modeling decisions for artiﬁcial intelligence · 2018. 10. 30. · doctoral consortium...

Doctoral Consortium Proceedings

The 11th International Conference on

Modeling Decisions for

Artificial Intelligence

MDAI 2014, Tokyo, Japan

October 29 - 31, 2014

ISBN-10: 84-697-1393-0ISBN-13: 978-84-697-1393-8

Editors:

Vicenc Torra

IIIA - Institut d’Investigacio en Intel·ligencia Artificial

CSIC - Consejo Superio de Investigaciones Cientıficas

Campus UAB, 08193 Bellaterra, Catalonia, Spain

E-mail: [email protected]

Yasuo Narukawa

Toho Gakuen

3-1-10 Naka, Kunitachi, Tokyo, 186-0004, Japan


Yasunori Endo

Faculty of Engineering, Information and Systems

University of Tsukuba

Ibaraki 305-8573, Japan


ISBN: 978-84-697-1393-8

Preface

This volume contains the extended abstracts of the presentations in the Doc-

toral Consortium of the 11th International Conference on Modeling Decisions for

Artificial Intelligence (MDAI 2014), held in Tokyo, Japan, October 29-31. The

rest of papers as well as regular papers have been separately published in the

Lecture Notes in Artificial Intelligence, Vol. 8825 (by Springer) and the USB

proceedings.

This conference followed MDAI 2004 (Barcelona, Catalonia), MDAI 2005

(Tsukuba, Japan), MDAI 2006 (Tarragona, Catalonia), MDAI 2007 (Kitakyushu,

Japan), MDAI 2008 (Sabadell, Catalonia), MDAI 2009 (Awaji Island, Japan),

MDAI 2010 (Perpinya, Catalonia, France), MDAI 2011 (Changsha, China),

MDAI 2012 (Girona, Catalonia), and MDAI 2013 (Barcelona, Catalonia, Spain)

with proceedings also published in the LNAI series (Vols. 3131, 3558, 3885, 4617,

5285, 5861, 6408, 6820, 7647, 8234).

The aim of this conference was to provide a forum for researchers to discuss

theory and tools for modeling decisions, as well as applications that encompass

decision making processes and information fusion techniques.

The conference was supported by the Japan Society for Fuzzy Theory and In-

telligent Informatics (SOFT), the Catalan Association for Artificial Intelligence

(ACIA), the European Society for Fuzzy Logic and Technology (EUSFLAT), the

UNESCO Chair in Data Privacy, the Spanish MICINN (TIN2011-27076-C03-

03), and the Spanish MEC (ARES - CONSOLIDER INGENIO 2010 CSD2007-

00004).

Vicenc Torra, Yasuo Narukawa, Yasunori Endo

October, 2014

Modeling Decisions for Artificial Intelligence – MDAI 2014

General chairs

Yasunori Endo, University of Tsukuba, Tsukuba, Japan

Program chairs

Vicenc Torra, IIIA-CSIC, Bellaterra, Catalonia, Spain

Yasuo Narukawa, Toho Gakuen, Tokyo, Japan

Advisory Board

Bernadette Bouchon-Meunier, Computer Science Laboratory of the University

Paris 6 (LiP6), CNRS, France

Didier Dubois, Institut de Recherche en Informatique de Toulouse (IRIT), CNRS,

France

Lluis Godo, IIIA-CSIC, Catalonia, Spain

Kaoru Hirota, Tokyo Institute of Technology, Japan

Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Poland

Sadaaki Miyamoto, University of Tsukuba, Japan

Michio Sugeno, European Centre for Soft Computing, Spain

Ronald R. Yager, Machine Intelligence Institute, Iona Collegue, NY, USA

Program Committee

Gleb Beliakov, Deakin University Australia

Gloria Bordogna, Consiglio Nazionale delle Ricerche, Italia

Tomasa Calvo, Universidad Alcala de Henares, Spain

Susana Dıaz, Universidad de Oviedo, Spain

Josep Domingo-Ferrer, Universitat Rovira i Virgili, Catalonia

Jozo Dujmovic, San Francisco State University, California

Katsushige Fujimoto, Fukushima University, Japan

Michel Grabisch, Universite Paris I Pantheon-Sorbonne, France

Enrique Herrera-Viedma, Universidad de Granada, Spain

Aoi Honda, Kyushu Institute of Technology, Japan

Masahiro Inuiguchi, Osaka University, Japan

Xinwang Liu, Southeast University, China

Jun Long, National University of Defense Technology, China

Jean-Luc Marichal, University of Luxembourg, Luxembourg

Radko Mesiar, Slovak University of Technology, Slovakia

Tetsuya Murai, Hokkaido University, Japan

Toshiaki Murofushi, Tokyo Institute of Technology, Japan

Guillermo Navarro-Arribas, Universitat Autonoma de Barcelona, Catalonia, Spain

Michael Ng, Hong Kong Baptist University

Gabriella Pasi, Universita di Milano Bicocca, Italia

Susanne Saminger-Platz, Jihannes Kepler University, Austria

Sandra Sandri, Instituto Nacional de Pesquisas Espaciais, Brasil

Roman S�lowinski, Poznan University of Technology, Poland

Laszlo Szilagyi, Sapientia-Hungarian Science University of Transylvania, Hun-

gary

Aida Valls, Universitat Rovira i Virgili, Catalonia, Spain

Vilem Vychodil, Palacky University, Czech Republic

Zeshui Xu, Southeast University, China

Yuji Yoshida, University of Kitakyushu, Japan

Local Organizing Committee Chair

Kenichi Yoshida, University of Tsukuba

Kazuhiko Tsuda, University of Tsukuba

Additional Referees

Roger Jardı-Cedo, Malik Imran Daud, Sara Hajian, Montserrat Batet, Yuchi

Kanzawa

Supporting Institutions

University of Tsukuba

The Catalan Association for Artificial Intelligence (ACIA)

The European Society for Fuzzy Logic and Technology (EUSFLAT)

The Japan Society for Fuzzy Theory and Intelligent Informatics (SOFT)

The UNESCO Chair in Data Privacy

The Spanish MEC (ARES - CONSOLIDER INGENIO 2010 CSD2007-00004)

and MICINN (TIN2011-27076-C03-03)

Table of Contents

c-Regression Models on Vertices for Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Tatsuya Higuchi, Sadaaki Miyamoto

Asymmetric K-Medoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Yousuke Kaizu, Sadaaki Miyamoto

Comparing Different Methods on Clustering Follow-Follower Relations on Twit-

ter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Keisuke Minakawa, So Miyahara, Yusuke Tamura, Sadaaki Miyamoto

The Strategies for Local Optimality Test in Bilevel Linear Optimization with

Ambiguous Objective Function of the Follower . . . . . . . . . . . . . . . . . . . . . . . . . 10

Puchit Sariddichainunta, Masahiro Inuiguchi

Constrained Mountain c-Regression Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Hengjin Tang, Sadaaki Miyamoto, Yasunori Endo

Even-sized Clustering Algorithm Based on Optimization . . . . . . . . . . . . . . . . . . 16

Tsubasa Hirano, Naohiko Kinoshita, Yasunori Endo, Yukihiro Hamasuna

A Note on Visualization of Asymmetric Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Yu Shiraishi, Akira Sugawara, Naohiko Kinoshita, Yasunori Endo

On Relation Between Kernelization and Quadratic-Regularization in Hard Non-

Metric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Kuniaki Iwakura, Yasunori Endo, Naohiko Kinoshita, Sadaaki Miyamoto

1

c-Regression Models on Vertices for Graphs

Tatsuya Higuchi∗ and Sadaaki Miyamoto∗∗

∗ Graduate School of Systems and Information EngineeringUniversity of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

[email protected]∗∗ Department of Risk Engineering, Faculty of Systems and Information Engineering

University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, [email protected]

Abstract. Considering a situation that some vertices of a graph havereal values as a dependent variables, kNN (k Nearest Neighbor) regres-sion is one of the useful methods. However, it is difficult for kNN re-gression to solve regression problems when some close vertices have dif-ferent values. In that case, the vertices need appropriately classifying.Therefore, we focus on Fuzzy c-Regression Models (FCRM) and newc-regression models inspired by FCRM are proposed in this study.

Keywords: social networking service, fuzzy c-regression models

1 Introduction

SNS (Social Networking Service) has been used around the world. Users of SNSare freely connected and the structure of SNS is expressed as a graph. The usersand their relationships are regarded as vertices and weighted edges respectively.It is assumed that each user has a value as degree of preference, evaluation value,or tendency of thought, for example. Such a value is useful information to knowthe structure of SNS. The problem comes down to regression analysis when thevertex is independent variable and the value is dependent variable.

In kNN (k Nearest Neighbor) regression, the estimated value is an average ofdependent variables of k nearest neighbor. Accordingly, the estimation is failedwhen some vertices of neighborhood have different values. It is exemplified thatthe close users have different interests. Vertices need classifying into some validclusters in such a case. Fuzzy c-Regression Models (FCRM) [2][1] is one of themost famous clustering methods, which is use a regression model as a prototypeof a cluster. Therefore, we propose a new c-regression method inspired by FCRMand show some numerical examples.

2 kNN Regression

A set of vertices, which are independent variables, is {x1, . . . , xN}. yn, n =1, . . . , N denote dependent variables. The edge which connects xn and xn′ is

MDAI 2014modeling decisions

2 T. Higuchi, S. Miyamoto

weighted by similarity wnn′ . In kNN regression,

yn =

(k∑

ℓ=1

wni

(ℓ)n

yi(ℓ)n

)/

(k∑

ℓ=1

wni

(ℓ)n

).

The indices of k nearest vertices of xn are denoted by {i(1)n , . . . , i(k)n }. kNN re-

gression is not good in the previously referred case.

3 Fuzzy c-Regression Models Using Similarity

In this section, we propose FCRM-SIM (Fuzzy c-Regression Models based onSimilarity). Regression model is generally given by

y = αTi ϕ(x) + bi, i = 1, . . . , c. (1)

ϕ(x) is a feature vector of vertex x. αi = (α(1)i , . . . , α

(N ′)i )T and N ′ is dimen-

sionality of the feature vector. In our method, the feature vector is

ϕ(xn) = wn = wn/∥wn∥, wn = (wn1, . . . , wnN )T.

The objective function is

J(U,B) =c∑

i=1

(y−Wβi)T (Ui)m (y − Wβi) + λ

c∑i=1

βTi βi,

y = (y1, . . . , yN )T,

βi = (αTi , bi)T,

B = (β1, . . . ,βc) ,

W =

wT1 1...

...wT

N 1

, Ui =

ui1 0 . . . 00 ui2 . . . 0...

.... . .

...0 0 . . . uiN

.

m is fuzzifying parameter and U = (uin), i = 1, . . . , c, n = 1, . . . , N is a mem-bership matrix. The optimum solution for U and B are respectively given by

uin =

c∑j=1

(yn − αT

i wn − bi

yn − αTj wn − bi

) 2m−1

−1

, βi =(WT (Ui)

mW + λIN

)−1WT (Ui)

my.

IN is an identity matrix. The objective function is minimized in respect of Uand B alternatively until convergence of membership matrix U .

4 Numerical Examples

Leave-one-out cross validation is introduced for evaluation. Note that there aretwo situations of “leave-one-out”.

1. A dependent variable of the vertex is “left out”.

2

c-Regression Models on Vertices for Graphs 3

2. The vertex is “left out”.

The artificial example has been made as follows. One hundred two-dimensionalvectors {x1, . . .x100} are randomly scattered on the plane [0, 1] × [0, 1] and ev-ery vertex belongs to cluster 1 or 2. All pairs of the vectors have similaritywnn′ = exp

(∥xn − xn′∥2

L2/σ2

S

)regardless of their cluster. wnn′ = 0 is reset

when wnn′ ≤ 0.1. Every vertex in cluster 1 has a dependent variable yn =0.5∥xn∥L2 + e, yn = 1.5∥xn∥L2 + e in cluster 2. e ∼ N(0, σ2

N) denotes Gaussiannoise. σ2

S = 1.0 is fixed and three examples when σ2N = 0.001, 0.01, and 0.1 are

used. k = 1, 2, . . . , 100 and λ = 0.001, 0.01, . . . , 1000 vary and one is selectedwhen the error is minimum. m = 2 and C = 2 are also fixed.

We find that the proposed method is better than kNN regression in thisexample because there are two clusters.

Table 1. leave-one-out CV error of kNN regression and FCRM-SIM

leave-one-out CV error (parameter)σ2

N = 0.001 σ2N = 0.01 σ2

N = 0.1

kNN 0.2787 (k = 40) 0.3024 (k = 40) 0.4568 (k = 57)

FCRM-SIM Situ. 1 0.06139 (λ = 1.0) 0.06552 (λ = 1.0) 0.1654 (λ = 1.0)Situ. 2 0.07461 (λ = 1.0) 0.07650 (λ = 1.0) 0.1867 (λ = 10.0)

5 Conclusion

We have proposed FCRM-SIM which use similarity to N sample vertices. Theyare efficient even when different clusters are close. FCRM-SIM are similar tokernel regression[3], but matrix W is not assumed to be positive semi-definite.A similarity vector is adopted as a feature vector in this study, but other featurevectors are also to be tried.

As a future study, kNN regression should be used instead of (1) of FCRM-SIM to classify samples.

This work has partly supported by the Grant-in-Aid for Scientific Research(KAKENHI) No. 26330270, JSPS, Japan.

References

1. S. Miyamoto, H. Ichihashi, K. Honda: Algorithms for Fuzzy Clustering, Springer,Berlin (2008)

2. R. J. Hathaway, J. C. Bezdek: Switching regression models and fuzzy clustering,IEEE Trans. on Fuzzy Systems, Vol. 1, No. 3, pp. 195-204, (1993)

3. S. Akaho: Kernel Multivariate Analysis, Iwanami-shoten, Tokyo (2008) (inJapanese).

3

Asymmetric K-Medoids

Yousuke Kaizu∗ , Sadaaki Miyamoto∗∗

∗Graduate School of Systems and Information EngineeringUniversity of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

[email protected]∗∗Department of Risk Engineering, Faculty of Systems and Information Engineering


1 Introduction

Clustering has now become a major tool in the area of data mining [1]. Re-cently, because of the spread of Social Networking Service(SNS), asymmetricdata handling is becoming popular. The method of K-medoids is known as arepresentative clustering technique as well as agglomerative hierarchical cluster-ing and fuzzy c-means; K-medoids is the method that minimize the summationof dissimilarity between medoids and points in the cluster.

However, K-medoids cannot classify asymmetric data like SNS data. In or-der to solve this problem, we propose asymmetric K-medoids that can classifyasymmetric data in this paper.

2 K-medoids and Asymmetric K-medoids

K-medoids is a variation of K-means. To apply K-means, the dissimilarity be-tween arbitrary vectors have to be calculated. However, K-medoids can classifythe data if we can calculate the dissimilarity between an arbitrary data pair.In K-medoids, cluster center is not a centroid but a representative point in thecluster: a cluster center is given below.

arg minx∈Gi

∑y∈(Gi−{x})

d(x, y)

K-means minimize the summation of dissimilarity between centroid of clusterand points in the cluster. In contrast, K-medoids minimize the summation ofdissimilarity between medoids and points in the cluster.

We proceed to describe asymmetric K-medoids. Ordinary K-medoids haveone medoid in one cluster. In the case of asymmetric K-medoids, however, wehave two medoids in one cluster. The proposed algorithm is given below.

Step 1 Set the initial cluster G1, · · · , Gn.

4


2 Y. Kaizu, S. Miyamoto

Step 2 Calculate respective medoids for each cluster in asymmetric data.

x(Gi) = arg minx∈Gi

∑xk∈Gi

d(x, xk)

y(Gi) = arg miny∈Gi

∑xk∈Gi

d(xk, y)

Step 3 Calculate the summation of similarity to each medoid, and classify thedata according to similarity.

xk → Gi ⇐⇒ arg min1�j�c

{d(x(Gj), xk) + d(xk, y(Gj))}

Step 4 Check the stopping criterion for {x(Gj), y(Gj)} (j = 1, . . . , c). If thecriterion is not satisfied, go back to Step 2.

3 Numerical Example

In this numerical examples, we demonstrate the usefulness of the asymmetricK-medoids for the data of foreign traveler in major countries 2001 from WorldTourism Organization (South Africa, America, Canada, China, Taiwan, HongKong, Korea, Japan, India, Indonesia, Singapore, Australia, New Zealand, Eng-land, France, Switzerland, Thailand, Malaysia) [2]. Where an edge has highersimilarity, the edge is shown by a thicker arrow. The star means out-directionmedoid and hexagram means in-direction medoid. We used Gephi [3], an inter-active visualization software for graph data.

Fig. 1. classification result of nineteen countries (two clusters)

5

Asymmetric K-Medoids 3

Fig. 2. classification result of nineteen countries (three clusters)

Fig. 3. classification result of nineteen countries (four clusters)

References

1. S. Miyamoto: Introduction to Cluster Analysis, Morikita-Shuppan, 1999 (inJapanese)

2. http://www.unwto-osaka.org/index.html3. https://gephi.org/

6

Comparing Different Methods on ClusteringFollow-Follower Relations on Twitter

Keisuke Minakawa∗ , So Miyahara∗ , Yusuke Tamura∗ , Sadaaki Miyamoto∗∗

∗Graduate School of Systems and Information EngineeringUniversity of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

{s1420586, s1320637, s1320630}@u.tsukuba.ac.jp∗∗Department of Risk Engineering, Faculty of Systems and Information Engineering


1 Introduction

Clustering on SNS has attracted many researchers’ attention and accordinglynew methods for SNS clustering have been developed (e.g., [1]). On the otherhand, traditional methods of clustering [4] have not been known to be effectivefor this purpose. In this paper we compare several methods of clustering: agglom-erative hierarchical clustering, the spectral clustering combined with DBSCANbased on our previous study [3]. In particular we show introducing core pointsis effective. A real data set extracted from Twitter is used for experiment.

2 Methods of Clustering

Let the objects to be clustered be {1, 2, . . . , N} and they are considered to benodes of a undirected graph. A = (aij) be the adjacency matrix. If follow i → jor follower j → i relation is represented by A, aij = 1 when either i → j orj → i. Hence A is a symmetric matrix with zero diagonal elements. Let B(j) bethe set linked to j by A: B(j) = {k : ajk = 1}. We define similarity S = (sij)between i and j by

sij =|B(i) ∩ B(j)||B(i) ∪ B(j)|

,

where |B(j)| is the number of elements in B(j).The following methods have been used for clustering, in which ‘core points’

introduced in DBSCAN have been introduced. Non-core points have been allo-cated by the kNN technique.

1. The single linkage (SL), the complete linkage (CL), and the average link-age (AL) in the agglomerative hierarchical methods [4] were used. Whencombined with core points, they are named as SL-CORE, CL-CORE, andAL-CORE.

2. The DBSCAN algorithm [2] were used. When combined with core points, itis called DBSCAN-CORE.

3. The spectral clustering [5] were also used. When combined with core points,it is called SC-CORE.

7


2 K. Minakawa, S. Miyahara, Y. Tamura, S. Miyamoto

4. Miyahara et al. [3] proposed an efficient algorithm combining DBSCAN andthe spectral clustering using core points. It is called DBSCAN-CORE-SC.

3 Experiment

As shown in Table 1, follow-follower relations were extracted from seven officialaccount of Japanese parties.

The used parameters are: σ2 = 0.1 (this parameter is needed only for thespectral clustering), MinPts = 20, k = 1 for all methods, and Eps = 0.71 forDBSCAN-kNN, Eps = 0.79for SC-CORE-kNN and DBSCAN-CORE-SC-kNN;Eps = 0.3 for AL-CORE-kNN, SL-CORE-kNN and CL-CORE-kNN.

We show the values of the Rand Index as Table 2, which show aout the samevalues. Moreover Figure 1 shows the visualization using Gephi [6], where clustersare shown by seven colors, of which details are omitted here.

Table 1. Parties, official accounts, and the number of follows

Party Official Account Number of Follows

Liberal Democratic Party of Japan(LDP) @jimin koho 188Democratic Party of Japan(DPJ) @dpjnews 169New Komeito @komei koho 196Japanese Communist Party(JCP) @jcp cc 75Social Democratic Party(SDP) @SDPJapan 191Your Party @your party 64Japan Restoration Party @j ishin 109

Total 992

Table 2. The obtained values of the Rand Index. The parentheses after each methodis the assumed number of clusters

Method RandIndex

DBSCAN-kNN(7) 0.89345SC-CORE-kNN(7) 0.89234DBSCAN-CORE-SC-kNN(7) 0.89234SL-CORE-kNN(7) 0.90347CL-CORE-kNN(7) 0.90592AL-CORE-kNN(7) 0.90593

8

Comparing Methods on Clustering Relations on Twitter 3

Fig. 1. Result of clustering using DBSCAN-CORE-SC-kNN. Gephi [6] is used for vi-sualization.

4 Discussion and Conclusion

We have still problems in selecting appropriate parameters. The present valuesare chosen so that the generated clusters are suited to the seven parties.

It has also been observed that without the use of core points, the agglomer-ative hierarchical methods do not produce good clusters.

Other observations include that the Louvain method [1] produces eight clus-ters, of which seven correspond to the assumed parties. If we neglect anothercluster, the Rand index will be as good as the above methods.

The experiments are still on-going and we cannot give our final results ofevaluations. However, the above results show the effectiveness of the introductionof core points.

This study has partly been supported by the Grant-in-Aid for Scientific re-search, JSPS, Japan, no.26330270.

References

1. Blondel, Vincent D., et al., Fast unfolding of communities in large networks, Journalof Statistical Mechanics: Theory and Experiment 2008. 10 (2008): P10008.

2. M. Ester, H.-P. Kriegel, J. Sander, X. Xu, A Density-Based Algorithm for Discover-ing Clusters in Large Spatial Databases with Noise, Proceedings of 2nd InternationalConference on Knowledge Discovery and Data Mining, pp.226-231, 1996.

3. S. Miyahara, Y. Komazaki, S. Miyamoto, An Algorithm Combining Spectral Clus-tering and DBSCAN for Core Points, V.N. Huynh et al, eds., Knowledge and Sys-tems Engineering, Proc. of the Fifth International Conference KSE2013, Vol.2, Ad-vances in Intelligent Systems and Computing 245, pp. 21-28, 2013.

4. S. Miyamoto: Introduction to Cluster Analysis, Morikita, 1999 (in Japanese)5. U. von Luxburg, A Tutorial on Spectral Clustering, Statistics and Computing, 17,

4, pp.395-416, 2007.6. https://gephi.org/

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modeling decisions for artiﬁcial intelligence · 2018. 10. 30. · doctoral consortium...

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