This final clause is badly written. Better would be, for example,
...but only a few of those attributes actually apply to any specific object.
Logically and semantically I have to say the entire (overly verbose) sentence doesn't seem very good in the first place. Every non-trivial object has a multitude of "attributes", but in an analytical context we're only interested in the handful of attributes that are relevant to the analysis.
For example, no business is interested in analysing the attribute of whether their customers' body-weights are an odd or even number of pounds, but some businesses might well want to analyse by above/below average weight (if they can get that information!).
In OP's context, "attributes" are "measurable qualities", for which it should be possible to assign a value to each and every object within the set. If for many objects the only value you can assign is "not applicable", the attribute itself is probably not relevant to the analysis.
OP's quote seems to imply that there's a special kind of real-world context wherein the analyst unavoidably faces problems mapping his "attributes" to his "set of objects". In fact, if this happens you're either using the wrong attributes, or the wrong sets. In short, you're a bad analyst.
TL;DR: If an attribute only "applies" to a few objects in a set, discard it from the analysis.