Fully Connected Neural Networks for GLRT Test: A Synthetic Data Approach

This thesis addresses the challenge of enhancing the performance of Neural Networks (NN) for one-class classification (OCC) problems, motivated by the computational constraints of One-Class Support Vector Machines (OCSVM) and the theoretical framework of the Generalized Likelihood Ratio Test with Unknown Alternative (GLRT-UA). Despite the proven convergence of OCSVMs to GLRT-UA under certain conditions, their performance is limited by computational inefficiency in high-dimensional data scenarios. To overcome this limitation, we propose a novel approach that uses an artificial dataset generated from the output of OCSVM to train NN, aiming to replicate the decision boundaries defined by OCSVM with improved computational efficiency. Through experimental simulation and false alarm miss-detected tests, we demonstrate that the proposed method enhances the performance of NNs, making them a good alternative in scenarios where OCSVMs are computationally impractical. This thesis bridges the theoretical and practical aspects of one-class classification, and also opens new possibilities for research and application in machine learning, especially in high-dimensional data contexts. Future directions include refining the proposed approach and extending its applicability to diverse datasets and problem settings.