Mining partial periodic correlations in time series

Recently, periodic pattern mining from time series data has been studied extensively. However, an interesting type of periodic pattern, called partial periodic (PP) correlation in this paper, has not been investigated. An example of PP correlation is that power consumption is high either on Monday or Tuesday but not on both days. In general, a PP correlation is a set of offsets within a particular period such that the data at these offsets are correlated with a certain user-desired strength. In the above example, the period is a week (7 days), and each day of the week is an offset of the period. PP correlations can provide insightful knowledge about the time series and can be used for predicting future values. This paper introduces an algorithm to mine time series for PP correlations based on the principal component analysis (PCA) method. Specifically, given a period, the algorithm maps the time series data to data points in a multidimensional space, where the dimensions correspond to the offsets within the period. A PP correlation is then equivalent to correlation of data when projected to a subset of the dimensions. The algorithm discovers, with one sequential scan of data, all those PP correlations (called minimum PP correlations) that are not unions of some other PP correlations. Experiments using both real and synthetic data sets show that the PCA-based algorithm is highly efficient and effective in finding the minimum PP correlations. Zhen He is a lecturer in the Department of Computer Science at La Trobe University. His main research areas are database systems optimization, time series mining, wireless sensor networks, and XML information retrieval. Prior to joining La Trobe University, he worked as a postdoctoral research associate in the University of Vermont. He holds Bachelors, Honors and Ph.D degrees in Computer Science from the Australian National University. X. Sean Wang received his Ph.D degree in Computer Science from the University of Southern California in 1992. He is currently the Dorothean Chair Professor in Computer Science at the University of Vermont. He has published widely in the general area of databases and information security, and was a recipient of the US National Science Foundation Research Initiation and CAREER awards. His research interests include database systems, information security, data mining, and sensor data processing. Byung Suk Lee is associate professor of Computer Science at the University of Vermont. His main research areas are database systems, data modeling, and information retrieval. He held positions in industry and academia: Gold Star Electric, Bell Communications Research, Datacom Global Communications, University of St. Thomas, and currently University of Vermont. He was also a visiting professor at Dartmouth College and a participating guest at Lawrence Livermore National Laboratory. He served on international conferences as a program committee member, a publicity chair, and a special session organizer, and also on US federal funding proposal review panel. He holds a BS degree from Seoul National University, MS from Korea Advanced Institute of Science and Technology, and Ph.D from Stanford University. Alan C. H. Ling is an assistant professor at Department of Computer Science in University of Vermont. His research interests include combinatorial design theory, coding theory, sequence designs, and applications of design theory.