Research On Large-scale Tensor Decomposition Method Based On Coupled Block Sampling

Due to the rapid development of technical means of acquiring and storing information,observational data always exhibits the characteristics of high dimension and large size.The analysis and processing of large-scale data has become the core and key of today’s information processing technology.Compared with traditional matrix-based processing methods,tensors(multidimensional arrays)are more suitable for the representation and analysis of such high-dimensional data.It not only can intuitively describe the multi-linear structure between high-order data,but also has good characteristics such as simplified model and strong uniqueness,so it has been widely used in the representation and processing of multi-dimensional data in recent years.However,traditional tensor decomposition algorithms will face the problems of high memory usage and computational complexity when dealing with large-scale data.The existing large-scale tensor decomposition algorithms that use partial data to reconstruct the original parameter model are usually based on the idea of block sampling and randomization,and use the sampled data to learn and update model parameters by mining the overall and local consistency of the tensor model.However,this processing method ignores the inherent coupling structure between different sampled data blocks from the same source,and does not take into account the prior information in the actual signal,so there are shortcomings in terms of computational efficiency and decomposition accuracy.In summary,this paper combines the existing core technologies of large-scale tensor decomposition such as randomization and block sampling,and integrates the idea of "coupling decomposition" into it to better tap the internal coupling structure between the samples,and proposes a coupled block sampling framework,and the corresponding large-scale tensor decomposition algorithm with high computational efficiency is discussed,and its application in many large-scale signal processing problems is discussed in combination with the prior information in some actual signals.The specific contents are summarized as follows:(1)This paper proposes a canonical polyadic algorithm for large-scale tensors based on coupled block sampling.Firstly,based on the ideas of randomization,block sampling,coupling decomposition,etc.,a coupled block sampling method is proposed,which can sample a set of tensor blocks with small size,covering all model parameters of the original tensor,and having a specific coupling relationship with each other.In addition,the existing coupled canonical polyadic algorithm is used to jointly solve the above sampling tensor blocks all at once.Finally,by fusing the results of the coupled tensor block decomposition,the existing problems of inconsistency in amplitude and order are solved,and the original large tensor model is completely restored.The performance of the algorithm is studied through numerical simulation experiments.In addition,we consider the f MRI-like simulation data,the proposed method is used to separate its components to verify the effectiveness of the algorithm.(2)This paper applies the proposed method to two typical large-scale data processing applications.First,we consider the problem of the DOA estimation problem of broadband arrays,the Vandermonde structure of the array space factor matrix is organically embedded into the proposed large-scale tensor decomposition algorithm to extract the array DOA.Then,we consider the problem of analysis and completion of MIMO wireless channel data,the proposed algorithm combined with the Vandermonde structure of the frequency dimension is used to decompose the multi-time "space-frequency" channel data,and analyze the time-varying characteristics of the frequency dimension.The "space-time-frequency" large-scale channel data on the partial frequency band of a single user obtained by measurement is decomposed,and the Vandermonde structure of the frequency dimension is used to complete the measurement data of the partial frequency band to the full frequency band,so as to obtain the full frequency band data at the current moment.The above two typical applications all demonstrate the effectiveness of the method proposed in this paper.