  In this paper, a novel framework for anomaly estimation is proposed. The
basic idea behind our method is to reduce the data into a two-dimensional space
and then rank each data point in the reduced space. We attempt to estimate the
degree of anomaly in both spatial and density domains. Specifically, we
transform the data points into a density space and measure the distances in
density domain between each point and its k-Nearest Neighbors in spatial
domain. Then, an anomaly coordinate system is built by collecting two
unilateral anomalies from k-nearest neighbors of each point. Further more, we
introduce two schemes to model their correlation and combine them to get the
final anomaly score. Experiments performed on the synthetic and real world
datasets demonstrate that the proposed method performs well and achieve highest
average performance. We also show that the proposed method can provide
visualization and classification of the anomalies in a simple manner. Due to
the complexity of the anomaly, none of the existing methods can perform best on
all benchmark datasets. Our method takes into account both the spatial domain
and the density domain and can be adapted to different datasets by adjusting a
few parameters manually.
