Change points detection in crime-related time series: an on-line fuzzy
  approach based on a shape space representation
Fabrizio Albertetti Lionel Grossrieder Olivier Ribaux Kilian Stoffel
The extension of traditional data mining methods to time series has been
effectively applied to a wide range of domains such as finance, econometrics,
biology, security, and medicine. Many existing mining methods deal with the
task of change points detection, but very few provide a flexible approach.
Querying specific change points with linguistic variables is particularly
useful in crime analysis, where intuitive, understandable, and appropriate
detection of changes can significantly improve the allocation of resources for
timely and concise operations. In this paper, we propose an on-line method for
detecting and querying change points in crime-related time series with the use
of a meaningful representation and a fuzzy inference system. Change points
detection is based on a shape space representation, and linguistic terms
describing geometric properties of the change points are used to express
queries, offering the advantage of intuitiveness and flexibility. An empirical
evaluation is first conducted on a crime data set to confirm the validity of
the proposed method and then on a financial data set to test its general
applicability. A comparison to a similar change-point detection algorithm and a
sensitivity analysis are also conducted. Results show that the method is able
to accurately detect change points at very low computational costs. More
broadly, the detection of specific change points within time series of
virtually any domain is made more intuitive and more understandable, even for
experts not related to data mining.