Hm, stretching seems handleable. How about also using the weight matrix, for example? Change into the eigenbasis above, then apply stretching to make all L2 norms size 1 or size 0. Then look at the weights, as stretching-and-rotation invariant quantifiers of connectedness?
Maybe doesn’t make much sense when considering non-linear transformations though.
Sai, who is a lot more topology-savy than me, now suspects that there is indeed a connection between this norm approach and the topology of the intermediate set. We’ll look into this.
Ah, right, you did mention polar coordinates.
Hm, stretching seems handleable. How about also using the weight matrix, for example? Change into the eigenbasis above, then apply stretching to make all L2 norms size 1 or size 0. Then look at the weights, as stretching-and-rotation invariant quantifiers of connectedness?
Maybe doesn’t make much sense when considering non-linear transformations though.
I think that’s the same as finding a low-rank decomposition, assuming I correctly understand what you’re saying?
Sai, who is a lot more topology-savy than me, now suspects that there is indeed a connection between this norm approach and the topology of the intermediate set. We’ll look into this.