  Feature selection places an important role in improving the performance of
outlier detection, especially for noisy data. Existing methods usually perform
feature selection and outlier scoring separately, which would select feature
subsets that may not optimally serve for outlier detection, leading to
unsatisfying performance. In this paper, we propose an outlier detection
ensemble framework with embedded feature selection (ODEFS), to address this
issue. Specifically, for each random sub-sampling based learning component,
ODEFS unifies feature selection and outlier detection into a pairwise ranking
formulation to learn feature subsets that are tailored for the outlier
detection method. Moreover, we adopt the thresholded self-paced learning to
simultaneously optimize feature selection and example selection, which is
helpful to improve the reliability of the training set. After that, we design
an alternate algorithm with proved convergence to solve the resultant
optimization problem. In addition, we analyze the generalization error bound of
the proposed framework, which provides theoretical guarantee on the method and
insightful practical guidance. Comprehensive experimental results on 12
real-world datasets from diverse domains validate the superiority of the
proposed ODEFS.
