Graph Laplacian and adjacency matrix
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Does anyone know an afficient way to compute sparse adjacency matrix and Graph Laclcian directly from a data matrix ?
I saw there are function called 'adjacency' and 'laplacian which get graph object and return the adjacency/graph laplacian matrix but i wonder if there are functions which calcute it directly over a data matrix?
That means i have large data matrix Nxd (where N is the number of data point , let assue 50,000 and d is a sample dimention , assume d=100)
I would like that the adjacency matrix will return NXN sparse matrix W which contain a measure of distance (euclidian/RBF or someting like that) between the data points (not all of them necesserly. lets assume that only to the 50 nearest neigbours so we get a sparse matrix).
and the laplacian is L=D-W where D is diagonal matrix contains W cloums' sum.
I tried to implement it by myself but i found it very inefficient so i wondered if there id something built-in in Matlab ?