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Spectral Graph Clustering: where does the 'scoring' function come from
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[QUOTE="Master1022, post: 6603803, member: 650268"] [B]Homework Statement:[/B] For an undirected graph with affinity matrix (i.e. weighted adjacency matrix) ##A##, how can we determine a good cluster using eigenvalues and eigenvectors. [B]Relevant Equations:[/B] Eigenvectors and eigenvalues Hi, I was reading through some slides about graph clustering. In the slides was a very short discussion about 'eigenvectors and segmentation'. I don't quite understand where one of the formulae comes from. [B]Context: [/B]We have some undirected graph with an affinity matrix (i.e. weighted adjacency matrix) ##A##. The slide poses the question: [I]What is a good cluster?[/I] It then says: "The element associated with the cluster should have large values connecting one another in the affinity matrix." and then quotes the following formula: [tex] \mathbf{w}_n ^T A \mathbf{w} [/tex] where it defines ##\mathbf{w}_{n} ^ T ##[I] = association of element ##i## to cluster ##n##. It then says we can impose a scaling requirement such that ## \mathbf{w}_n ^T \mathbf{w}_n = 1 ##. Putting these two equations together yields the familiar eigenvalue equation. [B]Question: [/B]Where does this first formula come from: ## \mathbf{w}_n ^T A \mathbf{w} ##? As much as I think about it, it doesn't really make much sense to me. I can understand the latter parts of the slide, so if I just move past my misunderstanding, then the rest falls into place. However, I am keen to understand what that 'score' is really calculating.[/I] [/QUOTE]
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Spectral Graph Clustering: where does the 'scoring' function come from
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