  To enhance the robustness of the Light Gradient Boosting Machine (LightGBM)
algorithm for image classification, a topological data analysis (TDA)-based
robustness optimization algorithm for LightGBM, TDA-LightGBM, is proposed to
address the interference of noise on image classification. Initially, the
method partitions the feature engineering process into two streams: pixel
feature stream and topological feature stream for feature extraction
respectively. Subsequently, these pixel and topological features are
amalgamated into a comprehensive feature vector, serving as the input for
LightGBM in image classification tasks. This fusion of features not only
encompasses traditional feature engineering methodologies but also harnesses
topological structure information to more accurately encapsulate the intrinsic
features of the image. The objective is to surmount challenges related to
unstable feature extraction and diminished classification accuracy induced by
data noise in conventional image processing. Experimental findings substantiate
that TDA-LightGBM achieves a 3% accuracy improvement over LightGBM on the
SOCOFing dataset across five classification tasks under noisy conditions. In
noise-free scenarios, TDA-LightGBM exhibits a 0.5% accuracy enhancement over
LightGBM on two classification tasks, achieving a remarkable accuracy of 99.8%.
Furthermore, the method elevates the classification accuracy of the Ultrasound
Breast Images for Breast Cancer dataset and the Masked CASIA WebFace dataset by
6% and 15%, respectively, surpassing LightGBM in the presence of noise. These
empirical results underscore the efficacy of the TDA-LightGBM approach in
fortifying the robustness of LightGBM by integrating topological features,
thereby augmenting the performance of image classification tasks amidst data
perturbations.
