基于图正则化和稀疏约束的增量型非负矩阵分解

摘要

Nonnegative matrix factorization (NMF) not only is a description of the data,but also has intuitive physical meaning after the decomposition of the matrix.With the aim to enhance the validity and classification accuracy,a more reasonable algorithm was proposed,which is graph regularized and incremental nonnegative matrix factorization with sparseness constraints (GINMFSC).It not only preserves the intrinsic geometry of data,but also makes full use of the last step decomposition results as incremental learning,and introduces sparseness constraint to coefficient matrix.Final ly,they are integrated into one single objective function and an efficient updating approach is produced.Compared with NMF,GNMF,INMF and IGNMF,experiments on several databases have shown that the proposed method achieves better clustering accuracy and sparsity while reducing the computation time.%非负矩阵分解(Nonnegative Matrix Factorization,NMF)不仅可以很好地描述数据而且分解后的矩阵具有直观的物理意义.为了提高算法的有效性和识别率,提出了一种更为合理的算法——基于图正则化和稀疏约束的增量型非负矩阵分解(Graph Regularized and Incremental Nonnegative Matrix Factorization with Sparseness Constraints,GINMFSC).该算法既保持了数据的几何结构,又充分利用上一步的分解结果进行增量学习,而且对系数矩阵施加了稀疏性约束,最后将它们整合于单个目标函数中,构造了一个有效的更新算法.在多个数据库上的仿真结果表明,相对于NMF,GNMF,INMF,IGNMF等算法,GINMFSC算法在降低运算时间的同时,还具有更好的聚类精度和稀疏性.