TY - GEN

T1 - Manifold learning in regression tasks

AU - Bernstein, Alexander

AU - Kuleshov, Alexander

AU - Yanovich, Yury

PY - 2015

Y1 - 2015

N2 - The paper presents a new geometrically motivated method for nonlinear regression based on Manifold learning technique. The regression problem is to construct a predictive function which estimates an unknown smooth mapping f from q-dimensional inputs to m-dimensional outputs based on a training data set consisting of given ‘input-output’ pairs. The unknown mapping f determines q-dimensional manifold M(f) consisting of all the ‘input-output’ vectors which is embedded in (q+m)-dimensional space and covered by a single chart; the training data set determines a sample from this manifold. Modern Manifold Learning methods allow constructing the certain estimator M* from the manifold-valued sample which accurately approximates the manifold. The proposed method called Manifold Learning Regression (MLR) finds the predictive function fMLR to ensure an equality M(fMLR) = M*. The MLR simultaneously estimates the m×q Jacobian matrix of the mapping f.

AB - The paper presents a new geometrically motivated method for nonlinear regression based on Manifold learning technique. The regression problem is to construct a predictive function which estimates an unknown smooth mapping f from q-dimensional inputs to m-dimensional outputs based on a training data set consisting of given ‘input-output’ pairs. The unknown mapping f determines q-dimensional manifold M(f) consisting of all the ‘input-output’ vectors which is embedded in (q+m)-dimensional space and covered by a single chart; the training data set determines a sample from this manifold. Modern Manifold Learning methods allow constructing the certain estimator M* from the manifold-valued sample which accurately approximates the manifold. The proposed method called Manifold Learning Regression (MLR) finds the predictive function fMLR to ensure an equality M(fMLR) = M*. The MLR simultaneously estimates the m×q Jacobian matrix of the mapping f.

KW - Dimensionality reduction

KW - Manifold learning

KW - Manifold learning regression

KW - Nonlinear regression

KW - Tangent bundle manifold learning

UR - http://www.scopus.com/inward/record.url?scp=84949752569&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-17091-6_36

DO - 10.1007/978-3-319-17091-6_36

M3 - Conference contribution

AN - SCOPUS:84949752569

SN - 9783319170909

VL - 9047

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

SP - 414

EP - 423

BT - Statistical Learning and Data Sciences - 3rd International Symposium, SLDS 2015, Proceedings

A2 - Gammerman, Alexander

A2 - Vovk, Vladimir

A2 - Papadopoulos, Harris

PB - Springer Verlag

T2 - 3rd International Symposium on Statistical Learning and Data Sciences, SLDS 2015

Y2 - 20 April 2015 through 23 April 2015

ER -