Master Thesis: Proposing a new probabilistic subspace learning method for structured data, 2016
In many fields in science and engineering we encounter data with high dimensionality, using which directly, owning to the many problems that it would cause is undesirable. Yet due to the limitations that real world problems pose, these data actually reside on subspaces of much lower dimensionality. Learning these subspaces is of special importance in the field of machine learning and pattern recognition. The reason for this importance is that in many cases due to the phenomenon of curse of dimensionality, using high dimension data directly would severely degrade the performance of classification methods and the dimensionality must be first reduced. In subspace learning methods we try to find a subspace that would reduce the dimensionality of the data while maximally increasing a certain criterion. For this purpose, many methods have been proposed one of the most famous and widely used of which is canonical correlation analysis (CCA). In canonical correlation analysis our goal is to find two subspaces for two sets of data so that in those subspaces those sets of data are maximally correlated. Over the years many extensions for this method have been proposed including a probabilistic interpretation which interprets CCA as solution of a latent variable probabilistic model. Another important extension of this method has been a two dimensional extension through which dimension of data with matrix form like image could be, without vectorization and the loss of locality information, reduced. In this research a method is proposed which offers the advantages of both the probabilistic interpretation and the two dimensional method. This is achieved through the use of matrix-variate distributions.
Key Words: Subspace learning, Dimensionality reduction, Probabilistic Model, Matrix-variate distribution