The study of anomalies in radon and thoron time series (RTTS) remains a potent area of research in earthquake precursory research and geophysical studies. In this study, an integrated framework has been presented by analyzing RTTS to detect anomalies potentially related to seismic events. Persistent spectrum analysis (PSA) is used to extract topological structures that portrays the underlying features, hidden patterns and extended dependencies within the RTTS signals. For further characterization and to examine the underlying dynamics of the signal, the non-linear techniques viz. Lyapunov exponent and Hurst exponent were employed to depict the chaotic and fractal behavior in RTTS signal. Additionally, by using the extracted features by PSA, the machine learning (ML) algorithm viz. Support vector machine (SVM) model has been employed for automated classification of normal and anomalous patterns within the RTTS signals. The SVM validates high sensitivity in detecting subtle abnormalities that are not visible through conventional statistical techniques. The anomalies detected through PSA are systematically related with the seismic events occurred during the study indicating a transient link with earthquakes. The findings of this study validates that the combined use of PSA, non-linear analysis, and SVM improves the ability of anomaly detection in RTTS signals and their correlation with seismic events. This methodology offers an encouraging roadmap toward enhancing the dependability of geochemical precursors in earthquake precursory research.