Whatever one makes of this argument, it does not strike me as an argument based on insights from computer science or machine learning. The real work is being done by an assumption about the legal standard together with what Professor Bellovin calls “intuitive reasoning.” The assumed legal standard is that the collection of location information constitutes a search when analysis of location data could plausibly support some sort of inference about a person (exactly what inference, we don’t quite know, but something). The “intuitive reasoning” is that a week seems about right as an answer.
One more thought. Even if Professor Bellovin is correct on the law and the intuition, I’m not sure why that would mean that a mosaic is created after seven days. I understand Bellovin’s argument to be that a mosaic could theoretically be created based on an analysis of seven days of tracking information. But it’s the analysis of the data that allegedly creates the mosaic, not the collection alone. So even if advances in computer science or even just intuition make a mosaic possible after seven days, I would think that whether a mosaic is created in any one case depends on how the location data is analyzed in that specific case. If there are ways of analyzing the data so that the government can’t make the search-triggering inferences while getting other information, then no search should occur under Bellovin’s legal standard even if the location data is collected indefinitely.