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

TL;DR

This study addresses the challenge of extracting physically interpretable information from non-linear relationships among molecular-line intensities. It introduces a framework that fuses Kernel PCA with Kernel SHAP to both capture non-linear structure and attribute feature contributions to specific molecular lines. Applied to ALMA Band 3 data for NGC 1068 with 13 lines, the approach reveals meaningful features up to the fourth component, beyond the conventional PCA that often limits interpretation to the first two components. LTE-based analysis further links KPC3-derived features to enhanced HCN, HCO$^+$, CN, and related species in the molecular outflow, illustrating a data-driven pathway to uncover chemical and physical processes in complex galactic environments. Overall, the framework offers a scalable, interpretable tool for the growing volume of multi-line observational data in extragalactic astrochemistry.

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.

Figures (6)

• Figure 1: The integrated intensity maps of NGC 1068. The left panel presents the $^{13}$CO($J$=1--0) integrated intensity map. The crosses indicate the positions of the SSC, SHC, and Pa$\alpha$ regions defined in Rico-villas+2021. Note that the circle marking the starburst ring is not a strict definition, but only shows its approximate location. The middle and right panels show the CS($J$=2--1) and HNC($J$=1--0) integrated intensity maps, respectively. The central circle indicates the field of view (FoV) of the [CI] data. The region outlined with dotted arrows marks the direction of the molecular outflow Saito+2022_CISaito+2022. The diameter of the circle is 1 kpc.
• Figure 2: Correlation plot between two standardized molecular lines. The color indicates the Mahalanobis distance, which accounts for the correlation between the two variables. The red ellipse represents a Mahalanobis distance of 1. These plots correspond to the maps shown in Figure 1 (left), Figure 2, and Figure 3 of Okubo+2025.
• Figure 3: Kernel PCA resutls. The first row shows the contribution ratio (CR) and cumulative contribution ratio (CCR). The second row displays the KPC1 map on the left and the KPC2 map on the right, while the third row shows the KPC3 map on the left and the KPC4 map on the right. The color represents the KPC$i$ scores. The black circle marks the field of view (FoV) of the [CI] data Saito+2022_CI. The crossed dashed lines denote the direction of the outflow Saito+2022.
• Figure 4: Kernel SHAP resutls. The top row shows the SHAP values for the KPC1 scores on the left and for the KPC2 scores on the right, while the second row shows those for the KPC3 scores on the left and for the KPC4 scores on the right. The color represents the standardized integrated intensity of each molecular line used in the analysis. In each figure, the x-axis corresponds to the SHAP value and the y-axis corresponds to the molecular lines. The black-outlined points indicate the grid at the AGN position.
• Figure 5: The left panel in the first row shows the cluster map, while the right panel presents the clustering result. The second row illustrates the relationship between the SHAP values and the scores in Cluster 2, and the third row shows the corresponding relationship for Cluster 4. The numbers in the plot represent the correlation coefficients.