Kernel Principal Component Analysis

Kernel Principal Component Analysis (KPCA) extends traditional PCA to handle nonlinear relationships in data by employing kernel functions to map data into higher-dimensional spaces. Current research focuses on applying KPCA to enhance interpretability in deep learning models (e.g., improving class activation maps in CNNs), developing robust and efficient KPCA algorithms for various applications (including fault detection, time series forecasting, and out-of-distribution detection), and integrating KPCA with other techniques like deep learning architectures and spectral clustering. These advancements are improving the accuracy and efficiency of dimensionality reduction, feature extraction, and anomaly detection across diverse fields, from computer vision and natural language processing to process monitoring and bioinformatics.