Explainable machine learning classification of \textit{Chandra} X-ray sources: SHAP analysis of multi-wavelength features

TL;DR

This study represents one of the earliest applications of XAI to large-scale astronomical data sets, demonstrating ML models’ potential for uncovering physically meaningful patterns in data in addition to classification.

Abstract

Extensive astronomical surveys, like those conducted with the {\em Chandra} X-ray Observatory, detect hundreds of thousands of unidentified cosmic sources. Machine learning (ML) methods offer an efficient, probabilistic approach to classify them, which can be useful for making discoveries and conducting deeper studies. In earlier work, we applied the LightGBM (ML model) to classify 277,069 {\em Chandra} point sources into eight categories: active galactic nuclei (AGN), X-ray emitting stars, young stellar objects (YSO), high-mass X-ray binaries, low-mass X-ray binaries, ultraluminous X-ray sources, cataclysmic variables, and pulsars. In this work, we present the classification table of 54,770 robustly classified sources (over $3σ$ confidence), including 14,066 sources at $>4σ$ significance. To ensure classification reliability and gain a deeper insight, we investigate the multiwavelength feature relationships learned by the LightGBM model, focusing on AGNs, Stars, and YSOs. We employ Explainable Artificial Intelligence (XAI) techniques, specifically, SHapley Additive exPlanations (SHAP), to quantify the contribution of individual features and their interactions to the predicted classification probabilities. Among other things, we find infrared-optical and X-ray decision boundaries for separating AGN/Stars, and infrared-X-ray boundaries for YSOs. These results are crucial for estimating object classes even with limited multiwavelength data. This study represents one of the earliest applications of XAI to large-scale astronomical datasets, demonstrating ML models' potential for uncovering physically meaningful patterns in data in addition to classification. Finally, our publicly available, extensive, and interactive catalogue will be helpful to explore the contributions of features and their combinations in greater detail in the future.

Figures (9)

• Figure 1: Location of the sources in Galactic coordinates belonging to different classes: AGN, Stars (top-left); YSO, HMXB (top-right); CV, LMXB (bottom-left); Pulsars, ULX (bottom-right) in Aitoff projection. Note: the pairs for the plot are selected for better visualisation.
• Figure 2: Confusion matrix corresponding to the confused sources (CMP1-CMP2 $\leq 0.05$) in the identified data set. The Y-axis shows the highest probable class, i.e., class 1 column in Table \ref{['tab:source-table']}, and the X-axis is the second highest probable class (class 2 column in Table \ref{['tab:source-table']}).
• Figure 3: Comparison of the distribution of sources in the training dataset to the sources in the newly identified dataset on the Optical ( Gaia) and IR ( WISE and 2MASS) color magnitude diagram.
• Figure 4: General workflow for local explanation of a black-box classifier model output using SHAP Analysis. Starting with the source's feature set $X_s$, the LightGBM model $f$ generates a raw model output $f(X_s)$ which is converted to CMP for the given class using the sigmoid ($\sigma$) function. This chain is indicated by black arrows. The blue arrows show the workflow of allocating the model output, $f(X_s)$, to the feature contributions using SHAP analysis. SHAP Value for each feature, $\phi_s(x_i)$, is calculated from Equation \ref{['eq:shap-calc']}. The green arrows outline equivalence between features' SHAP values and the model raw output $f(X_s)$ with additional model offset $\phi_0$. See §\ref{['sec:shap']} for details.
• Figure 5: Local explanation for the source 2CXO J01422.8-005331. The raw output of the LightGBM model for this source is $f(X_s)=4.83$. The individual features SHAP values $\phi_s({x_i})$ are given on the X-axis for the top 10 features $x_i$ on the Y-axis. The sum of contributions from all remaining features is indicated with the 'ARF' label in the last row.