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Article summary:
1. A new descent direction for rank-one SNMF is derived and a strategy for choosing the step size along this descent direction is established.
2. A progressive hierarchical alternating least squares (PHALS) method for SNMF is developed, which is parameter-free and updates the variables column by column.
3. The convergence to the Karush-Kuhn-Tucker (KKT) point set (or the stationary point set) is proved for PHALS.
Article analysis:
The article appears to be reliable and trustworthy as it provides evidence of its claims in the form of synthetical and real data sets that demonstrate the effectiveness and efficiency of the proposed method. Furthermore, it provides a detailed description of its methodology, including a new descent direction for rank-one SNMF, a strategy for choosing the step size along this descent direction, and a proof of convergence to the KKT point set or stationary point set. However, there are some potential biases that should be noted. For example, there may be an emphasis on certain aspects of the research while other aspects are not explored in depth or ignored altogether. Additionally, there may be one-sided reporting or unsupported claims made without sufficient evidence to back them up. Finally, possible risks associated with using this method may not be adequately addressed in the article.