Dual Locality Preserving Nonnegative Matrix Factorization for image analysis

Furui Liu

Abstract: Recently, Nonnegative Matrix Factorization(NMF) has been viewed as an effective method for data engineering for its part-based interpretability and superior performance. However, ordinary NMF merely views a r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> × r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> image as a vector in r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> × r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> dimensional space and the pixels of the image are considered independent. It fails to consider that an image is intrinsically a matrix, and pixels spatially close to each other may also be correlated in the final learned representation. In this paper, I construct a novel spatially nearest graph and propose a novel algorithm named Dual Locality Preserving Nonnegative Matrix Factorization (DLPNMF), which explicitly models both the spatial correlation between neighboring pixels inside images and the geometric structure among different image vectors. A multiplicative rule is also proposed to solve the corresponding optimization problem. The encouraging experimental results on benchmark image data have demonstrated the effectiveness of this algorithm.