© The Institution of Engineering and Technology
Low-rank representation (LRR) intends to find the representation with lowest rank of a given data set, which can be formulated as a rank-minimisation problem. Since the rank operator is non-convex and discontinuous, most of the recent works use the nuclear norm as a convex relaxation. It is theoretically shown that, under some conditions, the Frobenius-norm-based optimisation problem has a unique solution that is also a solution of the original LRR optimisation problem. In other words, it is feasible to apply the Frobenius norm as a surrogate of the non-convex matrix rank function. This replacement will largely reduce the time costs for obtaining the lowest-rank solution. Experimental results show that the method (i.e. fast LRR (fLRR)) performs well in terms of accuracy and computation speed in image clustering and motion segmentation compared with nuclear-norm-based LRR algorithm.
References
-
-
1)
-
5. Tron, R., Vidal, R.: ‘A benchmark for the comparison of 3-D motion segmentation algorithms’. IEEE Conf. Computer Vision and Pattern Recognition, Minneapolis, MN, USA, June 2007.
-
2)
-
A.S. Georghiades ,
P.N. Belhumeur ,
D.J. Kriegman
.
From few to many: illumination cone models for face recognition under variable lighting and pose.
IEEE Trans. Pattern Anal. Mach. Intell.
,
6 ,
643 -
660
-
3)
-
3. Martinez, A.M.: ‘The AR face database’, , 1998.
-
4)
-
2. Yang, J., Zhang, Y.: ‘Alternating direction algorithms for L1-problems in compressive sensing’, SIAM J. Sci. Comput., 2011, 33, (1), pp. 250–278 (doi: 10.1137/090777761).
-
5)
-
6. Ng, A.Y., Jordan, M.I., Weiss, Y.: ‘On spectral clustering: analysis and an algorithm’. Advances in Neural Information Processing Systems, Vancouver, Canada, December 2002.
-
6)
-
1. Liu, G., Lin, Z., Yan, S., et al: ‘Robust recovery of subspace structures by low-rank representation’, IEEE Trans. Pattern Anal. Mach. Intell., 2013, 35, (1), pp. 171–184 (doi: 10.1109/TPAMI.2012.88).
http://iet.metastore.ingenta.com/content/journals/10.1049/el.2014.1396
Related content
content/journals/10.1049/el.2014.1396
pub_keyword,iet_inspecKeyword,pub_concept
6
6