Feature Extraction Methods for Time Series Data in SAS ® Enterprise Miner TM

Because time series data have a unique data structure, it is not easy to apply some existing data mining tools directly to the data. For example, in classification and clustering problems, each time point is often considered a variable and each time series is considered an observation. As the time dimension increases, the number of variables also increases, in proportion to the time dimension. Therefore, data mining tasks require some feature extraction techniques to summarize each time series in a form that has a significantly lower dimension. This paper describes various feature extraction methods for time series data that are implemented in SAS Enterprise MinerTM. INTRODUCTION Time series data mining has four major tasks: clustering, indexing, classification, and segmentation. Clustering finds groups of time series that have similar patterns. Indexing finds similar time series in order, given a query series. Classification assigns each time series to a known category by using a trained model. Segmentation partitions time series. Time series data can be considered multidimensional data; this means that there is one observation per time unit, and each time unit makes one dimension. Some common data mining techniques are used for the tasks. However, in the real world, each time series is usually a high-dimensional sequence, such as stock market data whose prices change over time or data collected by a medical device. When the time unit is seconds, the dimensions of data that accumulate in just one hour are 3,600. Moreover, the dimensions are highly correlated to one another. The number of variables in training data increases proportionally as the time dimension increases. Most existing data mining tools cannot be used efficiently on time series data without a dimension reduction. Therefore, a dimension reduction is required through feature extraction techniques that map each time series to a lower-dimensional space. The most common techniques of dimension reduction in time series are singular value decomposition (SVD), discrete Fourier transformation (DFT), discrete wavelet transformation (DWT), and line segment methods. Some classical time series analyses, such as seasonal, trend, seasonal decomposition, and correlation analyses, are also used for feature extraction. This paper shows how to use SAS Enterprise Miner to implement the feature extraction techniques. But it does not attempt to explain these time series techniques in detail and instead invites the interested reader to explore some of the literature on the subject: Keogh and Pazzani (2000a), Keogh et al. (2000), and Gavrilov et al. (2000) for time series dimensionality reduction and the TIMESERIES procedure documentation in SAS/ETS for the classical time series analyses. This paper is organized as follows. First, it explains feature extraction and dimension reduction techniques that use classical time series analysis, and then it describes feature extraction techniques that use some well-known mathematical functions for dimension reduction. Next, it demonstrates the performance of dimension reduction techniques by presenting some examples. The paper uses SAS Enterprise Miner 13.1 to demonstrate these techniques.