Review Article
A Review of Subspace Segmentation: Problem, Nonlinear Approximations, and Applications to Motion Segmentation
Algorithm 1
Subspace segmentation—row echelon form approach—no noise.
Require: data matrix W. | 1: Find rref (W) of W. | 2: Find Brref (W) of W by setting all non-zero entries of rref (W) to 1. | 3: for all from 1 to do | 4: Pick the th column of Brref (W). | 5: if is pivot then | 6: continue | 7: end if | 8: for all from 1 to −1 do | 9: if is non-pivot and > 0 then | 10: Place in the same cluster . | 11: break | 12: end if | 13: end for | 14: end for | 15: for all do | 16: Pick any . | 17: Separate into unit vectors . {These vectors form a basis for a subspace | with dimension .} | 18: for all from 1 to do | 19: if then | 20: Place in the same cluster . {This is for handling pivot columns.} | 21: end if | 22: end for | 23: Place the corresponding columns in W into the same cluster . | 24: end for | 25: Renumber indices ’s of starting from 1. |
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