A new dissimilarity measure in time-dependent experiments

Most distance measures used in unsupervised learning methods including the Euclidean distance and correlation-based distances disregard the time order of observations. In this paper, we consider a new dissimilarity measure that incorporates the time order of observations for time-dependent experiments. It measures the distance between a linear combination of two consecutive observations. To consider the length of time interval between observations, we use the same measure with the weight of time length, Δ t_i. We show that this measure has larger asymptotic discriminating power than the Euclidean distance, and it also gives a good small sample performance.