Process mining provides enterprises with insights into their business processes based on event data extracted from information systems. Techniques such as process discovery, conformance checking, and performance analysis enable the modeling, evaluation, and optimization of processes. Meanwhile, an activity execution is recorded as events representing transitions within the lifecycle of an activity, and the collection of these events is referred to as an activity instance. To accurately represent activity instances, event logs, a commonly used format of event data in process mining, require the correlation of events. However, real-world event logs often lack such information, leading to unreliable or biased results. This paper presents a novel approach to identify activity instances. By correlating events using bipartite-graph matching and alignment, we identify activity instances conforming to the lifecycle of the activity. The experiments demonstrate the effectiveness of the method and its robustness to noise and missing events using event logs across various domains.