In this paper, a multi-step dimension-reduction approach is proposed for addressing nonlinear relationships within attributes. In this work, the attributes in the data are first organized into groups. In each group, the dimensions are reduced via a parametric mapping that takes into account nonlinear relationships. Mapping parameters are estimated using a low rank singular value decomposition (SVD) of distance covariance. Subsequently, the attributes are reorganized into groups based on the magnitude of their respective singular values. The group-wise organization and the subsequent reduction process is performed for multiple steps until a singular value-based user-defined criterion is satisfied. Simulation analysis is utilized to investigate the performance with five big data-sets.
R. Krishnan et al., "A Multi-Step Nonlinear Dimension-Reduction Approach with Applications to Bigdata," Procedia Computer Science, vol. 144, pp. 81 - 88, Elsevier, Apr 2018.
The definitive version is available at https://doi.org/10.1016/j.procs.2018.10.507
3rd International Neural Network Society Conference on Big Data and Deep Learning, INNS BDDL 2018 (2018: Apr. 17-19, Bali, Indonesia)
Mathematics and Statistics
Electrical and Computer Engineering
Intelligent Systems Center
Second Research Center/Lab
Center for High Performance Computing Research
Keywords and Phrases
Big data; Mapping; Singular value decomposition; Dimension reduction; Mapping parameters; Non-linear relationships; Nonlinear dimension; Parametric mapping; Simulation analysis; Singular values; Subsequent reduction; Deep learning
International Standard Serial Number (ISSN)
Article - Conference proceedings
© 2018 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
01 Apr 2018
Electrical and Computer Engineering Commons, Mathematics Commons, Statistics and Probability Commons
This research was supported in part by an NSF I/UCRC award IIP 1134721 and Intelligent Systems Center.