  Anomaly and similarity detection in multidimensional series have a long
history and have found practical usage in many different fields such as
medicine, networks, and finance. Anomaly detection is of great appeal for many
different disciplines; for example, mathematicians searching for a unified
mathematical formulation based on probability, statisticians searching for
error bound estimates, and computer scientists who are trying to design fast
algorithms, to name just a few. In summary, we have two contributions: First,
we present a self-contained survey of the most promising methods being used in
the fields of machine learning, statistics, and bio-informatics today. Included
we present discussions about conformal prediction, kernels in the Hilbert
space, Kolmogorov's information measure, and non-parametric cumulative
distribution function comparison methods (NCDF). Second, building upon this
foundation, we provide a powerful NCDF method for series with small
dimensionality. Through a combination of data organization and statistical
tests, we describe extensions that scale well with increased dimensionality.
