The rapid growth of cloud computing, connected devices, remote work, and software-defined infrastructure has expanded the scale and complexity of cyber threats. Conventional signature-based security controls are effective against known attack patterns but may struggle when attacks are novel, modified, low-and-slow, or hidden within legitimate activity. Anomaly detection offers a complementary approach by identifying deviations from learned patterns of normal system or network behaviour. In operational environments, however, labelled attack data are often limited, imbalanced, costly to obtain, and quickly outdated. Semi-supervised machine learning is therefore a promising strategy: it learns primarily from abundant unlabelled observations while using a smaller labelled set, or an assumption that most training data represent normal behaviour, to distinguish suspicious activity. This paper presents a research framework for real-time cybersecurity anomaly detection using semi-supervised machine learning. It reviews major anomaly-detection paradigms, discusses candidate models including one-class support vector machines, isolation-based methods, autoencoders, and teacher–student approaches, and proposes a streaming architecture that integrates feature extraction, online scoring, threshold calibration, alert prioritisation, and analyst feedback. Evaluation is framed around detection quality, false-alarm burden, latency, throughput, and robustness to concept drift. The paper also addresses data leakage, class imbalance, adversarial adaptation, privacy, explainability, and deployment governance. Rather than claiming unperformed experiments, it provides a reproducible evaluation plan and hypotheses that can be tested on public intrusion-detection datasets and, where possible, operational telemetry. The central argument is that practical performance depends not only on model choice but also on data quality, calibration, stream processing, and a disciplined human-in-the-loop response process.