A Complexity-Invariant Distance Measure for Time Series

The ubiquity of time series data across almost all human endeavors has produced a great interest in time series data mining in the last decade. While there is a plethora of classification algorithms that can be applied to time series, all of the current empirical evidence suggests that simple nearest neighbor classification is exceptionally difficult to beat. The choice of distance measure used by the nearest neighbor algorithm depends on the invariances required by the domain. For example, motion capture data typically requires invariance to warping. In this work we make a surprising claim. There is an invariance that the community has missed, complexity invariance. Intuitively, the problem is that in many domains the different classes may have different complexities, and pairs of complex objects, even those which subjectively may seem very similar to the human eye, tend to be further apart under current distance measures than pairs of simple objects. This fact introduces errors in nearest neighbor classification, where complex objects are incorrectly assigned to a simpler class. We introduce the first complexity-invariant distance measure for time series, and show that it generally produces significant improvements in classification accuracy. We further show that this improvement does not compromise efficiency, since we can lower bound the measure and use a modification of triangular inequality, thus making use of most existing indexing and data mining algorithms. We evaluate our ideas with the largest and most comprehensive set of time series classification experiments ever attempted, and show that complexity-invariant distance measures can produce improvements in accuracy in the vast majority of cases.