Research On One-against-all Partition Based Binary Tree Support Tensor Machine Algorithms

The binary tree support vector machine (SVM) algorithm is one of the mainstreamalgorithms for multi-class classification in the fields of pattern recognition and machinelearning. In order to reduce the training and testing time of one-against-all SVM (OAA-SVM)and reduced OAA-SVM (R-OAA-SVM), in this study, first, two OAA partition based binarytree SVM algorithms are proposed for multi-class classification. One is thesingle-space-mapped binary tree SVM (SBT-SVM) and the other is the multi-space-mappedbinary tree SVM (MBT-SVM).In real application, data of many classification problems is tensor type. Standard SVMbased on one-order tensor space can not deal directly with higher-order tensor model. Manyresearchers are developing more effective learning machines for tensor classification. HaoZ.etc presented a linear support higher-order tensor machine (SHTM) which combines themerits of linear C-support vector machine (C-SVM) and tensor rank-one decomposition. Inorder to make the proposed multi-space-mapped binary tree SVM can effectively deal withtensor type classification problem. The third OAA partition based multi-space-mapped binarytree SHTM algorithms are proposed.In these algorithms, one of the key issues is how to construct partition function to dividethe training samples flowing into each non-leaf node into two disjoint subsets. So, this paperproposes a modified similarity formulation to measure the similarity of a group of trainingsamples. The method defines a classifier score function to find the best data-division for everynonleaf node. To compare the performance with different partition functions for data-division,we use Partition function based on the within-set scatter、the within-set scatter、problem’scenter and randomly divided to conduct a test.A set of experiments is conducted on nine UCI datasets and two face recognition datasetsto demonstrate the first two algorithms’ performances. The results show that in term of testingaccuracy, MBT-SVM is comparable with one-against-one SVM (OAO-SVM), R-OAA-SVMand OAA-SVM and superior to SBT-SVM. In term of testing time, MBT-SVM is superior toOAO-SVM, binary tree of SVM (BTS), R-OAA-SVM and OAA-SVM and slightly longerthan SBT-SVM. In term of training time, MBT-SVM is superior to BTS, R-OAA-SVM and OAA-SVM and comparable with SBT-SVM. For the datasets with smaller class number andtraining sample number, the training time of MBT-SVM is comparable with that ofOAO-SVM. For the datasets with larger class number or training sample number, in mostcases, the training time of MBT-SVM is longer than that of OAO-SVM.To verify the MBT-SHTM algorithms’ performances, A series of experiments isconducted on seven second-order tensor face recognition datasets. The experimental resultsshow that MBT-SHTM is not only test precsion but also training and testing time obviousbetter than MBT-SVM.