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Grid Cells: Global positioning system that helps people navigate
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Inside the Nucleus: Chromosome Territories
Tan, Longzhi, et al. "Three-dimensional genome structures of single diploid human cells." Science 361.6405 (2018): 924-928.
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A Tensor is an 𝑑-way array
If you need more information, these references are helpful:�
The following slides contain material from Tammy Kolda, Charles Van Loan and Lars Elden
Tensor Decompositions
What is a Tensor
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Tensor
Definition:
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Notations
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Tensor Unfolding
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A Common Framework for Tensor Computations
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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Unfolding (matricizing) of a third-order tensor
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SVD Expansion
Tensor Decompositions
CP Model: Sum of d-way outer products, useful for interpretation
Tucker Model: Project onto high-variance subspaces to reduce dimensionality
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The Kronecker Product
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The Kronecker Product
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All Possible Entry- Entry Products
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Kronecker Products of Kronecker Products
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You have seen them before
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Block matrix
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Block Matrices: Addition
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Block Matrix: Multiplication
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Block Matrix: Transposition
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A block matrix can have block matrix entries
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Reshape
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Reshape
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SVD
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SVD
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The Tucker product
Definition:
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The Tucker product representation
Before…
Now…
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The Higher-Order SVD (HOSVD)
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The HOSVD of a matrix
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The HOSVD of a matrix