Non-negative Matrix Factorization Based On Local Similarity Learning

An important principle in scientific research is that there are always simple parts that play an important role in most chaotic things.The same is true in data processing,image recognition,artificial intelligence,machine learning,etc.With the vigorous development of computer technology and the Internet,and the improvement of data storage technology,the scale of original data has become larger and larger.At the same time,how to express data concisely and clearly is the goal of current research.Experiments show that multi-dimensional datum reduces the dimensionality of the original data through appropriate dimensionality reduction,and finally extracts the main characteristics of the data,which is currently the most effective and low method.In the current research,the non-negative matrix factorization is under the constraint of non-negative data,and the final matrix obtained by the factorization can effectively express the nature of the data itself.The current mainstream non-negative matrix factorization algorithms focus on learning the overall structure of the data to construct the basis matrix and coefficient matrix,while ignoring the local similarity that generally exists between the data.Therefore,a new type of non-negative matrix factorization model is proposed in this thesis.The model learns global structure and local similarity in a mutually promoting way.The finally learned algorithm model is more robust and can better extract the inherent geometric characteristics of the data.The proposed model first integrates local similarity learning into the matrix decomposition.At this time,the proposed model can learn the global structure and local structure of the data,and the basis matrix learned can well retain the inherent structure of the data.At the same time,the matrix is constrained to be orthogonal and applied to the local similarity,so that the local similarity and non-negative matrix factorization can promote each other.Then the proposed model use the properties of the kernel function to map the nonlinear data to the kernel space to realize the data separability,so that the model can learn the global and local nonlinear structure of the data.Finally,an effective multiplication update rule is constructed to solve the proposed model,and a comprehensive theoretical analysis is provided to ensure convergence,Extensive experiments confirmed the effectiveness of the proposed algorithm model.