从压缩数据中直接学习非负矩阵分解，省去多次访问原始数据
Learning nonnegative matrix factorizations from compressed data
- 基于随机拟合压缩数据，仅需访问原始数据1-2次
- 在压缩数据上优化，仍能逼近原始矩阵的低秩非负分解
- 适用于大规模数据，适合对效率要求高的场景
我们提出一种灵活且理论支持的可扩展非负矩阵分解框架。目标是直接从压缩测量中求解非负低秩成分，仅需访问原始数据一次或两次。通过可自适应或无感知的随机拟合方法进行压缩，构建仅依赖压缩数据的优化问题，但能恢复出接近原始矩阵的非负分解。所提出的优化问题可采用多种算法求解，特别讨论了适用于压缩问题的乘法更新法变体。实验验证了方法的有效性，并在真实应用场景中展示了其性能。
原文摘要 · Abstract (English)
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or twice. We consider compression through randomized sketching methods that can be adapted to the data, or can be oblivious. We formulate optimization problems that only depend on the compressed data, but which can recover a nonnegative factorization which closely approximates the original matrix. The defined problems can be approached with a variety of algorithms, and in particular, we discuss variations of the popular multiplicative updates method for these compressed problems. We demonstrate the success of our approaches empirically and validate their performance in real-world applications.
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