TCA issue computing matrix

[etiennevandebijl]

Hi,

I am implementing TCA and saw an issue in line 126 of _tca.py file:
Implemented is the following:
a = np.eye(n+m) + self.mu * K.dot(L.dot(K))
However, according to the authors, it should be: K.dot(L.dot(K)) + self.mu * np.eye(n+m) (mu should be multiplied with the identity matrix)
I hope this helps.

[antoinedemathelin]

Hi @etiennevandebijl,
Thank you for your help!
Are you sure that the optimization should be K.dot(L.dot(K)) + self.mu * np.eye(n+m)? In the TCA paper, I see np.eye(n+m) + self.mu * K.dot(L.dot(K)) (cf. last paragraph of page 3).

But maybe the adapt documentation is wrong, it is written that "The larger mu is, the less adaptation is performed." but it may be the opposite...

[etiennevandebijl]

Hi @antoinedemathelin,

Thank you for looking into this. Indeed, in this unpublished version of the article proposing TCA, it is written as np.eye(n+m) + self.mu * K.dot(L.dot(K)). However, in the published peer-reviewed version of TCA it is K.dot(L.dot(K)) + self.mu * np.eye(n+m), see page 204 right above Algorithm 1. It doesn't unfortunately result in the same result, but I think it might be a choice of which work to implement...