Graph Laplacian and adjacency matrix

조회 수: 20 (최근 30일)
Orr Streicher
Orr Streicher 2021년 5월 5일
답변: Christine Tobler 2021년 6월 11일
Hi,
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 ?
Thanks alot
  댓글 수: 1
AMA
AMA 2021년 6월 11일
Hi, I have the same problem
did you solve it ?
kind Regards

댓글을 달려면 로그인하십시오.

답변 (2개)

Bruno Luong
Bruno Luong 2021년 6월 11일
편집: Bruno Luong 2021년 6월 11일
Not sure what data format you have, but for graph
% TMW example
s = [1 2 2 3 3 3 4 5 5 5 8 8 9];
t = [2 3 4 1 4 5 5 3 6 7 9 10 10];
G = graph(s,t);
A = G.adjacency;
D = diag(sum(A)); % degree matrix
L = D - A; % laplacian matrix
disp(L)
(1,1) 2 (2,1) -1 (3,1) -1 (1,2) -1 (2,2) 3 (3,2) -1 (4,2) -1 (1,3) -1 (2,3) -1 (3,3) 4 (4,3) -1 (5,3) -1 (2,4) -1 (3,4) -1 (4,4) 3 (5,4) -1 (3,5) -1 (4,5) -1 (5,5) 4 (6,5) -1 (7,5) -1 (5,6) -1 (6,6) 1 (5,7) -1 (7,7) 1 (8,8) 2 (9,8) -1 (10,8) -1 (8,9) -1 (9,9) 2 (10,9) -1 (8,10) -1 (9,10) -1 (10,10) 2

Christine Tobler
Christine Tobler 2021년 6월 11일
Take a look at pdist in the Statistics and Machine Learning toolbox. If you apply this to your matrix, and then call squareform on the result, it should give you the W matrix you're looking for. There's a choice of different distance measures to choose from in pdist.

카테고리

Help CenterFile Exchange에서 Networks에 대해 자세히 알아보기

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by