A Parameterised Extension of Exponential Discriminant Analysis for Enhanced Classification
Keywords:
Linear Discriminant Analysis, Exponential Discriminant Analysis, Singularity, ClassificationAbstract
Exponential Discriminant Analysis (EDA) is an effective dimensionality reduction and classification technique for high-dimensional data, offering a robust alternative to conventional linear discriminant analysis by mitigating the singularity problems associated with scatter matrices. Despite its advantages, the conventional EDA framework relies on a fixed matrix exponential transformation, which limits its
flexibility in adapting to datasets with varying underlying structures. This study proposes a Modified Exponential Discriminant Analysis (MEDA) framework that extends the traditional EDA approach by introducing a tunable coefficient into the scatter matrix exponential transformation. The proposed modification provides adaptive control over the growth rate of the transformation, allowing more
effective scaling of scatter information and improved class separability. The performance of the proposed method was evaluated using benchmark datasets and compared with existing discriminant analysis approaches. Experimental results demonstrate that MEDA consistently achieves higher classification accuracy than the conventional EDA and related methods. These findings indicate that the proposed framework provides a more flexible and effective approach for dimensionality reduction and classification of high-dimensional data.
References
Agresti, A., & Finlay, B. (2009). Statistical methods for the social sciences (4th ed.). Pearson Prentice Hall.
Belhumeur, P. N., Hespanha, J. P., & Kriegman, D. J. (1997). Eigenfaces vs. Fisherfaces: Recognition using class-specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(7), 711–720. https://doi.org/10.1109/34.598228
Bruce, P., Bruce, A., & Gedeck, P. (2020). Practical statistics for data scientists (2nd ed.).O'Reilly Media.
Cannings, T. I., & Samworth, R. J. (2021). Random-projection ensemble classification. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 83(3), 509–542. https://doi.org/10.1111/rssb.12436
Clemmensen, L., Hastie, T., Witten, D., & Ersbøll, B. (2020). Sparse discriminant analysis. Technometrics, 62(3), 279–292. https://doi.org/10.1080/00401706.2019.1654879
Delaigle, A., & Hall, P. (2021). Achieving near perfect classification for functional data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 83(2), 305–332. https://doi.org/10.1111/rssb.12418
Ekhosuehi, V. U., & Iduseri, A. (2022). Logistic regression and discriminant analysis of academic staff mix by rank via research performance in a university setting. Journal of the Nigerian Statistical Association, 34, 40–60.
Friedman, J. (2020). Regularized discriminant analysis revisited. Journal of Computational and Graphical Statistics, 29(2), 427–436. https://doi.org/10.1080/10618600.2019.1696205
Gougeon, P. (2013). Measuring and optimizing computational performance in R. The R Journal, 5(1), 27–36. https://journal.r-project.org/archive/2013/RJ-2013-001/index.html
Gupta, V., & Rao, S. (2025). Random projection ensemble methods for high-dimensional quadratic discriminant analysis. arXiv. https://arxiv.org/abs/2505.23324
Huberty, C. J., & Olejnik, S. (2006). Applied MANOVA and discriminant analysis. John Wiley & Sons.
Iduseri, A., & Osemwenkhae, J. E. (2016). Using discriminant analysis to identify major prerequisites for success in specific courses of study in a university system. Journal of the Nigerian Association of Mathematical Physics, 33, 99–106.
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning: With applications in R. Springer. Texts in Statistics (STS, volume 103). https://doi.org/10.1007/978-1-4614-7138-
Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis (6th ed.). Pearson Prentice Hall.
Kumar, R., & Singh, P. (2025). Adaptive local discriminant analysis for complex data classification. Neural Networks, 178, Article 107551. https://doi.org/10.1016/j.neunet.2024.107551
Li, H., Wang, J., & Sun, Q. (2025). Convex reformulation of linear discriminant analysis for robust classification. arXiv. https://arxiv.org/abs/2503.13623
Liu, J., Cai, X., & Niranjan, M. (2023). GO-LDA: Generalised optimal linear discriminant analysis. arXiv. https://arxiv.org/abs/2305.14568
Lobna, A., Afif, M., & Sonia, G. (2016). The consumer loans payment default predictive model: An application in a Tunisian commercial bank. Asian Economic and Financial Review, 6(1), 27–42.
Mahadi, M., Ballal, T., Moinuddin, M., Al-Naffouri, T. Y., & Al-Saggaf, U. M. (2024). Regularized linear discriminant analysis using a nonlinear covariance matrix estimator. IEEE Transactions on Signal Processing, 72, 1049–1062. https://doi.org/10.1109/TSP.2024.3361715
Mai, Q., Zou, H., & Yuan, M. (2021). A direct approach to sparse discriminant analysis in ultra- high dimensions. Biometrika, 108(2), 247–262. https://doi.org/10.1093/biomet/asaa081
Martínez, A. M., & Kak, A. C. (2001). PCA versus LDA. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(2), 228–233. https://doi.org/10.1109/34.908974
Martinez, F., & Gomez, R. (2025). State-space discriminant models for nonstationary data classification. arXiv. https://arxiv.org/abs/2508.16073
Mika, S., Rätsch, G., Weston, J., Schölkopf, B., & Müller, K. R. (2000). Fisher discriminant analysis with kernels. Neural Networks, 13(6), 797–803.
Osemwenkhae, J. E., Iduseri, A., & Meka, F. (2019). Determinants of the level of stress experienced by teachers at different educational levels: A descriptive discriminant approach. Journal of the Nigerian Statistical Association, 31, 64–80.
Park, H., Drake, B. L., Lee, S., & Park, C. H. (2007). Fast linear discriminant analysis using QR decomposition and regularization (Technical Report). Georgia Institute of Technology.
Park, S., & Lee, D. (2023). Exponential trace ratio method for high-dimensional data analysis. Pattern Recognition Letters, 170, 12–20. https://doi.org/10.1016/j.patrec.2023.03.002
Ran, R., Fang, B., Wu, X., & Zhang, S. (2018). A simple and effective generalization of exponential matrix discriminant analysis and its application to face recognition. IEICE Transactions on Information and Systems, E101-D(1).
Sokolova, M., & Lapalme, G. (2009). A systematic analysis of performance measures for classification tasks. Information Processing & Management, 45(4), 427–437. https://doi.org/10.1016/j.ipm.2009.03.002
Stevens, J. (1996). Applied multivariate statistics for the social sciences (3rd ed.). Lawrence Erlbaum Associates.
Sugiyama, M. (2020). Local Fisher discriminant analysis for supervised dimensionality reduction. Pattern Recognition Letters, 130, 112–118.https://doi.org/10.1016/j.patrec.2019.11.015
Witten, D. M., & Tibshirani, R. (2021). Penalized classification using Fisher's linear discriminant. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 83(2), 386–410. https://doi.org/10.1111/rssb.12419
Xu, Y., Tao, D., & Xu, C. (2020). A survey on exponential discriminant analysis. IEEE Transactions on Neural Networks and Learning Systems, 31(10), 3859–3873. https://doi.org/10.1109/TNNLS.2019.2950614
Ye, J., & Li, Q. (2005). A two-stage linear discriminant analysis via QR decomposition. IEEE Transactions on Pattern Analysis and Machine intelligence, 27(6), 929–941. https://doi.org/10.1109/TPAMI.2005.127
Ye, J., Janardan, R., & Li, Q. (2022). Two-dimensional linear discriminant analysis. Advances in Neural Information Processing Systems, 35, 1567–1579.
Zhang, D., & Ye, J. (2014). Learning regularized LDA by clustering. Pattern Recognition, 47(9), 3034–3042. htps://doi.org/10.1016/j.patcog.2014.03.006
Zhang, T. P., Fang, B., Tang, Y. Y., Shang, Z., & Xu, B. (2010). Generalized discriminant analysis: A matrix exponential approach. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40(1), 186–197. https://doi.org/10.1109/TSMCB.2009.2021987
Zhang, X., Liu, H., & Wang, L. (2023). Locality-preserving discriminant analysis for high- dimensional data. Knowledge-Based Systems, 261, Article 110191. https://doi.org/10.1016/j.knosys.2022.110191
Zhao, L., & Chen, M. (2025). Multivariate functional discriminant analysis for irregular data. Machine Learning, 114(3), 567–589. https://doi.org/10.1007/s10994-024-06512-3
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Journal of the CISON
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution (CC BY) 4.0 International License.
