TY - GEN

T1 - Weakly Supervised Regression Using Manifold Regularization and Low-Rank Matrix Representation

AU - Berikov, Vladimir

AU - Litvinenko, Alexander

N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - We solve a weakly supervised regression problem. Under “weakly” we understand that for some training points the labels are known, for some unknown, and for others uncertain due to the presence of random noise or other reasons such as lack of resources. The solution process requires to optimize a certain objective function (the loss function), which combines manifold regularization and low-rank matrix decomposition techniques. These low-rank approximations allow us to speed up all matrix calculations and reduce storage requirements. This is especially crucial for large datasets. Ensemble clustering is used for obtaining the co-association matrix, which we consider as the similarity matrix. The utilization of these techniques allows us to increase the quality and stability of the solution. In the numerical section, we applied the suggested method to artificial and real datasets using Monte-Carlo modeling.

AB - We solve a weakly supervised regression problem. Under “weakly” we understand that for some training points the labels are known, for some unknown, and for others uncertain due to the presence of random noise or other reasons such as lack of resources. The solution process requires to optimize a certain objective function (the loss function), which combines manifold regularization and low-rank matrix decomposition techniques. These low-rank approximations allow us to speed up all matrix calculations and reduce storage requirements. This is especially crucial for large datasets. Ensemble clustering is used for obtaining the co-association matrix, which we consider as the similarity matrix. The utilization of these techniques allows us to increase the quality and stability of the solution. In the numerical section, we applied the suggested method to artificial and real datasets using Monte-Carlo modeling.

KW - Cluster ensemble

KW - Co-association matrix

KW - Low-rank matrix decomposition

KW - Manifold regularization

KW - Weakly supervised learning

UR - http://www.scopus.com/inward/record.url?scp=85111359382&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-77876-7_30

DO - 10.1007/978-3-030-77876-7_30

M3 - Conference contribution

AN - SCOPUS:85111359382

SN - 9783030778750

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

SP - 447

EP - 461

BT - Mathematical Optimization Theory and Operations Research - 20th International Conference, MOTOR 2021, Proceedings

A2 - Pardalos, Panos

A2 - Khachay, Michael

A2 - Kazakov, Alexander

PB - Springer Science and Business Media Deutschland GmbH

T2 - 20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021

Y2 - 5 July 2021 through 10 July 2021

ER -