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, Δti. We show that this measure has larger asymptotic discriminating power than the Euclidean distance, and it also gives a good small sample performance.