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A Non-Convex Optimization Framework for Large-Scale Low-rank Matrix Factorization
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  • Sajad Fathi Hafshejani ,
  • Saeed Vahidian ,
  • Zahra Moaberfard ,
  • Reza Alikhani ,
  • Bill Lin
Sajad Fathi Hafshejani
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Saeed Vahidian
UC San Diego, UC San Diego

Corresponding Author:[email protected]

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Zahra Moaberfard
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Reza Alikhani
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Low-rank matrix factorization problems such as non negative matrix factorization (NMF) can be categorized as a clustering or dimension reduction technique. The latter denotes techniques designed to find representations of some high dimensional dataset in a lower dimensional manifold without a significant loss of information. If such a representation exists, the features ought to contain the most relevant features of the dataset. Many linear dimensionality reduction techniques can be formulated as a matrix factorization. In this paper, we combine the conjugate gradient (CG) method with the Barzilai and Borwein (BB) gradient method, and propose a BB scaling CG method for NMF problems. The new method does not require to compute and store matrices associated with Hessian of the objective functions. Moreover, adopting a suitable BB step size along with a proper nonmonotone strategy which comes by the size convex parameter $\eta_k$, results in a new algorithm that can significantly improve the CPU time, efficiency, the number of function evaluation. Convergence result is established and numerical comparisons of methods on both synthetic and real-world datasets show that the proposed method is efficient in comparison with existing methods and demonstrate the superiority of our algorithms.
Dec 2022Published in Machine Learning with Applications volume 10 on pages 100440. 10.1016/j.mlwa.2022.100440