TY - GEN

T1 - Incremental construction of low-dimensional data representations

AU - Kuleshov, Alexander

AU - Bernstein, Alexander

PY - 2016

Y1 - 2016

N2 - Various Dimensionality Reduction algorithms transform initial high-dimensional data into their lower-dimensional representations preserving chosen properties of the initial data. Typically, such algorithms use the solution of large-dimensional optimization problems, and the incremental versions are designed for many popular algorithms to reduce their computational complexity. Under manifold assumption about high-dimensional data, advanced manifold learning algorithms should preserve the Datamanifold and its differential properties such as tangent spaces, Riemannian tensor, etc. Incremental version of the Grassmann&Stiefel Eigenmaps manifold learning algorithm, which has asymptotically minimal reconstruction error, is proposed in this paper and has significantly smaller computational complexity in contrast to the initial algorithm.

AB - Various Dimensionality Reduction algorithms transform initial high-dimensional data into their lower-dimensional representations preserving chosen properties of the initial data. Typically, such algorithms use the solution of large-dimensional optimization problems, and the incremental versions are designed for many popular algorithms to reduce their computational complexity. Under manifold assumption about high-dimensional data, advanced manifold learning algorithms should preserve the Datamanifold and its differential properties such as tangent spaces, Riemannian tensor, etc. Incremental version of the Grassmann&Stiefel Eigenmaps manifold learning algorithm, which has asymptotically minimal reconstruction error, is proposed in this paper and has significantly smaller computational complexity in contrast to the initial algorithm.

KW - Dimensionality reduction

KW - Incremental learning

KW - Machine learning

KW - Manifold learning

KW - Tangent bundle manifold learning

UR - http://www.scopus.com/inward/record.url?scp=84988019865&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-46182-3_5

DO - 10.1007/978-3-319-46182-3_5

M3 - Conference contribution

AN - SCOPUS:84988019865

SN - 9783319461816

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

SP - 55

EP - 67

BT - Artificial Neural Networks in Pattern Recognition - 7th IAPR TC3 Workshop, ANNPR 2016, Proceedings

A2 - Schwenker, Friedhelm

A2 - Abbas, Hazem M.

A2 - El Gayar, Neamat

A2 - Trentin, Edmondo

PB - Springer Verlag

T2 - 7th IAPR TC3 Workshop on Artificial Neural Networks in Pattern Recognition, ANNPR 2016

Y2 - 28 September 2016 through 30 September 2016

ER -