Fuzzy Support Tensor Machine

Most of the traditional data analysis and data mining methods are based on vector space. And lots ofcomplex data structures tend to be directly converted into vector before researching, such as images, videos,etc., which are tensor data. This direct conversion approach leads to potential shortcomings: Firstly, theoriginal data structure and correlation information may be broken, and secondly it may suffer from thecurse of dimensionality and small sample size problem. Support vector machine is a popular method forsmall sample size, nonlinear, high-dimensional and local minima problems, which has good generalization.It is necessary for support vector machine to be transformed into support tensor machine, which candirectly deal with multi-modal tensor data in pattern recognition and image classification. Therefore, theperformance of tensor classification has been improved.Support tensor machine, similar to support vector machine, is sensitive to outlier and noise data. In orderto further improve the performance of tensor data containing outlier and noise data, fuzzy support tensormachine has been proposed to deal with tensor data in this paper, which is an extension of fuzzy supportvector machine.In fuzzy support tensor machine (FSTM), membership degree for each instance is varied according to thecontribution of instance for classification, which can improve the robustness of support tensor machine foroutlier and noise data. There are two ways to determine the membership degree. In one way, membershipdegree can be determined by the distance from data to its own class center in original space. In other way,membership degree is determined by the distance from data to the estimated hyper-plane in original space.Due to non-convex property of the proposed FSTM, traditional iterative techniques is very time consumingand may suffer from local minima. In order to overcome these two shortcomings, rank-one decompositionis introduced to efficiently solve FSTM, which greatly reduces the complexity of the model.Experiments are conducted on four datasets, such as Yale-B、ORL、CMU PIE and USF HumanID. Fuzzysupport tensor machine is compared with support high-order tensor machine (SHTM). Experimental resultsshow that FSTM is more accurate than SHTM. In addition, the robustness of FSTM has been improved,especially for dataset containing noise and outlier.