Biased unconstrained non-negative matrix factorization for clustering

摘要

Clustering remains a challenging research hotspot in data mining. Non-negative matrix factorization (NMF) is an effective technique for clustering, which aims to find the product of two non-negative low-dimensional matrices that approximates the original matrix. Since the matrices must satisfy the non-negative constraints, the Karush–Kuhn–Tucker conditions need to be used to obtain the update rules for the matrices, which limits the choice of update methods. Moreover, this method has no learning rate and the updating process is completely dependent on the data itself. In addition, the two low-dimensional matrices in NMF are randomly initialized, and the clustering performance of the model is reduced. To address these problems, this paper proposes a biased unconstrained non-negative matrix factorization (BUNMF) model, which integrates the norm and adds bias. Specifically, BUNMF uses a non-linear activation function to make elements of the matrices to remain non-negative, and converts the constrained problem into an unconstrained problem. The matrices are renewed by sequentially updating the matrices’ elements using stochastic gradient descent to obtain an update rule with a learning rate. Furthermore, the BUNMF model is constructed by three different activation functions and their iteration update algorithms are given through detailed reasoning. Finally, experimental results on eight public datasets show the effectiveness of the proposed model.