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November 2, 2021

BIOINF/MATH 540: Mathematics of Biological Networks

Tensors and Hypergraphs

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What is a Tensor

 

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A Tensor is an 𝑑-way array

 

 

 

 

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A Tensor is an 𝑑-way array

 

 

 

 

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Notations

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Tensor

Definition:

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Tensor unfolding

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Illustration of row-wise and column-wise unfolding (flattening, matricizing) of a third-order tensor

Andrzej Cichocki, Rafal Zdunek, and Shun'ichi Amari. Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source (2009)

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A Common Framework for Tensor Computations

Tensor unfolding

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Reshape

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Reshape

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SVD

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SVD

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Hypergraphs

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Hypergraphs