Analyzing Tensor Power Method Dynamics in Overcomplete Regime

@article{Anandkumar2017AnalyzingTP,
  title={Analyzing Tensor Power Method Dynamics in Overcomplete Regime},
  author={Anima Anandkumar and Rong Ge and Majid Janzamin},
  journal={Journal of Machine Learning Research},
  year={2017},
  volume={18},
  pages={22:1-22:40}
}
We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. We consider the case where the tensor components are randomly drawn, and show that the simple power iteration recovers the components with bounded error under mild initialization conditions. We apply our analysis to unsupervised learning of latent variable… CONTINUE READING
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