A processing device in one embodiment comprises a processor coupled to a memory and is configured to obtain data characterizing a plurality of network sessions for a given user identifier. The network sessions are initiated from one or more user devices over at least one network and may comprise respective virtual private network (VPN) sessions. The processing device is further configured to extract features from the obtained data, to detect at least one potentially anomalous network session among the plurality of network sessions for the given user identifier by applying the extracted features to a support vector machine model, and to apply a rules-based verification process to the detected potentially anomalous network session in order to verify that the detected potentially anomalous network session is an anomalous network session. An alert is generated based on a result of the rules-based verification process and transmitted to a security agent.