![](https://d3ilqtpdwi981i.cloudfront.net/vrwsGloHJayK60KOjUouG82Pjw8=/425x550/smart/https://bepress-attached-resources.s3.amazonaws.com/uploads/99/cc/28/99cc2806-8b9c-402e-8770-acf16e44ce96/thumbnail_ac533b9f-5715-4fa8-a02d-bdc176cee995.jpg)
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.
- 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
Available at: http://works.bepress.com/jagannathan-sarangapani/198/
This research was supported in part by an NSF I/UCRC award IIP 1134721 and Intelligent Systems Center.