# Regularized Nonlinear Discriminant Analysis - An Approach to Robust Dimensionality Reduction for Data Visualization

### Martin Becker, Jens Lippel, André Stuhlsatz

#### Abstract

We present a novel approach to dimensionality reduction for data visualization that is a combination of two deep neural networks (DNNs) with different objectives. One is a nonlinear generalization of Fisher’s linear discriminant analysis (LDA). It seeks to improve the class separability in the desired feature space, which is a natural strategy to obtain well-clustered visualizations. The other DNN is a deep autoencoder. Here, an encoding and a decoding DNN are optimized simultaneously with respect to the decodability of the features obtained by encoding the data. The idea behind the combined DNN is to use the generalized discriminant analysis as an encoding DNN and to equip it with a regularizing decoding DNN. Regarding data visualization, a well-regularized DNN guarantees to learn sufficiently similar data visualizations for different sets of samples that represent the data approximately equally good. Clearly, such a robustness against fluctuations in the data is essential for real-world applications. We therefore designed two extensive experiments that involve simulated fluctuations in the data. Our results show that the combined DNN is considerably more robust than the generalized discriminant analysis alone. Moreover, we present reconstructions that reveal how the visualizable features look like back in the original data space.

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#### Paper Citation

#### in Harvard Style

Becker M., Lippel J. and Stuhlsatz A. (2017). **Regularized Nonlinear Discriminant Analysis - An Approach to Robust Dimensionality Reduction for Data Visualization** . In *Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: IVAPP, (VISIGRAPP 2017)* ISBN 978-989-758-228-8, pages 116-127. DOI: 10.5220/0006167501160127

#### in Bibtex Style

@conference{ivapp17,

author={Martin Becker and Jens Lippel and André Stuhlsatz},

title={Regularized Nonlinear Discriminant Analysis - An Approach to Robust Dimensionality Reduction for Data Visualization},

booktitle={Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: IVAPP, (VISIGRAPP 2017)},

year={2017},

pages={116-127},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006167501160127},

isbn={978-989-758-228-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: IVAPP, (VISIGRAPP 2017)

TI - Regularized Nonlinear Discriminant Analysis - An Approach to Robust Dimensionality Reduction for Data Visualization

SN - 978-989-758-228-8

AU - Becker M.

AU - Lippel J.

AU - Stuhlsatz A.

PY - 2017

SP - 116

EP - 127

DO - 10.5220/0006167501160127