On Trajectory Representation for Scientific Features Sameep Mehta India Research Labs, IBM New Delhi, India sameepmehta@in.ibm.com Srinivasan Parthasarathy, Raghu Machiraju Computer Science and Engineering Ohio State University, Columbus, OH, USA {srini, raghu}@cse.ohio-state.edu Abstract In this article, we present trajectory representation al- gorithms for tangible features found in temporally varying scientific datasets. Rather than modeling the features as points, we take attributes like shape and extent of the feature into account. Our contention is that these attributes play an important role in understanding the temporal evolution and interactions among features. The proposed representation scheme is based on motion and shape parameters includ- ing linear velocity, angular velocity, etc. We use these pa- rameters to segment the trajectory instead of relying on the geometry of the trajectory. We evaluate our algorithms on real datasets originating from different domains. We show the accuracy of the motion and shape parameter estimation by reconstructing the trajectories with high accuracy. Fi- nally, we present performance and scalability results. 1 Introduction and Motivation Moving objects pose unique and exciting challenges in spatio-temporal data mining and databases. The key issues include representing, analyzing, and indexing the move- ment of the objects to gain better understanding about the evolution of an individual object and also to understand complex relationships among objects. The problem be- comes even more challenging if the temporal behavior is characterized not only by the change in position but also by the change in shape, size and object type. In this paper, we present such a representation scheme for object trajectories. The main motivation behind our work comes from simple observations about objects/features (Features are defined as Region of Interest (ROIs) in scientific datasets. In this paper we use the term feature and object interchangeably) origi- nating from scientific datasets. These objects have shape and size, i.e., they occupy some volume in space. Modeling these object with a single representative point, e.g. center of mass, amounts to loss of meaningful information. This abstraction can often result in misleading information about the motion characteristics of the object. Consider a baseball which is moving and rotating simultaneously along an axis. By analyzing the trajectory using only the center of mass of the ball, we can only learn about the translational motion. The information about the rotational component cannot be extracted. However, instead of a single point, if we record the position of K representative points, along the surface of the ball, the presence of rotational motion can be detected, resulting in a better and more accurate description of the motion. Moreover, in scientific feature, the extent of ob- jects can also change over time. Ignoring this information can also result in an inaccurate and incomplete description of the motion and will hamper the overall mining process. Our representation includes both motion and shape parame- ters. Points sampled from the surface of the feature form the shape parameters. Motion is described by linear velocity v, angular velocity  ω and scaling co-efficient s. The choice of using the parametric representation is primarily based on three reasons i) this representation provides a meaningful description of the motion as understood by humans, ii) it lends itself very well for analysis and prediction algorithms and iii) the change in extent is easier to account for in this representation. All the parameters are collectively referred to as the Motion Parameter Vector (MPV). The movement of objects are based on laws of physics, re- sulting in smoothly varying trajectories which implies slow and gradual change in MPV. We take advantage of this prop- erty by segmenting the trajectory into sub-trajectories, such that the motion in each sub-trajectory can be represented by the same MPV. To reiterate, the key contributions of this article are: 1. We present robust and intuitive methods for represent- ing object trajectories by using important motion pa- rameters. Additionally, we also capture the change in the extent of the objects. 2. We empirically demonstrate the usefulness and perfor- mance of our algorithms on datasets originating from various domains. 3. We contend that our representation lends itself towards understanding and predicting the evolutionary behav- ior of an object. Additionally, complex relationships Proceedings of the Sixth International Conference on Data Mining (ICDM'06) 0-7695-2701-9/06 $20.00 © 2006