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Astronomical Data Analysis Software and Systems XII ASP Conference Series, Vol. 295, 2003 H. E. Payne, R. I. Jedrzejewski, and R. N. Hook, eds.

Predictive Mining of Time Series Data in Astronomy
Eric Perlman, Akshay Java Joint Center for Astrophysics, University of Maryland, Baltimore County, 1000 Hil ltop Circle, Baltimore, MD 21250 Abstract. We discuss the development of a Java toolbox for astronomical time series data. Rather than using methods conventional in astronomy (e.g., power spectrum and cross-correlation analysis) we employ rule discovery techniques commonly used in analyzing stock-market data. By clustering patterns found within the data, rule discovery allows one to build predictive models, allowing one to forecast when a given event might occur or whether the occurrence of one event will trigger a second. We have tested the toolbox and accompanying display tool on datasets (representing several classes of ob jects) from the RXTE All Sky Monitor. We use these datasets to illustrate the methods and functionality of the toolbox. We also discuss issues that can come up in data analysis as well as the possible future development of the package.

1.

Introduction

Many types of variable ob jects exist in the universe, including stars with predictable behavior (e.g., Cepheids), ob jects with behavior that is inherently unpredictable (e.g, AGN), and ob jects with both predictable and irregular variability patterns (e.g., X-ray binaries). Constant monitoring of variable ob jects has been a continuing interest in astronomy, beginning with 16th century astronomer David Fabricius, and extending through history to Herschel, Leavitt and others. Today, monitoring is done by a wide variety of techniques, observers and instruments, from dedicated amateurs, to professional astronomers interested in intensive monitoring of individual ob jects, to all-sky monitors such as the RXTE ASM and BATSE aboard CGRO. Despite being a new tool, all-sky monitors have already made important, if not decisive contributions to solving some of astronomy's most persistent mysteries, such as the cosmological origin of gamma-ray bursts and linking emission regions in AGN. With ma jor initiatives such as the Large-Area Synoptic Survey Telescope (LSST) and Supernova Acceleration Probe (SNAP), all-sky monitors are poised to become a ma jor discovery tool in astronomy. To maximize the utility of large monitoring programs, it is important to devise ways of handling large amounts of data in real time and find not only variability but also predictive patterns among these large data streams. It was with these goals in mind that we undertook this pro ject.

431 c Copyright 2003 Astronomical Society of the Pacific. All rights reserved.


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Handle Missing Data by Interpolation

Figure 1. 2.

A flow chart describing the basic rule discovery algorithm.

Clustering and Rule Discovery

The need to understand time series data is not unique to astronomy: time series data exists in a wide variety of fields including geology and atmospheric science as well as many business applications. The common problem is how to efficiently find patterns in the data. Fourier transform and power spectrum methods, commonly used in astronomy research, are well suited for finding patterns with well-determined periodicities (e.g., see Scargle 1997). However, they may be less helpful for ob jects with irregular behavior, and are not optimized to serve as predictive tools. Our approach was to employ clustering and rule discovery, which are optimized for finding patterns that do not rely on a regular periodicity. We first attempt to represent the dataset as a collection of patterns, by sliding a window through the time series to get subsequences. We then cluster these points using the greedy clustering algorithm explained in Das, Gunopulos & Mannila (1997). Once a good fit is achieved, these clusters can then be considered as the basic shapes of the time series, with the entire series composed of superpositions and/or combinations of these basic shapes. The next and main step of the process is to find interesting probabilistic rules between the clusters in the two time series. These rules are of the form: "If a cluster A occurs in time series 1 then we can say with confidence c that B will occur in time series 2 within time T". Figure 1 displays a flow chart of the basic algorithm used in predictive time series analysis. 3. Data Analysis Structure and Usage

Two goals are possible with this approach, each requiring a slightly different analysis tree: (1) to schedule a telescope more intelligently to observe ob jects


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Figure 2. Flow charts for the possible use of this algorithm in scheduling a telescope. when they are at their brightest or most interesting stage, or (2) as an analysis tool to find patterns within a (possibly multivariate) time series (see Figure 2). Within the time-series analysis (TSA) module, the user can control three main parameters: the window size, the minimum cluster distance and the time period for prediction. The TSA module analyzes the time series data and performs trend prediction and rule discovery on both real time and historical data. This output can either be used directly for data analysis for a paper or to forecast both the activity level of an ob ject and the ability of the telescope or satellite to perform the desired observations. All of these factors could be considered in the light of the constraints imposed by individual investigators as well as the review committee. The goal of such a process would be to maximize the scientific usefulness of all the observations. If, for example, a given observation required that a source be above a certain flux level, such a program might have a better chance of ensuring that this was so during the observations. 4. Results, Limitations and Future Work used RXTE ASM datasets for various ject classes. In Figure 3, we show one SMC X-1. SMC X-1 shows interesting timescales: a long time-period behavior

To test and validate the toolbox, we ob jects, spanning several different ob particularly interesting dataset, from periodic behavior on several different


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Figure 3. A screenshot display the rules generat a basic pattern. As each frequency and associated

of the Java GUI application that is used to ed. Each color represents an occurrence of rule is cicked on, the GUI shows the rule's confidence values.

as well as short time-scale variations superposed upon the long-period behavior, but occurring only when the ob ject is bright (see e.g., Kahabka & Li 1999). The toolkit was found to be particularly effective for predicting short-period rules. Longer-period rules can be found by varying the window size, although possibly at the expense of losing short time-scale rules as the window size becomes larger than the rules in question. We can also find longer-period rules with smoothing techniques. The current implementation of the toolkit consist of a rule inference engine, programmed in C and a visualizer, programmed in Java. The current toolkit has several limitations. First, the current toolkit can analyze only a single time series at any time. This obviously gives it limited functionality, as many ob jects are studied with multiple instruments. Second, it has limited ability to deal with missing data. In addition, one could envision multiple processing options, including the incorporation of dynamic time warping techniques, which could be particularly useful to spot quasi-periodic oscillations. References Agarwal, R., Inmielinski, T., Swami, A. 1993, in Proc. ACM SIGMOD, 207 Das, G., Gunopulos, D., & Mannila, H. 1997, Principles of Data Mining and Knowledge Discovery (Springer), 88 Hetland, M. L. 2002, in Data Mining in Time Series Databases, ed. M. Last, A. Kandel and H. Bunke (World Scientific), in press. Kahabka, P. & Li, X-D. 1999, A&A, 345, 117 Scargle, J. D. 1997, in Astronomical Time Series, ed. D. Maoz, A. Steinberg & E. M. Leibowitz (Dordrecht: Kluwer), 1