Nonlinear Dimensionality Reduction with Missing Data using Parametric Multiple Imputations
(2019) I E E E Transactions on Neural Networks and Learning Systems — Vol. 30, n° 4, p. 1166-1179 (2019)
Files
20190412_de_Bodt_et_al_IEEETNNLS.pdf
Open Access - Adobe PDF
- 1.77 MB
Details
- Authors
De Bodt, Cyril 
Mulders, Dounia
- Abstract
- (en) Dimensionality reduction (DR) aims at faithfully and meaningfully representing high-dimensional data into a low-dimensional (LD) space. Recently developed neighbor embedding DR methods lead to outstanding performances, thanks to their ability to foil the curse of dimensionality. Unfortunately, they can not be directly employed on incomplete data sets, which become ubiquitous in machine learning. Discarding samples with missing features prevents their LD coordinates computation and deteriorates the complete samples treatment. Common missing data imputation schemes are not appropriate in the nonlinear DR context either. Indeed, even if they model the data distribution in the feature space, they can at best enable the application of a DR scheme on the expected data set. In practice, one would instead like to obtain the LD embedding with the closest cost function value on average with respect to the complete data case. As state-of-the-art DR techniques are nonlinear, the latter embedding results from minimizing the expected cost function on the incomplete database, not from considering the expected data set. This paper addresses these limitations by developing a general methodology for nonlinear DR with missing data, being directly applicable with any DR scheme optimizing some criterion. In order to model the feature dependencies, a high-dimensional extension of Gaussian mixture models is first fitted on the incomplete data set. It is afterward employed under the multiple imputation paradigm to obtain a single relevant LD embedding, minimizing the cost function expectation. Extensive experiments demonstrate the superiority of the suggested framework over alternative approaches.
- Affiliations
Citations
De Bodt, C., Mulders, D., Verleysen, M., & Lee, J. (2019). Nonlinear Dimensionality Reduction with Missing Data using Parametric Multiple Imputations. I E E E Transactions on Neural Networks and Learning Systems, 30(4), 1166-1179. https://doi.org/10.1109/TNNLS.2018.2861891 (Original work published 2019)