(b)46IllustrationPrincipal Component Analysis (Linear).Batch-Learning Self-Organizing Map (Nonlinear).Gene classification by codon usage.(a)Fig.1ExampleofDomainDiscretization.(a)：：Mesh-basedMethod，，(b)：：MeshlessMethod．．Fig.2TherelativeerrorεasafunctionsofthenumberNofboundarynodes.Here,▲▲：：ExtendedBoundaryNodeMethod，，▼▼：：BoundaryElementMethod．．ContentContent：Clustering powers of the conventional multivariate analysis methods Clustering powers of the conventional multivariate analysis such as principal component analysis (PCA) become rather poor methods such as principal component analysis (PCA) become when a large amount of data are analyzed. We introduce a novel rather poor when a large amount of data are analyzed. We neural-network algorithm with high clustering power, a self-introduce a novel neural-network algorithm with high organizing map (SOM). The unsupervised neural network algorithm clustering power, a self-organizing map (SOM). The is an effective tool for clustering and visualizing high-dimensional unsupervised neural network algorithm is an effective tool data; it converts complex nonlinear relations among high-for clustering and visualizing high-dimensional data; it converts complex nonlinear relations among high-dimensional data into simple geometric relations that can be viewed dimensional data into simple geometric relations that can be in two dimensions. This method can be used to identify categories viewed in two dimensions. This method can be used to from raw data with a high clustering power and trace factors identify categories from raw data with a high clustering reflected in individual categories. On the basis of batch-learning, we power and trace factors reflected in individual categories. modified the conventional SOM to make the learning process and On the basis of batch-learning, we modified the conventional resulting map independent of the order of data input.SOM to make the learning process and resulting map independent of the order of data input.Appealing point：Batch-Learning Self-Organizing Maps have a wide range of applications. As we developed the BL-SOM software from scratch, we can customize it according to the application. Batch-Learning Self-Organizing Maps have a wide range of applications. As we developed the BL-SOM software from scratch, we can customize it according to the application.Yamagata UniversityGraduate School of Science and Engineering Research Interest ：BioinformaticsYamagata University Graduate School of Science and EngineeringE-mail ：kinouchi@yz.yamagata-u.ac.jpResearch InterestTel ：+81-238-26-3363BioinformaticsFax：+81-238-26-3363E-mail ・ kinouchi@yz.yamagata-u.ac.jpTel ・ +81-238-26-3363HP ：http://ei4web.yz.yamagata-u.ac.jp/Fax ・ +81-238-26-3363HP・http://ei4web.yz.yamagata-u.ac.jp/Special objectivesContentContent：Themesh-basedmethods(theFEMandtheBEMetal.)havebeen The mesh-based methods (the FEM and the BEM et al.) developedasanumericalmethodforsolvingtheboundary-valuehave been developed as a numerical method for solving the problemforPDEs.However,atargetdomainmustbedividedintoaboundary-value problem for PDEs. However, a target domain setofelementsasthepreprocessingofthemesh-basedmethods(Seemust be divided into a set of elements as the preprocessing Fig.1).Inordertoresolvetheabovedemerit,manymeshlessof the mesh-based methods (See Fig. 1). In order to resolve methodshavebeensofarproposed.Thosemethodsaregottenthe above demerit, many meshless methods have been so attentionasanext-generationnumericalmethod.far proposed. Those methods are gotten attention as a next-Inourpreviousworks,theboundary-typemeshlessmethodhasgeneration numerical method.beenextendedforthepurposeofimprovingaccuracyandcalculation In our previous works, the boundary-type meshless method speed.Asaresults,itisshownthattheaccuracyoftheproposedhas been extended for the purpose of improving accuracy methodisextremelyhigherthantheBEM(SeeFig.2).Weareand calculation speed. As a results, it is shown that the currentlystudyingtheresearchwhichisaimedtofurtherimprovetheaccuracy of the proposed method is extremely higher than performanceoftheproposedmethod.the BEM (See Fig. 2). We are currently studying the research which is aimed to further improve the performance of the Appealingpoint：proposed method.Forthefuture,weaimtoapplytheproposedmeshlessmethodtoengineeringproblems.Special objectives For the future, we aim to apply the proposed meshless Yamagata UniversityGraduate School of Science and Engineering method to engineering problems.Research Interest ：Simulation ScienceYamagata University Graduate School of Science and Engineering E-mail ：saitoh@yz.yamagata-u.ac.jpResearch InterestTel ：+81-238-26-3178Simulation ScienceFax：+81-238-26-3178E-mail ・ saitoh@yz.yamagata-u.ac.jpTel ・ +81-238-26-3178HP ：https://saitohlab.yz.yamagata-u.ac.jp/Fax ・ +81-238-26-3178HP・https://saitohlab.yz.yamagata-u.ac.jp/Nonlinear Multivariate Analysis with Batch-Learning Self-Organizing MapNonlinear Multivariate Analysis with Batch-Learning Self-Organizing MapAssociate Professor Makoto KinouchiAssociate ProfessorMakoto KINOUCHIDevelopment of High-Performance Meshless MethodDevelopment of High-Performance Meshless MethodAssociate Professor Ayumu SaitohAssociate Professor Ayumu Saitoh
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