Bayesian tensor completion algorithm based on multiple measurement values

Abstract

The invention provides a Bayesian tensor complementation algorithm based on multiple measurement values, which comprises the following steps of: representing multiple measurement value data by using multiple tensors, and setting each measurement value of each tensor element of the tensors to obey Gaussian distribution; performing CP decomposition on the tensor to obtain a corresponding factor matrix, and setting parameters of the factor matrix to obey conjugate prior distribution; and then a Gibbs sampling method is adopted to sample the posterior condition distribution of each parameter, an estimated value of the tensor is output, interpolation is performed on missing values in the multi-measurement-value data based on the estimated value of the tensor, and thus data completion is realized. In conclusion, according to the complementation method, aiming at measurement data which is low in measurement precision and high in cost and is repeatedly measured for multiple times in some areas, the Gibbs sampling method is combined with CP decomposition to realize data complementation, and compared with a complementation method in the prior art, due to the fact that information of all the measurement data can be utilized by the method, the data complementation efficiency is improved. Therefore, a more accurate estimation value can be provided, and more accurate data completion is realized.

Description

technical field [0001] The invention belongs to the technical field of tensor completion, and in particular relates to a Bayesian tensor completion algorithm based on multiple measurement values. Background technique [0002] Tensors are high-dimensional arrays, a generalization of vectors and matrices, and can be used to express multidimensional data with complex intrinsic structures. Tensors are a natural representation of real-world high-dimensional data. For example, a color image can be viewed as a three-dimensional tensor, where one dimension is the color pattern and the other two are spatial variables. A video consisting of color images is a tensor with four dimensions, and the fourth dimension is the time variable. Therefore, tensor analysis is currently an important tool in multidimensional data analysis, and has applications in many fields, such as computer vision, data mining, and collaborative filtering. Therefore, the data completion method based on tensor an...

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Problems solved by technology

[0004] The present invention is carried out in order to solve the above-mentioned problems, and provides an efficient method MBGCP (Multiple Bayesian Gaussian CANDECOMP / PARAFAC) for tensor data with high measurement accuracy and low cost and repeated measurement times in some areas, using Gibbs The sampling method combines the decomposition to estimate the missing tensor element data. Compared with the existing method, the data at the same point is averaged and then BGCP (Bayesian Gaussian CANDECOMP / PARAFAC) is used to estimate the missing value. This method can use all data information, To provide a more accurate estimated value, the present invention adopts the following technical solutions:

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