Research On Structured Matrix Factorization Algorithm

With the development of information technology,we have entered the era of big data.How to effectively mine useful information from data has always been a research hotspot in the field of data mining.The data analysis method based on matrix factorization can effectively excavate the structured information in the data,so it is of great theoretical and application value to study the structured matrix factorization algorithms.This paper intends to design a structured matrix factorization algorithm that satisfies multiple applications based on the Concept Factorization(CF)model and the Extreme Learning Machine(ELM)model.The main research work of this article is as follows:(1)Joint structured graph learning and clustering algorithm based on concept factorization model.The core content of graph-based learning methods is to construct a graph and then do machine learning tasks on the graph.The quality of the graph is related to the performance of the algorithm,so the key to this method is how to construct a high-quality graph.Traditional graph-based learning methods usually have two major problems:1)"Machine learning before constructing the graph" causes the construction to be separated from the subsequent learning process;2)Structural constraints are rarely imposed on the graph during the construction process makes the graphs less discriminative.Aiming at the above problems,this paper proposes a joint structured graph learning and clustering(JSGCF)algorithm based on the concept factorization model.The algorithm treats the concept factorization model as a self-representation model,and proposes to treat the coefficient product matrix as a graph correlation matrix.Based on the rank constraint condition,the number of connected subgraphs of the corresponding graph is emphasized as the number of clusters,thereby constructing a high-quality graph directly used for clustering.Experimental results show that the proposed JSGCF algorithm has better clustering performance than the Kmeans,NCut,NMF,CF,and LCCF algorithms.(2)Extreme learning machine algorithm based on matrix factorization.ELM is a learning algorithm based on a single hidden layer feedforward neural network.Its biggest feature is that the weights of hidden layer nodes are randomly determined without updating and only the output weights are calculated during the learning process.However,ELM does not consider the structured information in the data when processing the data,resulting in insufficient performance when processing certain high-dimensional data.In this paper,based on the ELM model,this paper proposes a factorized extreme learning machine(FELM)algorithm.The algorithm is based on matrix factorization technology,by adding a hidden layer between the ELM hidden layer and the output layer to factorize the output weights,so as to effectively consider the structured discrimination information of the data,and combine the group sparse representation method to better fit the data.And then build a learning algorithm based on double hidden layer feedforward neural network.Emotion recognition experiments based on EEG signals show that the proposed FELM algorithm has better classification performance than SVM and ELM algorithms.