It’s always good to check some videos, which I always feel it’s a much easier way to catch up the key ideas, and also enjoy a “relax”.
I found this one is particular interesting, which explains a lot to me for the “unlinear” in the manifold assumption.
-> Differences with clustering methods, such as k-means:
Clustering not according to the “cluster”, but according to certain “structures”, such as lines, surface, etc
-> The unlinear is relating to the assumed manifold ( line, surface…) to be un-linear
-> Each manifold subspace is not necessary to be the same structure, or to be have the same dim ( degree of the polynomial)
I think this is most “loose” point, with the advantage to model complex structure, but with the disadvantage of the lack of constraints. Also, to estimate the parameters of “subspace”, such as dim may not be a trivial work especially for complex data set.