Research And Application On A Data Reduction Method Based On Tensor Field

It is an exigent demand to analyze the law of high-order and high-dimensional information refer to images,videos,drug molecules,text,spatial data and genes in machine learning and data mining.Relative to traditional methods vectorizing data,tensor methods provide a more natural description for data and tensor field provides a viable mathematical measure to study the global and local relationship of data sets.The high-order and high-dimensional data are studied in this paper.The main research results are concluded as follows:(1)Introduction of concepts including multi-linear algebra,tensor space,tensor field and tensor bundle;(2)Data reduction model based on tensor field,machine learning model based on tensor bundle and data sets classification model based on tensor field are given,all of which make use of the existing tensor decomposition technique.(3)The algorithm of tensor bundle with reference to pattern recognition and the algorithm of data sets classification based on tensor field is implemented.(4)Examples for proposed models and algorithms are given.