TY - GEN

T1 - LDR-LLE

T2 - 4th International Symposium on Visual Computing, ISVC 2008

AU - Goldberg, Yair

AU - Ritov, Ya'Acov

PY - 2008

Y1 - 2008

N2 - The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique that is widely used for its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in a low-dimensional embedding. We show that the reconstruction weights computed by LLE capture the high-dimensional structure of the neighborhoods, and not the low-dimensional manifold structure. Consequently, the weight vectors are highly sensitive to noise. Moreover, this causes LLE to converge to a linear projection of the input, as opposed to its non-linear embedding goal. To resolve both of these problems, we propose to compute the weight vectors using a low-dimensional neighborhood representation. We call this technique LDR-LLE. We present numerical examples of the perturbation and linear projection problems, and of the improved outputs resulting from the low-dimensional neighborhood representation.

AB - The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique that is widely used for its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in a low-dimensional embedding. We show that the reconstruction weights computed by LLE capture the high-dimensional structure of the neighborhoods, and not the low-dimensional manifold structure. Consequently, the weight vectors are highly sensitive to noise. Moreover, this causes LLE to converge to a linear projection of the input, as opposed to its non-linear embedding goal. To resolve both of these problems, we propose to compute the weight vectors using a low-dimensional neighborhood representation. We call this technique LDR-LLE. We present numerical examples of the perturbation and linear projection problems, and of the improved outputs resulting from the low-dimensional neighborhood representation.

UR - http://www.scopus.com/inward/record.url?scp=70149117739&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-89646-3_5

DO - 10.1007/978-3-540-89646-3_5

M3 - Conference contribution

AN - SCOPUS:70149117739

SN - 3540896457

SN - 9783540896456

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 43

EP - 54

BT - Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings

Y2 - 1 December 2008 through 3 December 2008

ER -