  The problem of outlier detection is extremely challenging in many domains
such as text, in which the attribute values are typically non-negative, and
most values are zero. In such cases, it often becomes difficult to separate the
outliers from the natural variations in the patterns in the underlying data. In
this paper, we present a matrix factorization method, which is naturally able
to distinguish the anomalies with the use of low rank approximations of the
underlying data. Our iterative algorithm TONMF is based on block coordinate
descent (BCD) framework. We define blocks over the term-document matrix such
that the function becomes solvable. Given most recently updated values of other
matrix blocks, we always update one block at a time to its optimal. Our
approach has significant advantages over traditional methods for text outlier
detection. Finally, we present experimental results illustrating the
effectiveness of our method over competing methods.
