Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous state-of-the-art. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.
翻译:最近的文件为氯化石蜡和高压环分解开发了交替最小方(ALS)方法,其每平方位分解成本在低级分解的输入高压条目数量上为次线,然而,当选择参数以实现某些最坏情况的保证时,这些方法的渗透成本仍然指数取决于多方位模式的数量。我们在本文件中为成本不具有这种指数依赖性的氯化石蜡和高压环分解提出了基于取样的反光线方法,从而大大改进了以前的先进工艺。我们提供了详细的理论分析,并在特征提取实验中应用了这种方法。