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danielemarinazzo / KernelGrangerCausality

Code to evaluate nonlinear Granger causality using the kernel trick to reduce complexity
BSD 3-Clause "New" or "Revised" License
34 stars 14 forks source link

Hello, I would like to inquire about a question regarding a formula in a paper. #3

Closed symbold closed 5 months ago

symbold commented 5 months ago

Hello, I would like to inquire about a question regarding a formula in a paper. Why is the 2-norm of ( x - \tilde{x} ) equal to ( 1 - \tilde{x}^T \tilde{x} )? 微信截图_20240518113717

danielemarinazzo commented 5 months ago

The expansion gives xTx - 2 xTx̃' + x̃'Tx̃'. But xTx̃' = x̃'Tx̃' given that x-x̃' is orthogonal to x̃'. So we're left with xTx-x'Tx̃'. xTx is equal to 1.

symbold commented 5 months ago

I got it, thank you very much for your help.