In reply to Brett.

In high dimensions, outliers often have reasonable values in all coordinates. There does not need to be a set of "unusual" values that you can detect. Rather, it is the combination of values across all variables that causes the observation to be an outlier. For example, 140 is a high, but not alarming, value for systolic BP. Similarly, 55 is a low, but not alarming, value of diastolic BP. But a patient whose BP is 130 over 55 is probably an outlier because diastolic and systolic BP tends to be correlated.