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چكيده انگليسي :

Proposing A New Probabilistic Subspace Learning Method For Structured Data Saeid Momenzadeh s momenzadeh@ec iut ac ir Aprill 30 2016 Department of Electrical and Computer Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Dr Mehran Safayani safayani@cc iut ac ir Abstract In many fields of science and engineering we encounter data with high dimensionality Using the high dimensionaldata directly owning to the many problems that it would cause is undesirable Due to the limitations that real world prob lems pose these data actually reside on subspaces of much lower dimensionality Learning these subspaces is of specialimportance in the field of machine learning and pattern recognition The reason for this importance is that in many cases dueto the phenomenon of curse of dimensionality using high dimesion data directly would severely degrade the performanceof classification methods and therefore the dimensionality must be first reduced Subspace learning methods try to find a subspace that reduces the dimensionality of the data while maximally increasinga certain criterion Many subspace learning methods have been proposed one of the most well known and widely used ofwhich is canonical correlation analysis In canonical correlation analysis our goal is to find two subspaces for two sets ofdata so that in those subspaces those sets of data are maximally correlated This method is one of the most important toolsfor analysis of multiview data and has recieved a lot of attention lately One of the most important advances in the field of subspace learning has been the introduction of probabilistic subspacelearning methods These methods interpret subspace learning as solving a latent variable probabilistic model The existenceof probabilistic model offers many advantages the most important of which is that these models are extendible and itspossible to extend the probabilistic model in different ways Many subspace learning methods are only applicable to vector data and when the data have structure such as matrix data they should be first vectorized When this happens locality information gets lost and also the covariance matrices becomehuge To avoid these problems two dimensional methods have been proposed These methods can reduce dimensionalityof matrix data without vectrorization In this thesis a two dimensional probabilistic interpretation of canonical correlation analysis is proposed which has thebenefits of probabilistic mathods and also avoids vectorizing matrix data The proposed probabilistic model is based onmatrix variate distributions Two approaches for solving this probabilistic model are proposed one of which is simplifyingthe model and solving it through the expectation maximisation algorithm and the other is solving the model using thevariational method The performance of the proposed method for synthetic and real data is assesed and its superiority torival methods in experiments with real data is shown Key Words Subspace learning Dimensionality reduction Probabilistic Model Matrix variate dis tribution

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