Scalable Subspace Clustering with Application to Motion Segmentation 277
13.4.1 Dimension reduction
Dimension reduction is an essential pr e processing step for obtaining a g ood
motion segmentation. To realize this goal, the truncated SVD is often ap-
plied [5, 12, 17, 24].
To project the measurement matrix W ∈ R
2F ×N
to X = [x
1
, ..., x
N
] ∈
R
D×N
, where D is the desired projection dimension, the matrix W is decom-
posed via SVD as W = UΣV
T
and the first D columns of the matrix V are
chosen a s X
T
.
The value of D for dimension reduction is also a major concern in motion
segmentation. This value has a large impact on the speed and acc uracy of the
final result, so it is very important to select the best dimension to perform
the segmentation. The dimension