Yousef Saad Department Of Computer Science And Engineering

Graph-based methods
➤ Start with a graph of data. e.g.:
graph of k nearest neighbors (k-NN
graph)
Want: Do a projection so as to preserve
the graph in some sense
➤ Define a graph Laplacean:
e.g.,: wij =
L = D − W
1 if j ∈ Ni
0 else
with Ni = neighborhood of i (excl. i)
D = diag
⎡
x
i
x j
y i
⎣dii =
j=i
y j
wij
⎤
⎦
CSE Colloquium 11/09/09 p. 62