Normalize Cut in Matrix Form
);
,
(
)
,
(
:
i
node
from
costs
of
sum
the
is
;
)
,
(
:
matrix
cost
the
is
,
j
i
i
i
w
j
i
j
j
i
=
=
ĺ
W
D
D
W
W
After lots of math, we get:
•
Solution given by “generalized” eigenvalue problem:
•
•
Solved by converting to standard eigenvalue problem:
•
•
•
optimal solution corresponds to second smallest eigenvector
•
for more details, see
–
J. Shi and J. Malik,
Normalized Cuts and Image Segmentation
, IEEE
Conf. Computer Vision and Pattern Recognition(CVPR), 1997