(b) is presented to the subjects while they walk along routes on a map. Therefore, the subjects perceive only the part of surroundings while walking. They should memorize the relative position between an origin and a destination, and the distance between them. After walking along routes on a map, the subjects draw the route on a computer display according to their SFD from memory. A drawing example of the route from START to GOAL shown in Fig.6(a) is illustrated in Fig.6(b). After drawing the route, the subjects express their own SFD of each road with linguistic expressions such as the distance of walking briefly, the distance of walking a little, the distance of walking for a while, the distance of walking by far, and the distance of walking for quite a long time. Using differences between the drawn route and the route that the subjects move on, two kinds of fuzzy sets are obtained.
(b)Drawn route (a)Route for moving
Figure 6: Example of drawing route in Sketch Map method
5.4 Evaluation 5.4.1
Satisfaction Degree of Route
The subjects walk along the routes selected by the present system in each situation, whose origins and destinations are all the same as shown in Fig.5. They also evaluate the satisfaction degrees of the routes in the presented situation from the viewpoint of only impressions effected by the photo of landmarks or views along the routes. Three mid kinds of routes Rmax and Rmin are considered in situaj j , Rj tion S j ( j = 1, 2, 3), which indicate the routes with the highest, middle and the lowest Route point among all routes, respectively. After walking along one route, the subjects evaluate the satisfaction degree of the route with a 5-point scale. The subjects walk along 9 routes in total and evaluate the satisfaction degrees of each route. 5.4.2
Validitity of REM
Experimental data are analyzed in order to confirm that the REMs appropriately reflect each subject’s own preference in road attributes. Two descriptions I j and NI j showing impressions of a route are prepared in situation S j ( j = 1, 2, 3). The descriptions are composed of two road attributes in initial road attribute set X init , for example, a pleasant and lively route. The description I j has the road attributes with the largest and the second largest Shapley index values in individual road attribute set X final of the REM, and the description NI j has the road attributes with the smallest and the ¯ where X¯ desecond smallest Shapley index values in set X, notes X init \X final . Two descriptions I j and NI j are presented to the subjects in random order, and the subjects choose the preferable one in situation S j . There are 33 trials in a total since 11 subjects reply to questionnaire in 3 situations. If only one road attribute is employed for the REM, the road attributes with only the largest and the smallest Shapley index values are considered in I j and NI j , respectively.
5.5 Experimental Results and Remarks Fig.7 shows the average of the satisfaction degrees of mid Rmax and Rmin among all subjects in all situations. The j j , Rj vertical axis indicates the average of the satisfaction degrees. The average value of the satisfaction degrees of Rmax is j mid min larger than that of R j and R j with a significant difference (p < .05). Fig.8 shows Rmax presented to subject 2 in each situation. j Fig.9 shows Rmax presented to each subject in situation S2 . j It is found that although the origin and the destination are
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tributes. The REM can be applied to a retrieval system with a subjective evaluation such as restaurants, movies and so on. The subjective evaluation models should adapt to each user because the evaluation result changes based on individual users’ subjectivity. The REM is considered to be suitable for the retrieval system with subjective evaluation because of its individualization function. There are some problems to be solved in a future. The present system acquires subjective information, i.e., fuzzy measures, road attributes and fuzzy sets by off-line using questionnaire data and the Sketch Map method, respectively. The road attribute values are also obtained with questionnaire after walking each road in a traveling map. The road attribute values, however, should be aquired before a user walks along each road in the traveling map. It is necessary to aquire the road attributes values by on-line using some learning method.
Figure 7: Satisfaction degrees of routes
(a)Situation S1
(b)Situation S2
(c)Situation S3
Figure 8: Rmax of subject 2 in each situation j both the same, various routes are presented to the subjects according to the subjects and the situations. The subjects reply that I j is preferable to NI j at the rate of 91% of all trials. These results show that individual road attribute set X final of the REM reflects subjects’ own preference in road attributes well. The subjects turn accurately the instructed intersections at the rate of 79% of all intersections in all the selected routes. These results show that the present system provides the subjects with useful guidance by linguistic expressions fitting their own SFD.
6
Conclusions
This paper describes the pedestrian navigation system that selects routes based on users’ own preference for routes. The system has the route selection part and the route guidance part. The route selection part consists of the REM and the preference database. The REM applies fuzzy measures and integrals to estimate the satisfaction degree of a road, and is constructed based on users’ own preference for route selection. The route guidance part has the SFD database, and fuzzy sets are applied to generate instructions with linguistic expressions reflecting users’ own SFD. The experimental results show that various routes are selected according to the subjects and the situations and that satisfaction degrees of the routes selected by the present system are higher than those of other routes. The analysis results of experimental data show that the REMs reflect subjects’ own preference in road at-
References [1] S. Rogers, C. N. Fiechter and P. Langley: “An Adaptive Interactive Agent for Route Advice”, Proc. of Int’l Conf. on Autonomous Agent, pp. 198–205, (1999). [2] Y. Akasaka and T. Onisawa: “Pedestrian Navigation System Reflecting Users’ Subjectivity and Taste”, Proc. of Int’l Conf. on Control, Automation and Systems, pp. 995–1000, (2003). [3] Y. Akasaka and T. Onisawa: “Construction of Pedestrian Navigation System and Its Evaluation”, Proc. of IEEE Int’l Conf. on Fuzzy Systems, #1392, (2004). [4] T. Onisawa and S. Sakakibara: “Study on Cognitive Map and Its Linguistic Expressions”, Proc. of Fuzzy System Symposium, pp. 109–112, (2001). (in Japanese) [5] Japan Society for Fuzzy Theory and Systems Ed.: “Lecture Fuzzy 3, Fuzzy Measures”, Nikkan-KogyoShinbun-Sha, (1993). [6] M. Grabisch and M. Roubens: “Application of the Choquet Integral in Multicriteria Decision Making”, Fuzzy Measures and Integrals, M. Grabisch, T. Murofushi and M. Sugeno, eds., Physica-Verlag, pp. 348–374, (2000). [7] L. S. Shapley: “A Value for n-person Games”, Contributions to the Theory of Games, H. W. Kuhn, and A. W. Tucker, eds., Princeton University, pp. 307–317, (1953). [8] N. Foreman and R. Gillett: “Handbook of Spatial Research Paradigms and Methodologies”, Taylor & Francis, (1997).
(a)Subject 3
(b)Subject 5
(c)Subject 9
(d)Subject 10
Figure 9: Rmax of each subject in situation S2 j
[9] M. Grabisch: “A New Algorithm for Identifying Fuzzy Measures and Its Application to Pattern Recognition”, Proc. of IEEE Int’l Conf. on Fuzzy Systems, pp. 145– 150, (1995).
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Individualized Pedestrian Navigation Using Fuzzy Measures and Integrals Takehisa Onisawa Graduate School of Systems and Information Engineering, University of Tsukuba, Japan [email protected]
Yuta Akasaka Onisawa Lab., Graduate School of Systems and Information Engineering, University of Tsukuba, Japan [email protected] Abstract – This paper proposes the pedestrian navigation system selecting a route based on users’ own preference for routes. The present system consists of a route selection part and a route guidance part. The route selection part selects the route with the highest subjective satisfaction degree which are estimated by a road evaluation model (REM). The REM applies fuzzy measures and integrals to calculate the subjective satisfaction degrees of a road. The route guidance part gives users instructions with linguistic expressions fitting to users’ own sensuous feeling of distance (SFD). Experimental results show that the route selected by the present system is preferable to other routes and the REM appropriately reflects users’ own preference. Keywords: route selection, linguistic expressions, subjective information, individualization.
1 Introduction Navigation systems for car drivers or pedestrians have come into wide use recently. The navigation systems usually show the shortest route from an origin to a destination. If users consider only time it takes to reach the destination, they may be satisfied with the shortest route presented by the navigation systems. The shortest route, however, does not make users satisfied in every situation. For example, in the situation of going for a stroll for recreation, users may not be satisfied with the shortest route if they would like to go through streets with beautiful roadside trees. Even if the presented route is a little longer than the shortest one, users find satisfaction in the route selected based on their own preference for routes [1]. We have already proposed the pedestrian navigation system that selects routes based on users’ own preference [2] [3]. In our previous studies, road attributes such as road pleasantness, road crowdedness, are assigned to a road, and the system selects routes that users would like to walk along in a situation, which is dependent on users’ companion, the weather and so on. For example, they would like to take a walk with their friend or they would like to walk in a
0-7803-9298-1/05/$20.00©2005 IEEE
calm spring day. In the route selection, fuzzy measures and integrals are applied to express the importance of each road attribute on the evaluation of a road and estimate the satisfaction degree of a road in a given situation, respectively. The fuzzy measures are obtained by questionnaire data of each user, so that the obtained fuzzy measures reflect users’ own preference for routes. Furthermore, the proposed system leads users to their destination along the selected route with linguistic expressions fitting their own SFD [4]. The road attributes, however, are fixed in the previous studies, and the same road attributes are used for the evaluation of a road among all users. In order to reflect users’ own preference for the route selection more than the previous system, this paper aims at not only obtaining the users’ own fuzzy measures but also choosing the road attributes based on users’ subjectivity. Chapter 2 defines fuzzy measures and integrals used for the evaluation on a road. Chapter 3 shows the system structure and also explains the route selection part including a road evaluation model(REM), and the route guidance part, which both are components of the proposed system. The REM and its construction method are described in Chapter 4. Subject experiments to confirm the validity of the present system are performed in Chapter 5. Conclusions are described in the final chapter. In this paper, a road means a line segment connecting two intersections, and a route means a path with an origin and a destination, which is composed of roads.
2
Fuzzy Measures and Integrals
2.1 Definition Let P(X) be a power set of a finite set X = {x1 , . . . , xn }, i.e., the set of all subsets in a set X. And let us consider a real function as a set function on a set X. Definition1: Fuzzy measures g on set X are defined [5] as set function g : P(X) → [0, ∞] satisfying Eqs.(1) and (2). g(∅) = 0, (1) A ⊂ B ⊂ X ⇒ g(A) ≤ g(B). (2)
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Figure 2: Evaluation model with fuzzy measures and integrals Figure 1: Choquet integral
Table 1: Example of fuzzy measure g(∅) g({x1 }) g({x2 }) g({x3 })
In this paper, fuzzy measures are considered as g : P(X) → [0, 1], g(X) = 1 for simplicity. Although various types of integrals are proposed as fuzzy integrals with respect to fuzzy measures, Choquet integrals are considered in this paper. Definition2: Choquet integrals of a measurable function f with respect to fuzzy measures g are defined by Eq.(3) [5]. ∞ (C) f (x)dg = g {x | f (x) > t} dt, (3) 0
where f is set function f : X → [0, ∞]. When function f is a simple function defined by Eq.(4), n (ακ − ακ−1 ) · χAκ (x), (4) f (x) = κ=1
(0 = α0 ≤ α1 ≤ · · · ≤ αn , X = A1 ⊃ A2 ⊃ · · · ⊃ An ) Choquet integrals of function f are obtained by Eq.(5). n (ακ − ακ−1 ) · g(Aκ ), (5) (C) f (x)dg = κ=1
where χAκ (x) denotes characteristic functions of sets Aκ (κ = 1, 2, . . . , n). Fig.1 illustrates Choquet integrals defined by Eq.(5). The horizontal axis shows the values of fuzzy measures g and the vertical axis shows the values of function f . The area of the shaded part in Fig.1 is the value of Choquet integrals.
2.2 Evaluation Model with Fuzzy Measures and Integrals Multiattribute evaluation models [6] are one of the main field that fuzzy measures and integrals are applied to. Fuzzy measures and integrals are interpreted as below when they are employed for the evaluation model of an object with some attributes. Let O be an evaluation object with n attributes included in attribute set X = {x1 , . . . , xn }. Attribute values f (xi ) (i = 1, . . . , n) are the evaluation values of object O from the viewpoint of each attribute xi (i = 1, . . . , n). Furthermore, fuzzy measures g(A) (A ⊂ X) defined on set X mean the importance of attribute sets A at the evaluation of object O. The value of Choquet integrals is considered as the total evaluation value of object O, which have attribute values f (xi ) (i = 1, . . . , n), based on fuzzy measures g expressing the importance of attributes. Fig.2 shows the evaluation model with fuzzy measures and integrals.
= = = =
0.0 0.3 0.3 0.3
g({x1 , x2 }) g({x1 , x3 }) g({x2 , x3 }) g({x1 , x2 , x3 })
= = = =
0.6 0.4 0.8 1.0
2.3 Shapley Index The Shapley index is introduced in order to estimate the importance of attribute xi ∈ X. Let A \ B be a difference set of sets A, B ⊂ X, i.e., x ∈ A \ B ⇔ x ∈ A and x B. The importance of attribute xi is not determined only by g({xi }). Considering fuzzy measures g defined on set X = {x1 , x2 , x3 } as shown in Table1, the importance of attribute x3 are not necessarily assessed at 0.3, despite g({x3 }) = 0.3. The incremental importance should be also taken into consideration. For example, the incremental importance degrees by adding {x3 } to {x1 } and {x3 } to {x1 , x2 } are 0.1 and 0.4, respectively. It is necessary to consider relation between attribute x3 and all of attribute sets D ⊂ X \ {x3 } at the estimation of the importance of attribute x3 . In this study, the Shapley index [7] is used for estimating the importance of attributes. Definition3: Let g be fuzzy measures on attribute set X = {x1 , . . . , xn }. The Shapley index ϕ(g)(xi ) for every attribute xi ∈ X with respect to g is defined by Eqs.(6) and (7) [7]. ϕ(g)(xi ) = γX (D) · [g(D ∪ {xi }) − g(D)],
(i = 1, . . . , n) (6)
D⊂X\{xi }
(|X| − |D| − 1)! · |D|! , |X|! where |X| denotes the number of elements of set X. γX (D) =
(7)
The Shapley index ϕ(g)(xi ) implies the weighted average of the importance of attribute xi since g(D ∪ {xi }) − g(D) (xi D) represents the incremental importance when {xi } is added to D. That is, the larger the Shapley index value ϕ(g)(xi ), the more attribute xi possesses the importance on the evaluation.
3
System Structure
3.1 Overview of System The present system consists of two main parts, the route selection part and the route guidance part, as shown in Fig.3. The route selection part has information on users’ own preference for routes, called preference database. The database has road attribute values, i.e., users’ subjective evaluations of each road from the viewpoints of road attributes such as road pleasantness, road quietness, and fuzzy measures expressing
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Eq.(8), among all routes from the origin to the destination.
&
/
Route point =
!
#
0
&
"
"
#
(
+
,
q (Road point) p , (Road length) p p=1
(8)
!
-
where the route consists of q roads, (Road point) p is Road point of the p-th road and (Road length) p is the distance of the p-th road.
"
"
#
+
,
$
"
"
#
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-
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Figure 3: System structure
(a)Traveling map
(b)Interface for traveling
3.4 Route Guidance Part
(c)Picture of landmark
Figure 4: Example of user interface
the importance of each road attribute on the evaluation of a road. Given an origin, a destination and a situation in which users walk, the route selection part selects the route from the origin to the destination reflecting users’ own preference for routes. The route guidance part has information on users’ own sensuous feeling of distance, called SFD database. The database has fuzzy sets expressing users’ cognitive distance of each road and fuzzy sets expressing the meaning of linguistic terms expressing users’ cognitive distance. The route guidance part presents the route selected by the route selection part with linguistic expressions, e.g., go straight for a while. Users are given instructions repeatedly until they reach their destination.
3.2 User Interface for Traveling Users move on the map shown in Fig.4(a) with the user interface for traveling shown in Fig.4(b). Each road has landmarks or views as shown by dots in Fig.4(a), and the photo of a landmark or a view is presented to users when they move there. Fig.4(c) shows an example of the landmark photo when users move in front of CAFE shown in Fig.4(b). Users feel impressions of the road by the photos.
The route guidance part gives users the instructions of the route selected by the route selection part. The instructions are expressed in the form of (the distance to the intersection users turn next, the direction users go to after passing the intersection), e.g., go straight for a while and turn to the right. The given instructions reflect users’ own SFD. Information on users’ SFD is expressed by two kinds of fuzzy sets which are preserved in the SFD database. One is the fuzzy set expressing users’ cognitive distance of each road and the other is the one that expresses the meaning of linguistic terms expressing users’ cognitive distance. These fuzzy sets are obtained by the Sketch Map method [8] mentioned in 5.3. In order to express the route with linguistic expressions that reflect users’ own SFD, the route guidance part calculates the fitness value of two fuzzy sets defined by Eq.(9). 1 [sup{μA˜ (x) ∧ μB˜ (x)} + inf{μA˜ (x) ∨ μB˜ (x)}], (9) 2 where μA˜ (x) and μB˜ (x) are membership functions of fuzzy ˜ respectively, B˜ denotes the complement of sets A˜ and B, ˜ fuzzy set B, ∧ and ∨ stand for the minimum and the maximum operations, respectively, and sup and inf are the supremum and the infimum operations, respectively. In this study fuzzy set A˜ expresses users’ own cognitive distance of each road and fuzzy set B˜ expresses the meaning of linguistic terms expressing users’ cognitive distance. The route guidance part calculates the fitness value and gives linguistic terms expressing the distance to the next intersection and the direction of which fitness value is the largest. This procedure is repeated every time users turn each intersection until users reach the destination. If users are out of the selected route, this part gives users the instruction to go back and shows the route from the losing point to the destination with linguistic expressions. fitness =
4
Road Evaluation Model (REM)
4.1 Overview of REM
3.3 Route Selection Part Given an origin, a destination and a situation in which users move on a map, the route selection part selects the route out of many ones from the origin to the destination based on users’ own preference for route selection. The route selection part consists of the REM and the preference database. The REM calculates Road point, which users’ own satisfaction degree of a road, by using fuzzy measures and integrals. The route selection part selects the route with the highest Route point, i.e., the satisfaction degree of a route defined by
Given the situation in which users have a walk, the REM estimates the satisfaction degree of a road, i.e., Road point. The REM makes use of the evaluation model with fuzzy measures and integrals described in 2.2 for the evaluation on the satisfaction degree of a road. The evaluation model with fuzzy measures and integrals is applied as follows. • object O : a road • attribute xi : a word expressing the attribute of the road (road attribute)
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• attribute value f (xi ) : the evaluation value of the road from the viewpoint of road attribute xi (road attribute value) • fuzzy measures g : the importance degrees of each attribute set on the evaluation of the satisfaction degree of the road • Choquet integral (C) f (x)dg : the satisfaction degree of the road (Road point)
Table 2: Example of constructing REM temp
X1 = X init x1 , 0.08 x2 , 0.30 x3 , 0.13 x4 , 0.23 x5 , 0.26 0.2 0.085
xi , ϕ(g)(xi ) temp
1 / |Xm | identifying error
Let X = {x1 , . . . , xn } indicate the road attribute set of a road, and g be fuzzy measures defined on set X. Given the situation, the REM obtains Choquet integrals with road attribute values f (xi ) and fuzzy measures g preserved in the preference database. The REM assesses the result of Choquet integrals at Road point, i.e., the satisfaction degree of the present road.
temp
temp
= X final
X2
X3
x2 , 0.26 x4 , 0.26 x5 , 0.48 0.3 0.083
x5 , 1.00 1.0 0.11
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4.2 Construction Method of REM
,
The REM is composed of road attribute set X and fuzzy measures g on set X. The individual road attribute sets and the individual fuzzy measures are obtained as follows so that users’ own preference is reflected directly in the REM. Let X init = {x1init , . . . , xinit N } denote the initial road attribute set, and temp Xm (m = 1, 2, . . . ) indicate the subset of set X init satisfying temp temp temp X1 = X init and Xm ⊇ Xm+1 . step1: Identifying fuzzy measures of N road attributes in set temp Xm (m = 1), i.e., set X init . step2: Choosing the road attribute(s) with large Shapley intemp dex values from set Xm , and eliminating not chosen road attribute(s). Adding 1 to m. temp step3: Composing set Xm of the road attribute(s) chosen in step2. step4: Identifying fuzzy measures of the road attribute(s) in temp set Xm . temp step5: Repeating step2, step3 and step4 until set Xm becomes an empty set. temp step6: Determining that set Xm making the identifying ertemp ror smallest among all sets Xm (m = 1, 2, . . . , m) is final final final set X = {x1 , . . . , xn } (⊆ X init ), i.e., the individual road attribute set. step7: Constructing the REM with individual road attribute set X final and individual fuzzy measures g defined on set X final . Fuzzy measures are identified in step1 and step4 by HLMS (Heuristic Least Mean Squares) [9]. The HLMS obtains fuzzy measures so that the mean square error between the satisfaction degrees of roads obtained by Eq.(5) and those evaluated by users themselves on questionnaire is minimized. The road attributes with the Shapley index values satisfying Eq.(10) are chosen in step2. 1 temp ϕ(g)(xi ) > temp (i = 1, . . . , |Xm |), (10) |Xm | temp temp where |Xm | is the number of elements of set Xm . If all road attributes xi (i = 1, . . . , |X|) in a set X have the equivalent importance degrees on the evaluation of a road, all the
Figure 5: Prepared map in experiments Shapley index values ϕ(g)(xi ) (i = 1, . . . , |X|) are obtained by Eq.(11), ϕ(g)(xi ) =
g(X) 1 = |X| |X|
(i = 1, . . . , |X|),
(11)
since the Shapley index has a property Eq.(12) [7]. |X|
ϕ(g)(xi ) = g(X) = 1.
(12)
i=1
In this study, the road attribute xi with the Shapley index values satisfying Eq.(10) is regarded as important on the evaluation of a road and chosen in step2. Table2 shows the example of constructing the REM by the proposed method. temp Set X2 with the smallest identifying error among all sets temp Xm (m = 1, 2, 3) is considered to be users’ own road attribute set X final .
5
Experiments
The experiments are performed in order to confirm the validity of the present system. There are 11 subjects and three situations S j ( j = 1, 2, 3). S1 : They would like to take a walk alone, S2 : They would like to take a walk with their parents, S3 : They would like to pass the time until an appointment. Subjects’ own REMs, preference databases and SFD databases are constructed. The subjects walk along the routes selected by their own REMs according to instructions given by the route guidance part, and evaluate the satisfaction degrees of the selected routes. Fig.5 shows the traveling map prepared for the experiments.
5.1 Construction of REM The subjects’ own REMs are obtained in situations S j ( j = 1, 2, 3) by the method described in 4.2. Thirty roads with some landmarks or views are prepared in order to obtain
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the REMs. These roads are not included in the traveling map as shown in Fig.5. After the subjects walk along each road, they evaluate the satisfaction degrees of the roads in each situation with a 5-point scale, 1 : dissatisfied, 2 : a little dissatisfied, 3 : neutral, 4 : a little satisfied, 5 : satis fied. Let zkj ( j = 1, 2, 3; k = 1, . . . , 30) be the satisfaction degree of the k -th road in situation S j . They also evaluate the road from the viewpoints of 8 road attributes, x1init : lively, x2init : sophisticated, x3init : solitary, x4init : fancy, x5init : crowded, x6init : calm, x7init : pleasant, x8init : refreshing with a 5-point scale, 1 : they don’t think so at all, 2 : they don’t think so very much, 3 : neutral, 4 : they think so a little, 5 : they think so. Let X init = {x1init , . . . , x8init } denote the ini tial road attribute set. Let f1k , . . . , and f8k (k = 1, . . . , 30) be the road attribute values of the k -th road. The individual REMs in situations S j ( j = 1, 2, 3), which are composed of individual road attribute set X final ⊆ X init and individual fuzzy measures g defined on set X final , are obtained with the set of 30 data ( f1k , . . . , f8k , zkj ; j = 1, 2, 3, k = 1, . . . , 30) under the following quantifications of questionnaire results; 1 → 0.0, 2 → 0.25, 3 → 0.5, 4 → 0.75, 5 → 1.0.
5.2
Construction of Preference Database
The subjects walk along 84 roads which are included in the traveling map as shown in Fig5, and evaluate each road from the viewpoints of x1init , . . . , and x8init . Let f1k , . . . , and f8k (k = 1, . . . , 84) be the road attribute values of the k-th road with respect to road attributes x1init , . . . , and x8init , respectively. Fuzzy measures g in situation S j ( j = 1, 2, 3) obtained in 5.1 and road attributes values f1k , . . . and f8k (k = 1, . . . , 84) of the roads shown in Fig.5 are preserved in subjects’ own preference databases.
5.3
Construction of SFD Database
The Sketch Map method [8], which is used in the field of spatial cognition research, is applied to the acquisition of subjects’ own quantitative sensuous feeling of distance. In this method, the subjects move along given routes and keeps them in mind. And then the subjects sketch surroundings, landmarks and so on from memory. In this study, only the user interface as shown in Fig.4(b) is presented to the subjects while they walk along routes on a map. Therefore, the subjects perceive only the part of surroundings while walking. They should memorize the relative position between an origin and a destination, and the distance between them. After walking along routes on a map, the subjects draw the route on a computer display according to their SFD from memory. A drawing example of the route from START to GOAL shown in Fig.6(a) is illustrated in Fig.6(b). After drawing the route, the subjects express their own SFD of each road with linguistic expressions such as the distance of walking briefly, the distance of walking a little, the distance of walking for a while, the distance of walking by far, and the distance of walking for quite a long time. Using differences between the drawn route and the route that the subjects move on, two kinds of fuzzy sets are obtained.
(b)Drawn route (a)Route for moving
Figure 6: Example of drawing route in Sketch Map method
5.4 Evaluation 5.4.1
Satisfaction Degree of Route
The subjects walk along the routes selected by the present system in each situation, whose origins and destinations are all the same as shown in Fig.5. They also evaluate the satisfaction degrees of the routes in the presented situation from the viewpoint of only impressions effected by the photo of landmarks or views along the routes. Three mid kinds of routes Rmax and Rmin are considered in situaj j , Rj tion S j ( j = 1, 2, 3), which indicate the routes with the highest, middle and the lowest Route point among all routes, respectively. After walking along one route, the subjects evaluate the satisfaction degree of the route with a 5-point scale. The subjects walk along 9 routes in total and evaluate the satisfaction degrees of each route. 5.4.2
Validitity of REM
Experimental data are analyzed in order to confirm that the REMs appropriately reflect each subject’s own preference in road attributes. Two descriptions I j and NI j showing impressions of a route are prepared in situation S j ( j = 1, 2, 3). The descriptions are composed of two road attributes in initial road attribute set X init , for example, a pleasant and lively route. The description I j has the road attributes with the largest and the second largest Shapley index values in individual road attribute set X final of the REM, and the description NI j has the road attributes with the smallest and the ¯ where X¯ desecond smallest Shapley index values in set X, notes X init \X final . Two descriptions I j and NI j are presented to the subjects in random order, and the subjects choose the preferable one in situation S j . There are 33 trials in a total since 11 subjects reply to questionnaire in 3 situations. If only one road attribute is employed for the REM, the road attributes with only the largest and the smallest Shapley index values are considered in I j and NI j , respectively.
5.5 Experimental Results and Remarks Fig.7 shows the average of the satisfaction degrees of mid Rmax and Rmin among all subjects in all situations. The j j , Rj vertical axis indicates the average of the satisfaction degrees. The average value of the satisfaction degrees of Rmax is j mid min larger than that of R j and R j with a significant difference (p < .05). Fig.8 shows Rmax presented to subject 2 in each situation. j Fig.9 shows Rmax presented to each subject in situation S2 . j It is found that although the origin and the destination are
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tributes. The REM can be applied to a retrieval system with a subjective evaluation such as restaurants, movies and so on. The subjective evaluation models should adapt to each user because the evaluation result changes based on individual users’ subjectivity. The REM is considered to be suitable for the retrieval system with subjective evaluation because of its individualization function. There are some problems to be solved in a future. The present system acquires subjective information, i.e., fuzzy measures, road attributes and fuzzy sets by off-line using questionnaire data and the Sketch Map method, respectively. The road attribute values are also obtained with questionnaire after walking each road in a traveling map. The road attribute values, however, should be aquired before a user walks along each road in the traveling map. It is necessary to aquire the road attributes values by on-line using some learning method.
Figure 7: Satisfaction degrees of routes
(a)Situation S1
(b)Situation S2
(c)Situation S3
Figure 8: Rmax of subject 2 in each situation j both the same, various routes are presented to the subjects according to the subjects and the situations. The subjects reply that I j is preferable to NI j at the rate of 91% of all trials. These results show that individual road attribute set X final of the REM reflects subjects’ own preference in road attributes well. The subjects turn accurately the instructed intersections at the rate of 79% of all intersections in all the selected routes. These results show that the present system provides the subjects with useful guidance by linguistic expressions fitting their own SFD.
6
Conclusions
This paper describes the pedestrian navigation system that selects routes based on users’ own preference for routes. The system has the route selection part and the route guidance part. The route selection part consists of the REM and the preference database. The REM applies fuzzy measures and integrals to estimate the satisfaction degree of a road, and is constructed based on users’ own preference for route selection. The route guidance part has the SFD database, and fuzzy sets are applied to generate instructions with linguistic expressions reflecting users’ own SFD. The experimental results show that various routes are selected according to the subjects and the situations and that satisfaction degrees of the routes selected by the present system are higher than those of other routes. The analysis results of experimental data show that the REMs reflect subjects’ own preference in road at-
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(a)Subject 3
(b)Subject 5
(c)Subject 9
(d)Subject 10
Figure 9: Rmax of each subject in situation S2 j
[9] M. Grabisch: “A New Algorithm for Identifying Fuzzy Measures and Its Application to Pattern Recognition”, Proc. of IEEE Int’l Conf. on Fuzzy Systems, pp. 145– 150, (1995).
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