A New Framework for Multi-Line Analysis Combined Kernel PCA and Kernel SHAP: A Case of NGC 1068 ALMA Band 3 Data

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Abstract
We present a new framework for multi-line analysis that combines kernel principal component analysis (Kernel PCA), an unsupervised machine-learning method, and Kernel SHapley Additive exPlanations (Kernel SHAP), an explainable artificial intelligence (XAI) technique. To enable a comparison with PCA-based studies, which have been widely used in multi-line analyses, we apply our framework to integrated intensity maps of 13 molecular lines from Atacama Large Millimeter/submillimeter Array (ALMA) Band 3 archival data of the nearby galaxy NGC 1068. Previous PCA-based studies of NGC 1068 reported that physically meaningful structures are mainly captured up to the second component. In contrast, our framework can interpret physically meaningful features up to the fourth component. Furthermore, by comparing the results obtained from our framework with molecular column densities derived from local thermodynamical equilibrium (LTE) analysis, we suggest that the abundance of HCO+ is relatively enhanced in the molecular outflow region extending to a radius of about 400 pc from the galactic center, likely due to the effects of ultraviolet radiation and highly dense gas. These results show that our framework can provide data-driven insights into physical and chemical features that have not been clearly identified in previous studies. It also provides an efficient tool for interpreting the rapidly increasing amount of multi-line observational data.
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