The study of manifold learning and its applications in anomaly detection and supervised learning

​Grant Funding for Young Researchers 2025-2027

This project seeks to advance the field of machine learning through novel approaches to manifold learning. Specifically, the project aims to tackle high-dimensional data problems by leveraging new architectures of autoencoders, including transformer-based designs, while introducing methods to enhance computational efficiency and scalability.
The project is based on the earlier developed alternating algorithm for the manifold learning task. The work will be focused on solving critical issues of that algorithm, such as (a) the computational cost of singular value decomposition (SVD) in high-dimensional settings and (b) the lack of a robust theoretical foundation for alternating algorithms. It will also explore the application of manifold learning in detecting anomalies within nonlinear discrete dynamical systems and improving supervised learning through regularization techniques based on manifolds pre-trained on unsupervised data.
Our research approaches and key ideas include: (a) development of new optimization algorithms with rank constraints on an autoencoder’s Jacobian, improving existing methods for constructing low-dimensional manifolds; (b) introduction of early termination and hyperparameter optimization techniques to accelerate learning without sacrificing the quality of an autoencoder; (c) theoretical analysis of the alternating algorithm for the convex main term with an additional Ky-Fan antinorm-based penalty; (d) experimental validation of anomaly detection in time-series data through manifold learning-based frameworks, using both synthetic and real-world datasets; (e) to enhance robustness and generalization power of supervised learning models, we leverage structures of a manifold, pre-trained on unsupervised data, for defining an objective of supervised learning task.
Our research will significantly influence the scientific and technical capabilities of Nazarbayev University and its team, strengthening their competitiveness. The methods and algorithms developed in this project hold high potential for application across industries, including finance, healthcare, and advanced manufacturing, where robust anomaly detection and model regularization are critical. By enabling more efficient and scalable machine learning solutions, the project contributes to the socio-economic development of Kazakhstan, fostering local expertise in AI and ML research and promoting technological modernization. Ultimately, the project bridges theoretical advancements with practical implementations, ensuring readiness for both academic and industrial adoption.