Ambient classroom sensing systems offer a scalable and non-intrusive way to find connections between instructor actions and student behaviors, creating data that can improve teaching and learning. While these systems effectively provide aggregate data, getting reliable individual student-level information is difficult due to occlusion or movements. Individual data can help in understanding equitable student participation, but it requires identifiable data or individual instrumentation. We propose ClassID, a data attribution method for within a class session and across multiple sessions of a course without these constraints. For within-session, our approach assigns unique identifiers to 98% of students with 95% accuracy. It significantly reduces multiple ID assignments compared to the baseline approach (3 vs. 167) based on our testing on data from 15 classroom sessions. For across-session attributions, our approach, combined with student attendance, shows higher precision than the state-of-the-art approach (85% vs. 44%) on three courses. Finally, we present a set of four use cases to demonstrate how individual behavior attribution can enable a rich set of learning analytics, which is not possible with aggregate data alone.