I have a dataset with different types of user events, and I'd like to set a metric of user activity. I don't have any labeled data of the actual perceived activity level of users. The data consists of around 10 different types of events (count of events normalized by usage time). For example:
+---------+--------+--------+--------+--------+--------+
| UserId | Event1 | Event2 | Event3 | Event4 | Event5 |
+---------+--------+--------+--------+--------+--------+
| 10252 | 0.048 | 1.266 | 0.777 | 1.224 | 0.551 |
| 982850 | 0.000 | 0.000 | 1.085 | 1.356 | 0.526 |
| 1009937 | 0.000 | 0.000 | 0.245 | 0.049 | 0.025 |
| 1029718 | 0.000 | 0.000 | 0.440 | 0.313 | 0.652 |
+---------+--------+--------+--------+--------+--------+
Looking at the distribution of the events, they all have an exponential-like type of distribution.
Additionally, there's correlation between most of the events. Strongest correlation is around .3
I would like to be able to tell on a scale from 0 to 1, how active a user is, regardless of his/her usage time.
If I were to have only one event, I would fit a distribution to the data and use the probability as the predictor. Because I have multiple events and there's correlation between them, I wonder what would be the best way to model this.
I tried PCA (even though the dada is not normally distributed) and didn't get very promising results (no elbow, 95% of variance is explained by 7 out of 10 PCs).
Any advise would be greatly appreciated!