  Detecting outliers which are grossly different from or inconsistent with the
remaining dataset is a major challenge in real-world KDD applications. Existing
outlier detection methods are ineffective on scattered real-world datasets due
to implicit data patterns and parameter setting issues. We define a novel
"Local Distance-based Outlier Factor" (LDOF) to measure the {outlier-ness} of
objects in scattered datasets which addresses these issues. LDOF uses the
relative location of an object to its neighbours to determine the degree to
which the object deviates from its neighbourhood. Properties of LDOF are
theoretically analysed including LDOF's lower bound and its false-detection
probability, as well as parameter settings. In order to facilitate parameter
settings in real-world applications, we employ a top-n technique in our outlier
detection approach, where only the objects with the highest LDOF values are
regarded as outliers. Compared to conventional approaches (such as top-n KNN
and top-n LOF), our method top-n LDOF is more effective at detecting outliers
in scattered data. It is also easier to set parameters, since its performance
is relatively stable over a large range of parameter values, as illustrated by
experimental results on both real-world and synthetic datasets.
