Algorithmic Research On Classification And Regression Problems For Tensor Input

As we all know,Tensor types of data has greatly drawn the attention of people.Recently,several tensor learning method appear,but the majority of them dealing with tensor regression problems work on vector spaces that are derived by stacking the original tensor elements in a more or less arbitrary order.This vectorization of data causes many new problems.First,the structural information is destroyed.Second,the vectorization of a tensor may bring an extremely high dimensionality vector which may lead to high computational complexity,overfitting and large memory requirement.Therefore,a more effective algorithm for tensor regression and classification problems is meaningful.In this article,We studied algorithmic on classification and regression problems for tensor input from two aspects.First,taking advantage of the structural information of the tensors as much as possible.Second,turn the tensors into vectors whose dimension are as small as possible.According to the first policy,on one hand,inspired by the relation between photochrome and the gray pictures,we reformulate the tensor sample training set and form the new model(LS-STRM-SMT)for tensor regression problem.With the introduction of projection matrices and another fixed point algorithm,we turn the LS-STRM-SMT model into several related LS-SMRM models.And then algorithm for LS-SMRM is applied to solve them.On the other hand,as we all know,the nuclear norm of matrix can be regarded as a description of rank of the matrix to some degree,so we choice a definition of the nuclear norm of the tensor to describe the rank of the tensor and then a novel method called as support tensor machine based on nuclear norm of the tensor(STM-NNT),is proposed based on the nuclear norm and of the tensor,which can be applied to deal with tensor classification problem more efficiently.From the second policy,the T-svd decomposition is applied for a pretreatment of the tensor input so that we can get a lower dimensional vector,and then method for vector can be used to solve them.The experiments in the later section indicate that the algorithm we proposed all have a good performance.