Joint Exploration of Kernel Functions Potential for Data Representation and Classification: A First Step Toward Interactive Interpretable Dimensionality Reduction

Dimensionality reduction (DR) approaches are often a crucial step in data analysis tasks, particularly for data visualization purposes. DR-based techniques are essentially designed to retain the inherent structure of high-dimensional data in a lower-dimensional space, leading to reduced computational complexity and improved pattern recognition accuracy. Specifically, Kernel Principal Component Analysis (KPCA) is a widely utilized dimensionality reduction technique due to its capability to effectively handle nonlinear data sets. It offers an easily interpretable formulation from both geometric and functional analysis perspectives. However, Kernel PCA relies on free hyperparameters, which are usually tuned in advance. The relationship between these hyperparameters and the structure of the embedded space remains undisclosed. This work presents preliminary steps to explore said relationship by jointly evaluating the data classification and representation abilities. To do so, an interactive visualization framework is introduced. This study highlights the importance of creating interactive interfaces that enable interpretable dimensionality reduction approaches for data visualization and analysis.