Parallelize Research And Application Of Tensor Decomposition Algorithm Based On GAS Computing Model

Tensor is a multi-dimensional extension of the matrix,naturally representing the multi-dimensional data.Tensor data is widely used in many fields such as social network,recommendation system and so on.Tensor decomposition is the main method to analyze the tensor data,which can be used for principal component analysis,data compression,missing value completion,etc.The current tensor decomposition algorithm is mostly based on the MATLAB,which is a typical centralized processing method.When dealing with large scale tensor data,the size of the data is larger than the single machine's memory,making the traditional tensor decomposition algorithm cannot satisfy the computing demand.The distributed processing method can divide the massive data into several nodes to participate in the operation,which saves the computation time and reduce the operation cost.Graph is a fundamental data structure that describes the interactions and complex relationships between different entities.In many fields,such as social network,graphs are used to capture the complex data.This paper mainly studies how to describe a tensor on the graph structure and parallels the tensor decomposition algorithm on graph structure based on the GAS computing model.The innovations and major work of this article are as follows:1)Parallel matrix decomposition algorithm based on GAS computing modelMatrix is a two-order tensor that widely used in social network analysis and recommendation system.We design a graph model of matrix decomposition after analyzing the principle of matrix decomposition and implement the parallel matrix decomposition SGD algorithm and ALS algorithm on the graph structure based on the GAS computing model.Moreover,the effectivity and scalability of the parallel matrix decomposition algorithm are verified on the PowerGraph framework.2)Parallel tensor decomposition algorithm based on GAS computing modelWe extend the matrix decomposition algorithm to high-dimensional tensor and design the graph model of tensor decomposition.The parallel tensor decomposition CP-ALS algorithm is realized on the graph model based on GAS computing model.Furthermore,the effectivity and scalability of the parallel tensor decomposition algorithm are verified on the PowerGraph framework.3)Parallel missing data completion algorithm based on tensor decompositionThe raw data obtained in real problems is not always complete,and there are often missing values.It is necessary for us to complete the missing data according to the existing values in original data.In order to solve this problem,the missing data completion algorithms are designed based on tensor decomposition algorithms(two-order tensor and three-order tensor).As for large scale data,we parallel the completion algorithm on the graph structure based on GAS computing model and verify the effectivity and scalability of the algorithm through the Movie Lens data set.