L. V. E. Koopmans

Ahmad Mouri Sardarabadi, Alle-Jan van der Veen, L. V. E. Koopmans

For subspace estimation with an unknown colored noise, Factor Analysis (FA) is a good candidate for replacing the popular eigenvalue decomposition (EVD). Finding the unknowns in factor analysis can be done by solving a non-linear least square problem. For this type of optimization problems, the Gauss-Newton (GN) algorithm is a powerful and simple method. The most expensive part of the GN algorithm is finding the direction of descent by solving a system of equations at each iteration. In this paper we show that for FA, the matrices involved in solving these systems of equations can be diagonalized in a closed form fashion and the solution can be found in a computationally efficient way. We show how the unknown parameters can be updated without actually constructing these matrices. The convergence performance of the algorithm is studied via numerical simulations.

Samira Rezaei, Amirmohammad Chegeni, Bharath Chowdhary Nagam et al.

This research studies the impact of high-quality training datasets on the performance of Convolutional Neural Networks (CNNs) in detecting strong gravitational lenses. We stress the importance of data diversity and representativeness, demonstrating how variations in sample populations influence CNN performance. In addition to the quality of training data, our results highlight the effectiveness of various techniques, such as data augmentation and ensemble learning, in reducing false positives while maintaining model completeness at an acceptable level. This enhances the robustness of gravitational lens detection models and advancing capabilities in this field. Our experiments, employing variations of DenseNet and EfficientNet, achieved a best false positive rate (FP rate) of $10^{-4}$, while successfully identifying over 88 per cent of genuine gravitational lenses in the test dataset. This represents an 11-fold reduction in the FP rate compared to the original training dataset. Notably, this substantial enhancement in the FP rate is accompanied by only a 2.3 per cent decrease in the number of true positive samples. Validated on the KiDS dataset, our findings offer insights applicable to ongoing missions, like Euclid.