Abstract
We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural network, the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real-world data illustrate the effectiveness and performance of the proposed method.
Highlights
Dimensionality reduction plays a fundamental role in image processing, and many researchers have been seeking effective methods to solve this problem
Motivated by previous researches in matrix factorization, in this paper, we propose a novel method, called graph sparse nonnegative matrix factorization (GSNMF), for dimensionality reduction, which can be used for semi-supervised learning problems
To examine the clustering performance of GSNMF, we present the experiment in two databases including IRIS and COIL20
Summary
Dimensionality reduction plays a fundamental role in image processing, and many researchers have been seeking effective methods to solve this problem. This gives rise to a low-dimensional compact representation of the original data points, which can facilitate clustering or classification Among these matrix factorization methods, one of the most used methods is nonnegative matrix factorization (NMF) [3], which requires the decomposed matrices to be nonnegative. In the light of locality preserving projection, a graph regularized nonnegative matrix factorization method (GNMF) has been proposed to impose the geometrical information on the data space. Motivated by previous researches in matrix factorization, in this paper, we propose a novel method, called graph sparse nonnegative matrix factorization (GSNMF), for dimensionality reduction, which can be used for semi-supervised learning problems. (i) Traditional algorithms for GNMF [11] and NMF [3] can trap into local optimum solution, and these algorithms are sensitive to initial values, while our proposed algorithm using inertial projection neural network can avoid these problems.
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