  Many methods based on sparse and low-rank representation been developed along
with guarantees of correct outlier detection. Self-representation states that a
point in a subspace can always be expressed as a linear combination of other
points in the subspace. A suitable Markov Chain can be defined on the
self-representation and it allows us to recognize the difference between
inliers and outliers. However, the reconstruction error of self-representation
that is still informative to detect outlier detection, is neglected.Inspired by
the gradient boosting, in this paper, we propose a new outlier detection
framework that combines a series of weak "outlier detectors" into a single
strong one in an iterative fashion by constructing multi-pass
self-representation. At each stage, we construct a self-representation based on
elastic-net and define a suitable Markov Chain on it to detect outliers. The
residual of the self-representation is used for the next stage to learn the
next weaker outlier detector. Such a stage will repeat many times. And the
final decision of outliers is generated by the previous all results.
Experimental results on image and speaker datasets demonstrate its superiority
with respect to state-of-the-art sparse and low-rank outlier detection methods.
