  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.
