The proliferation of cloud computing has introduced significant cybersecurity challenges, emphasizing the need for advanced anomaly detection systems to safeguard critical data and infrastructure. This research presents a novel approach that integrates motif discovery with machine learning techniques to enhance the detection of anomalies in cloud security logs. Motifs, extracted as domain-specific features, were introduced to capture contextual patterns in the data, improving model interpretability and performance. Despite achieving exceptional accuracy (99.93%) and strong precision and recall for majority classes, initial experiments revealed a critical limitation in handling rare, minority-class anomalies, often indicative of high-impact security threats. To address this imbalance, the Synthetic Minority Oversampling Technique (SMOTE) was applied, effectively augmenting minority class representation and enabling the model to achieve uniform precision, recall, and F1-scores across all classes. This integration demonstrated the model's capability to process bulk cloud logs accurately, classify known threats reliably, and detect rare anomalies critical for Zero Trust architectures. The findings underline the importance of robust preprocessing methodologies, such as motif discovery, and advanced oversampling techniques to mitigate class imbalance in cybersecurity datasets. The research further recommends iterative motif refinement, hybrid oversampling approaches, and adaptive real-time deployment to ensure resilience against evolving threat landscapes. This work establishes a foundational framework for scalable and adaptive anomaly detection in cloud computing environments, addressing both operational efficiency and critical security needs.