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I have been researching modern exploratory data analysis techniques, and came across two promising approaches: Topological Data Analysis (TDA) and Tensor Decomposition/Factorization (TF).

I am looking for a laymen's overview of the differences between the two approaches, particularly regarding the outputs of the analysis. My understanding is that TDA provides a summary of the intrinsic shape of the data (i.e. the manifold the data were sampled from - e.g. sphere); whereas; TF helps reveal the latent factors and structure of the data (e.g. TF can be used to reveal latent time-dependent topics using a 3-tensor of the form user x term x time).

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