Knowledge Graph And Speech Image Data Completion Based On Tensor Decomposition

With the continuous development of science and technology,data acquisition technique is becoming more and more mature,and the data dimension acquired in many application fields is becoming higher and higher.Taking advantage of tensor,a highdimensional data structure,the collected data can be represented directly,thus reduce the possibility of information loss.Tensor form is highly valued in a series of applications and there are many tensor-based data processing technoligies such as tensor completion,tensor classification and so on.In this thesis,the focus is on tensor completion,which aims to recover the whole data based on partial observed ones.The specific research work of this thesis is as follows:(1)Based on the fact that semi-tensor product can reduce the number of parameters,and considering the physical meaning of each part of the knowledge graph,this thesis reconstructed the dimensions of each intermediate value of the scoring function,and proposed a knowledge graph completion model named STuckER(Semi-TuckER),which not only has low spatial complexity but also can guarantee the prediction accuracy.Since the commonly used knowledge graphs are usually incomplete and the knowledge graphs can be represented by binary tensors,a knowledge graph completion model based on tensor decomposition is proposed.However,the disadvantage of this kind of model is the large number of parameters.Therefore,this thesis considers to replace the traditional tensor mode-n product with the help of semi-tensor product to break the strict constraint that the corresponding dimensions of multiplying elements are equal,so that the number of parameters in the decomposition model can be compressed.However,through the analysis of the two intermediate models proposed in this thesis,TuckER-SF(TuckER-SemiFactors)and TuckER-SC(TuckER-SemiCore),it is found that directly using the semi-tensor product can reduce the number of parameters in the model,but at the cost of reducing the prediction performance,which is not desirable.Therefore,in this thesis,the structure of the model is further improved.By rearranging the information obtained from the same embedding in the mode-n semi-tensor product into the same dimension,the model information can be more closely combined,so that the model can reduce the number of parameters to half of its original while ensuring the same accuracy of completion.The proposed model is named STuckER,and experiments are carried out on four standard knowledge graph datasets.The experimental results prove the validity and accuracy of the proposed method.(2)It is found that the projection of tensor data preprocessed by the kernel trick can have better low-rank characteristics compared with the original data.Therefore,in this thesis,a kernel tensor completion method is developed,which can handle the completion of some high-rank multidimensional data and is named KF-HRTC(Kernelized Factorization-High Rank Tensor Completion).The key point of this method is the use of kernel trick,which is used to project high-rank data into high dimensional feature space,so that it presents low-rank characteristics in the projection space,and then use low-rank completion method in the projection space,so as to achieve the completion task of highrank data.At the same time,because the method proposed in this thesis is based on tensor form,it can effectively avoid the loss of multidimensional information in matrix method,and therefore can achieve better completion effect.High-rank speech and image data are used for comparative experiments,and the results show that the RSE value of KF-HRTC algorithm is considerably improved compared with that of traditional methods at different sampling rates,and the improvement can reach about 0.25 in some datasets,which fully proves the effectiveness of the proposed algorithm.