a model of data reduction based on tensor field.pdf

A Model of Data Reduction Based on Tensor FieldXiangliang LiSchool of computer science and technologySoochow UniversitySuzhou,Chinaxiangliangli@Fanzhang LiSchool of computer science and technologySoochow UniversitySuzhou,Chinalfzh@ Abstract—There has been much interest in the use ofmutilinear algebra as a general technique of dimensionreduction of large amounts of Tensor data in recent years.Some tensor based methods has been successfully applied toimage processing signal processing and web search. Thenatural forms described by tensor are kept in arbitrarycoordinates and according to this invariability of tensor it isable to deal with data under the framework of tensor field. Inthis paper a tensor field learning model combining availablealgorithms of dimension reduction based on tensor ispresented. The model reveals that some tensor features couldbe acquired from the original data and the representation ofreduction data is obtained on the basis of tensor fieldtransformation implemented by an algorithm. An examplerefer to reduction of image data is given and the result showsthe remarkable effect of the transformation algorithm.Keywords-mutilinear algebra;tensor field; data reductionI.INTRODUCTIONMany application domains are faced with multimodaldata, due to the increasing number of parameters ordimensions of the physical system under study. As a generaltechnique of dimension reduction, the methods based onmutilinear algebra has been applied to areas such as facerecognition[1], web search[2] and documents analysis[3].