Here are my uninsightful contribution. I guess you can easily tell from my questions that I don't understand this paper.

1. What's the difference between segmentation and clustering? I thought segmentation is only clustering with affinity metric that is related to image properties. Is this correct, or are there any more profound differences. It seems that the algorithms that we talked about can be used directly to non-image data (such as linguistic corpus.)

2. I don't really understand how spectral methods can be understood as continous approximations of discrete graphs. What does "continous" mean in this sense?

3. I think Proposition 2 is neat in that it gives a more complete description to the eigenvectors. However, the idea of agrregated Markov chain is quite abstract to me, and I don't have any intuition about what it means in terms of image. It seems to say that "the eigenvectors are piecewise constant when the image can be segmented in to k partitions (eg. k Markov processes)", but isn't that circular?

4.I don't understand how the KL divergence comes into play
in the algorithm (probably because I don't know any Markov chain). It seems suggest that the whole algorithm can be interpreted in a information-theoretical framework.

5. Not related to this paper: What are the useful features if we want to segment 3D images (eg. MRI)?