Query on calculating angles between dPCs: Encoder (V) vs. Decoder (W) matrix

[XiaoyuZeng]

Thank you for developing and maintaining this highly valuable repository！

I am currently investigating the geometric overlap between the low-dimensional representations of two distinct task variables. To accurately calculate the angle (or principal angles) between the optimal dPCs corresponding to these two variables, I would like to clarify whether I should use the encoding axes or the decoding axes.

Specifically, in your MATLAB implementation, should this orthogonality computation be performed using the columns of the Encoder matrix (V) or the Decoder matrix (W)?
The original 2016 eLife paper evaluates the "Angles between dPCs" using the encoding axes ($f_1$ and $f_2$), which logically maps to the Encoder matrix (V) in the code. However, since the latent trajectories are projected via the Decoder matrix (W), I want to rigorously confirm the mathematically appropriate matrix for assessing the overlap of representational subspaces between different marginalizations.

Thank you for your time.

[dkobak]

I still think that evaluating angles between encoding axes is conceptually more meaningful. In my mind the decoding axes are more of a auxiliary concept, only needed to recover the latent factors.