If the dataset is something like:
An effective approach to identify anomalies is to create a statistical model of the numerical values, and computing the probability of a specific data value. If the probability is low, then the value is anomalous.
Generally, to accurately model these data and avoid false positives these models needs to be more sophisticated than a simple Normal distribution. In addition, these data are generally periodic and so the models need to allow for daily and weekly patterns.
LOF methods can be effective on static low dimensional datasets, but suffer from similar issues to kernel density functions (overfitting, linear space complexity etc.).
Further details are available here:
We have built an app to automatically identify anomalies in numeric and categorical data using these techniques: