A Quantum-inspired Classical Algorithm for Separable Non-negative Matrix Factorization

Non-negative Matrix Factorization (NMF) asks to decompose a (entry-wise) non-negative matrix into the product of two smaller-sized nonnegative matrices, which has been shown intractable in general. In order to overcome this issue, separability assumption is introduced which assumes all data points are in a conical hull. This assumption makes NMF tractable and widely used in text analysis and image processing, but still impractical for huge-scale datasets. In this paper, inspired by recent development on dequantizing techniques, we propose a new classical algorithm for separable NMF problem. Our new algorithm runs in polynomial time in the rank and logarithmic in the size of input matrices, which achieves an exponential speedup in the low-rank setting.

Authors

• Zhihuai Chen TCS Lab, Huawei Technologies Co., Ltd., China
• Yinan Li Central South University
• Xiaoming Sun Institute of Computing Technology, Chinese Academy of Sciences University of Chinese Academy of Sciences
• Pei Yuan
• Jialin Zhang Nanjing University of Aeronautics and Astronautics

Keywords

• Machine Learning Applications: Applications of Unsupervised Learning
• Machine Learning Applications: Big data; Scalability