An autoencoder-like deep NMF representation learning algorithm for clustering

Clustering plays a crucial role in the field of data mining, where deep non-negative matrix factorization (NMF) has attracted significant attention due to its effective data representation. However, deep matrix factorization based on autoencoder is typically constructed using multi-layer matrix factorization, which ignores nonlinear mapping and lacks learning rate to guide the update. To address these issues, this paper proposes an autoencoder-like deep NMF representation learning (ADNRL) algorithm for clustering. First, according to the principle of autoencoder, construct the objective function based on NMF. Then, decouple the elements in the matrix and apply the nonlinear activation function to enforce non-negative constraints on the elements. Subsequently, the gradient values corresponding to the elements update guided by the learning rate are transformed into the weight values. This weight values are combined with the activation function to construct the ADNRL deep network, and the objective function is minimized through the learning of the network. Finally, extensive experiments are conducted on eight datasets, and the results demonstrate the superior performance of ADNRL.