Nonnegative Matrix Factorization with Local Similarity Learning
This is an incremental improvement for data analysis and machine learning applications, addressing a specific limitation in matrix factorization techniques.
The paper tackled the problem of existing nonnegative matrix factorization methods ignoring local data structure by proposing a new method that learns local similarity and clustering mutually, resulting in a more representative representation with confirmed effectiveness in experiments.
Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new type of nonnegative matrix factorization method, which learns local similarity and clustering in a mutually enhancing way. The learned new representation is more representative in that it better reveals inherent geometric property of the data. Nonlinear expansion is given and efficient multiplicative updates are developed with theoretical convergence guarantees. Extensive experimental results have confirmed the effectiveness of the proposed model.