such great presentation with great insights. so we can interpret a vector as a scalar function on the vertex set. multiplication with the adj matrix can be seen as averaging out this function wrt to its neighbors. so in a way, this is like the linear-algebraic version of the heat equation
this smoothing interpretation makes the normalized laplacian the undisputed discrete counterpart to the riemannian laplacian. in short, the C0 story of the laplacian is measuring the difference between the function value and its average (this is an adaptation of harmonic functions satisfying the mean-value-property). therefore, the discrete analog of this story is to consider I - AD^{-1}, where I is the id matrix, A is the adj matrix, and D is the diagonal matrix.
If A and B nodes have two edges to each other, in the adjacency matrix (UNDIRECTED G) is it Aij=1 or 2(there's an edge yes=1, there are two edges =2)? Which one is correct? Also if A-B there's no edge but B-A a has an edge(direction) it should be calculated for both right?
I got a little confused till I realized that Adjacency matrix must be symmetrical (so the pic on the presentation was misleading?). So for n nodes the A matrix must be nxn and symmetrical.
Quite possibly the best concise definition to a problem and solution I've seen
Give this man everything
This guy deserves work in Stanford!! He is awesome!!
This guy is a prof in stanford. :p
Great explanation of Laplacian matrix and graph concepts.
Very clear so far! Thank you
such great presentation with great insights.
so we can interpret a vector as a scalar function on the vertex set. multiplication with the adj matrix can be seen as averaging out this function wrt to its neighbors. so in a way, this is like the linear-algebraic version of the heat equation
this smoothing interpretation makes the normalized laplacian the undisputed discrete counterpart to the riemannian laplacian. in short, the C0 story of the laplacian is measuring the difference between the function value and its average (this is an adaptation of harmonic functions satisfying the mean-value-property). therefore, the discrete analog of this story is to consider I - AD^{-1}, where I is the id matrix, A is the adj matrix, and D is the diagonal matrix.
If A and B nodes have two edges to each other, in the adjacency matrix (UNDIRECTED G) is it Aij=1 or 2(there's an edge yes=1, there are two edges =2)? Which one is correct? Also if A-B there's no edge but B-A a has an edge(direction) it should be calculated for both right?
The clusters are so clear when you look at the adjacency matrix
I got a little confused till I realized that Adjacency matrix must be symmetrical (so the pic on the presentation was misleading?). So for n nodes the A matrix must be nxn and symmetrical.
Hi, I'd like to ask what if the undirected graph is weighted (not binary), will the process of spectral clustering be changed?
I understood the concepts but he never defined what the Graph Laplacian Matrix was....
outstanding
can’t ignore how he pronounces “pieces”
good
he sounds like a young slovaj zizek
on point haha
I REALLY WANNA TO LEARN, BUT I CAN'T ACCEPT THE PRONUNCIATION! Drive Me Crazy.