What makes Spectral clustering better than Kmeans clustering? I understand that Kmeans clustering is the final step of Spectral. But why is it that the previous steps involved in Spectral clustering make it a more convenient clustering approach?
Visually speaking, k means cares about distance (Euclidean?) while spectral is more about connectivity since it is semi-convex.
So, your problem will direct you to which to use (geometrical or connectivity).
See more at: https://www.google.es/url?sa=t&source=web&rct=j&url=http://www.cis.hut.fi/Opinnot/T-61.6020/2008/spectral_kmeans.pdf&ved=2ahUKEwj27u_BkM7cAhVSOBoKHZH4DxIQFjACegQICxAP&usg=AOvVaw1wlx7URr__chq6JcteR9np
Spectral clustering usually is spectral embedding, followed by k-means in the spectral domain.
So yes, it also uses k-means. But not on the original coordinates, but on an embedding that roughly captures connectivity. Instead of minimizing squared errors in the input domain, it minimizes squared errors on the ability to reconstruct neighbors. That is often better. The main reason why spectral clustering is not too popular is because it is slow (usually involves building a O(n²) affinity matrix, and finding the eigenvectors can be up to O(n³) time) and you still need to rely on the original distances/similarities to build the input graph before embedding. Most of the difficulty of clustering is in handling the data to get reliable distances/similarities...