臺灣博碩士論文加值系統

Abstract
Based on the fractal dimension, the tri-plots can classify two large and not equal sizes of the time series datasets. The tri-plots measure three function values which include two self-plots and one cross-plot. The self-plot affords the character of one individual dataset. The cross-plot describes the relation between two datasets. Originally, the tri-plots just can get the relation in two datasets, but we can use tri-plots many times for multi-datasets. The time series data like typhoon trajectories, we are interested in the differences among the different annual events, e.g. ENSO and La Niña. In here, we propose the tri-plots method to analyze and classify different annual typhoon trajectories.
On the other hand, the Markov chain model is used to deal with the time series data in data mining filed. Markov chain establishes the probability relation between two consecutive time steps and estimate one model for one trajectory. Basically, every trajectory has own probability model. We can repeat this process until all datasets finished computing. In implementation, we combine several trajectories to be one trajectory in order to corresponding physical meaning and saving executing time. After all trajectories of all datasets finished estimating their own model, the dissimilarity matrix can be given by comparing all trajectory models pairs, that is, the dissimilarity matrix describes the relations between the trajectories. So, we use the Markov chain model to be another alternative method for different annual events trajectories classification problems.
After the calculation of the tri-plots, the ENSO and La Niña years typhoon tracks can be separated by the classifier, the smooth support vector machines（SSVM）, which can get the training error about 0.023~0.268 and the testing error about 0.271~0.334. For Markov chain, the SSVM classifier can get the training error around 0.122~0.272 and the testing around 0.248~0.308. It is worth noting that the performance of Markov chain with the threshold of the pace is better than the original Markov chain. The training error of Markov chain with threshold is around 0.031~0.173 and the testing around 0.181~0.287. Moreover, the tri-plots or Markov chain model concentrates the information of all events to one distribution figure that presents the dissimilarity of these typhoon trajectories or depicts which years should be probably regarded as one group. We believe that they can be very helpful for realizing ENSO and La Niña atmospheric circulation and for establishing typhoon databases. Moreover, we think tri-plots and Markov chain can be used to find the intrinsic patterns in other traditional weather data.

Contents

Abstract i
Acknowledgements iii
List of Tables vi
List of Figures vii
Chapter 1 Introduction 1
1.1 Motivation 1
1.2 Related Work 5
Chapter 2 Methodology 7
2.1 Fractal Dimension and Tri-plots 7
2.2 Markov Chain Model 10
Chapter 3 The Data 12
Chapter 4 Performance of the Tri-plots 17
4.1 Feature Selection 17
4.2 Topographical Effect 22
4.3 Distribution of all Cases 23
Chapter 5 Performance of Markov Chain Model 28
5.1 The Characteristics of the Features 28
5.2 Distribution Classification and Verification 30
Chapter 6 Conclusions and Discussions 34
Appendix 37
Bibliography 41

Bibliography
Belussi, A. and C. Faloutsos. Estimating the selectivity of spatial queries using the ‘correlation’ fractal dimension. In the 21-th conference of Very Large Data Bases, pages 299-310, 1995.
Bishop, C. M. Pattern recognition and machine learning. Springer press, 2006.
Camargo, S, J., A. W. Robertson, S. J. Gaffney, and P. Smyth. Cluster analysis of typhoon tracks. Part I: general properties. Journal of Climate, vol. 20, pages 3635-3653, 2007a.
Camargo, S, J., A. W. Robertson, S. J. Gaffney, and P. Smyth. Cluster analysis of typhoon tracks. Part II: large circulation and ENSO. Journal of Climate, vol. 20, pages 3654-3676, 2007b.
Chan, J. C. L. and W. M. Gray. Tropical cyclone movement and surrounding flow relationships. Monthly Weather Review, vol. 100, pages 1354-1374, 1982.
Emanuel, K. Divine wind: the history and science of hurricanes. Oxford university press, USA, 2005.
Gaffney, S. and P. Smyth. Trajectory clustering with mixtures of regression models. In the International Conference on Knowledge Discovery and Data Mining, pages 63-72, 1999.
Harr, P. A. and R. L. Elsberry. Tropical cyclone track characteristics as a function of large-scale circulation anomalies. Monthly Weather Review, 119, pages 1448-1468, 1991.
Hsieh, W. Machine learning methods in the environmental sciences. Cambridge university press, Cambridge, 2009.
Jordan, M. I. An introduction to probabilistic graphic models. In preparation.
Lee, J.-G., J. Han, and K.-Y. Whang. Trajectory clustering: A partition-and-group framework. International Conference on Management of Data, pages 593-640, 2007.
Lee, Yuh-Jye and O. L. Mangasarian. SSVM: A smooth support vector machine for classification. Comput. Optim. Appl., 20(1), pages 5-22, 2001.
Lin, H. Trajectory based on behavior analysis for verification and recognition. National Taiwan University of Science and Technology, master thesis, Taipei, 2009.
Miller J., P. B. Weichman, and M. C. Cross. Statistical mechanics, Euler’s equation, and Jupiter’s Red Spot. Physics Review, A 45, pages 2328–2359, 1992.
Risi, C. Statistical synthesis of tropical cyclone tracks in a risk evaluation perspective. Massachusetts Institute of Technology, internship report, Cambridge, 2004.
Strogatz, S. H. Nonlinear dynamics and chaos: with applications to Physics, Biology, Chemistry, and engineering. Westview press, 2001.
Tenebaum, J. B., V. d. Silva, and J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290, pages 2319-2323, 2000.
Traina, A., C. Traina, S. Papadimitriou, and C. Faloutsos. Tri-Plots: Scalable tools for multi dimensional data. In the International Conference on Knowledge Discovery and Data Mining, pages 184-193, 2001.
Vlachos, M. D. Gunopulos, and G. Kollios. Discovering similar multidimensional trajectories. In the International Conference on Data Engineering, pages 673-684, 2002.
Wang, B., H. Rui and J. C. L. Chan. How strong ENSO events affect tropical activity over the western North Pacific. Journal of Climate, vol. 15, pages 1643-1658, 2002.
Webster, P. J., G. J. Holland, J. A. Curry, and H.-R. Chang. Changes in tropical cyclone number, duration, and intensity in a warming environment. Science, 309, pages 1844-1846, 2005.
World Meteorological Organization. El Niño/La Niña update. 2009.