This paper studies automatic segmentation of multiple
motions from tracked feature points through spectral embedding
and clustering of linear subspaces. We show that
the dimension of the ambient space is crucial for separability,
and that low dimensions chosen in prior work are not
optimal. We suggest lower and upper bounds together with
a data-driven procedure for choosing the optimal ambient
dimension. Application of our approach to the Hopkins155
video benchmark database uniformly outperforms a range
of state-of-the-art methods both in terms of segmentation
accuracy and computational speed