||In the field of artificial intelligence, high-order tensor data have been studied and analyzed, such as the automated optical inspection and MRI. Therefore, tensor decompositions and classification algorithms have become an important research topic.|
In a traditional neural network or machine learning method, the classification algorithm inputs training data in the form of vectors, and the trained model can identify and classify the testing data. In order to conform the input constraints, high-order tensor data are often expanded into high-dimensional vectors. However, it also leads to the loss of spatially related information adjacent to different orders, thus damages the performance of the classification.
This thesis proposes a classification model combining non-negative Tucker decomposition and high-order tensors principal component analysis, and extracts feature core tensors successively to improve the accuracy of classification. Comparing with to neural network classifiers, we replace affine transformations with tensor transformations, which optimizes tensor projections to avoid missing information representing the spatial relationships in different orders, so that it extracts more complete features. For signal processing and medical image fields, data will lose its physical significance at negative values. So many non-negative decomposition and analysis methods have also become important research issues. The non-negative Tucker decomposition referred in this paper is one of them, and it is also one of the classic high-order extensions of non-negative matrix factorization. In the classification model, non-negative Tucker decomposition can not only maintain the non-negative physical meaning, but also can ignore the difference between same class, which makes the classification accuracy increase.
This study explores the computational time cost and classification accuracy of the model. In the experiment of image recognition, the training time of the high-order tensor principal component analysis was reduced to half after combining non-negative Tucker decomposition. In terms of accuracy, the smaller the number of training data, the more pronounced the lead of our model is.