Representation learning is an important topic in machine learning, pattern recognition, and data mining research. Among many representation learning approaches, semi-nonnegative matrix factorization (SNMF) is a frequently-used one. However, a typical problem of SNMF is that usually there is no learning rate guidance during the optimization process, which often leads to a poor representation ability. To overcome this limitation, we propose a very general representation learning framework (DNSRF) that is based on a deep neural net. Essentially, the parameters of the deep net used to construct the DNSRF algorithms are obtained by matrix element update. In combination with different activation functions, DNSRF can be implemented in various ways. In our experiments, we tested nine instances of our DNSRF framework on six benchmark datasets. In comparison with other state-of-the-art methods, the results demonstrate the superior performance of our framework, which is thus shown to have a great representation ability.

Clustering is a popular research topic in the field of data mining, in which the clustering method based on non-negative matrix factorization (NMF) has been widely employed. However, in the update process of NMF, there is no learning rate to guide the update as well as the update depends on the data itself, which leads to slow convergence and low clustering accuracy. To solve these problems, a generalized deep learning clustering (GDLC) algorithm based on NMF is proposed in this article. Firstly, a nonlinear constrained NMF (NNMF) algorithm is constructed to achieve sequential updates of the elements in the matrix guided by the learning rate. Then, the gradient values corresponding to the element update are transformed into generalized weights and generalized biases, by inputting the elements as well as their corresponding generalized weights and generalized biases into the nonlinear activation function to construct the GDLC algorithm. In addition, for improving the understanding of the GDLC algorithm, its detailed inference procedure and algorithm design are provided. Finally, the experimental results on eight datasets show that the GDLC algorithm has efficient performance.