Unsupervised Classification of Binary SMBH Candidates in Gaia DR3: A Machine Learning Approach to Astrometric Jitter and Cluster-Based Candidate Identification

We present an unsupervised machine learning analysis of astrometric variability in Gaia DR3 quasars, aimed at identifying indirect signatures of unresolved binary supermassive black holes (SMBHBs). Using a filtered sample of ∼10,000 high-quality quasars, we extract key features including RUWE, astrometric excess noise, parallax, color index, and G-band magnitude. These features are normalized and reduced using Principal Component Analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE) to uncover low-dimensional structure. We apply both K-Means and DBSCAN clustering algorithms to the projected feature space. The K-Means algorithm identifies three distinct populations, with one cluster exhibiting statistically higher excess noise and intermediate RUWE values, suggestive of potential centroid jitter induced by binary SMBH orbital motion. The clustering results are further validated using silhouette scores and consistent spatial separability in t-SNE projections. A catalog of candidate high-jitter quasars is compiled from the most deviant cluster, comprising over 3500 sources. These candidates are promising targets for future multi-wavelength follow-up using VLBI, variability surveys, and higher-precision Gaia astrometry. Our work demonstrates that unsupervised learning techniques offer a powerful, scalable alternative to classical threshold-based methods for probing the hidden binary SMBH population at cosmological distances. This study represents one of the first applications of machine learning to stochastic astrometric variability in extragalactic sources and provides a reproducible framework for future discovery in Gaia DR4 and LSST-era datasets.