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研究生： 黃俊榮
Huang, Chun-Jung
論文名稱： 以資料建構法分析小樣本問題：理論與應用
Data Construction Method to Small Sample Sets: Theory and Applications
指導教授： 王小璠
Wang, Hsiao-Fan
口試委員:
學位類別： 博士
Doctor
系所名稱： 工學院 - 工業工程與工程管理學系
Department of Industrial Engineering and Engineering Management
論文出版年： 2009
畢業學年度： 97
語文別： 英文
論文頁數： 151
中文關鍵詞： 資料建構法 、小樣本問題 、資訊缺口 、學習 、預測
外文關鍵詞： Data Construction Method (DCM), Small-sample-sets, Information gaps, Learning, Prediction
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    • 小樣本問題泛指因資料量不足導致分析績效不佳與錯誤推論的情況。欲解決此類問題，收集更多的資料顯然是最直接而有效的方式。然而，某些情況下，欲獲得足夠的資料是相當困難，甚至不可行的。舉例而言，當商品具有短生命週期的特性，為能快速回應市場需求，企業常須從有限的資料中擬訂生產策略；特別是現實生活中的災害性地震、海嘯、龍捲風、恐怖攻擊、精神疾病等罕見事件，其可用資料本就稀少，但多數卻伴隨著難以估量的社會成本支出。因此，如何從少量的資料中萃取出更多的有效資訊，是個刻不容緩的議題。
    本論文定義了多重集合除法，從而發展出一個名為資料建構法的新方式，用來在原始樣本所給定的數值範圍內產生額外的資料，以克服因資料量太小資料行為無法顯現的問題。另一方面，資料建構法可由額外產生的資料推導出隸屬函數，以作為進一步分析之用。藉由上述的特性，資料建構法將可以用來填補小樣本所造成的資訊缺口，並提高推論的正確性。
    論文中，首先說明了資料建構法的理論背景、特性、與相關步驟。為驗證資料建構法的有效性，本論文運用額外產生的資料於建構信賴區間以估計未知母體平均數，與改善監督式類神經網路的分類正確率等小樣本議題，並比較數個既存的方法於這兩項議題的績效。實驗的結果顯示，資料建構法所產生的額外資料不僅能提供有效的資訊，分析績效也表現較佳。爾後，本論文將資料建構法應用於評估台灣災害性地震的分佈與預測精神分裂症患者何時病症復發等個案。研究結果顯示，資料建構法所推導出的隸屬函數，對於這兩個空間與時間上的稀少事件議題，皆能提供良好的預測績效。

    Small sample problems indicate that the lack of sufficient training data leads to poor prediction performance and erroneous conclusions as well. For that matter, collecting more data is the simplest and most direct choice. However, in some cases it is difficult, even impossible, to pursue additional data for analysis. For example, ever since the product life cycle became shorter and shorter, it has become more and more difficult to collect sufficient data for acquiring management knowledge in the early stages in manufacturing systems. It indeed has been an awkward situation for managers. Also, there are some circumstances, namely rare events, to infrequently occur in the real world, e.g. severe earthquakes, tsunamis, tornados, terrorist attacks, and periodic psychotic episodes of individual schizophrenics. In analyzing such events, their available data are rare in nature, and what is more, they often go along with high socio-economic cost. Thus, how to bring out the information from a small sample as more as possible remains a critical issue.
    To serve the needs above, we have advanced a heuristic measure termed as Data Construction Method (DCM) based on the multiset division. The DCM can not only generate addition data within the domain value of the given sample for revealing the data’s patterns, but also creates the membership function from the generated data for further applications. In this way, the DCM is taken to filling up the information gaps caused by small-sample-sets.
    To demonstrate the effectiveness of DCM, after presenting the DCM’s theoretic background, properties, and algorithm, we compared the DCM with several existing approaches in estimating the population mean and improving the supervised neural network learning performance. The results show that the DCM performs better in a comparative manner. Then, we applied the membership function derived from the DCM data to the studies of predicting the severe earthquakes in Taiwan and forecasting the psychotic episode of individual schizophrenics. The results show that the DCM can provide an appropriate reference for prediction.

    致謝………………………………………………………………………iv 中文摘要…………………………………………………………………………v ABSTRACT…………………………………………………………………vi NOTATIONS……………………………………………………………viii Chapter 1 INTRODUCTION………………………………………………1 1.1 Motivation and Purposes of the Study………………………1 1.2 Summary and the Research Framework…………………………4 Chapter 2 LITERATURE REVIEW…………………………………………6 2.1 Resampling Methods………………………………………………6 2.1.1 Cross-validation………………………………………………7 2.1.2 Jacknife…………………………………………………………9 2.1.3 Bootstrap………………………………………………………10 2.2 Artificial Neural Network……………………………………15 2.3 Functional Approaches to Virtual Data Generation……19 2.3.1 The Principle of Information Diffusion…………………20 2.3.2 The Method of Intervalized Kernel Density Estimation24 2.4 Summary……………………………………………………………27 Chapter 3 METHODOLOGY………………………………………………29 3.1 Preliminary Concepts & Definitions………………………29 3.1.1 The 1-DCM with Its Solution Procedure…………………29 3.1.2 The m-DCM with Its Solution Procedure…………………35 3.2 The Properties of the DCM Data……………………………39 3.3 The Proposed Approach…………………………………………41 3.3.1 The Algorithm of 1-DCM………………………………………41 3.3.2 The Algorithm of m-DCM………………………………………42 3.4 Summary……………………………………………………………43 Chapter 4 APPLICATIONS OF 1-DCM TO ESTIMATE POPULATION MEAN WITH CONFIDENCE INTERVAL FROM SMALL-SAMPLE-SETS……………45 4.1 Problem Description……………………………………………45 4.2 Simulation Experiment…………………………………………46 4.2.1 An Illustrative Example……………………………………46 4.2.2 Sensitivity Analyses on c and k Values…………………48 4.2.3 Comparative study……………………………………………53 4.3 Conclusions………………………………………………………63 Chapter 5 APPLICATIONS OF m-DCM TO IMPROVE SUPERVISED NEURAL NETWORK LEARNING WITH SMALL-SAMPLE-SETS………………65 5.1 Problem Description……………………………………………65 5.2 Implementation and Analysis…………………………………65 5.2.1 Numerical Illustration of the m-DCM Algorithm………65 5.2.2 Sensitivity Analyses…………………………………………72 5.2.3 Comparative Study……………………………………………79 5.3 Conclusions………………………………………………………82 Chapter 6 CASE STUDY ON SPATIAL DISTRIBUTION OF SEVERE EARTHQUAKES IN TAIWAN………………………………………………83 6.1 Problem Description……………………………………………83 6.2 Experiment Design and Analysis……………………………85 6.2.1 Numerical Example……………………………………………85 6.2.2 Case Study on the Disastrous Earthquakes in East Taiwan……………………………………………………………………90 6.2.3 Summary…………………………………………………………101 6.3 Conclusions……………………………………………………105 Chapter 7 CASE STUDY ON TEMPORAL DISTRIBUTION OF PERIODIC PSYCHOTIC EPISODE OF INDIVIDUAL SCHIZOPHRENICS……………107 7.1 Problem Description…………………………………………107 7.2 Experiment Design and Analysis……………………………109 7.2.1 Description of Experiment…………………………………109 7.2.2 An Illustrative Example……………………………………114 7.2.3 Results of Experiment………………………………………118 7.3 Conclusions……………………………………………………120 Chapter 8 SUMMARY AND DISCUSSION………………………………122 8.1 Summary…………………………………………………………122 8.2 Discussion with Further Studies…………………………123 APPENDIX………………………………………………………………125 REFERENCES……………………………………………………………141

    1. Abu-Mostafa Y. S., Hints and the VC-dimension, Neural Computation 5: 278-288, 1993.
    2. Ang, R. P., Use of Jackknife statistic to evaluate result replicability, Journal of General Psychology 125: 218-228, 1998.
    3. Ayuso-Gutiérrez, J.L., and del Río Vega, J.M., Factors influencing relapse in the long-term course of schizophrenia. Schizophr. Res. 28:199-206, 1997.
    4. Banks, J., Carson II, J.S., Nelson, B.L., and Nicol, D.M., Discrete Event System Simulation. 4th edition, Prentice Hall International Editions, 2005.
    5. Barnett, A.H., Mackin, P., Chaudhry, I., Farooqi, A., Gadsby, R., Heald, A., Hill, J., Millar, H., Peveler, R., Rees, A., Singh, V., Taylor, D., Vora, J., and Jones, P.B., Minimising metabolic and cardiovascular risk in schizophrenia: diabetes, obesity and dyslipidaemia, J. Psychopharmacol. 21: 357-373, 2007.
    6. Bier M. Vicki, Statistical methods for the use of accident precursor data in estimating the frequency of rare events, Reliability Engineering & System Safety, 41(3): 267-280, 1993.
    7. Blizard D. Wayne, Multiset Theory, Notre Dame Journal of Formal Logic 30(1): 36-66, 1989.
    8. Bosch, P. V., Personal communication, 2002.
    9. Breiman, L., Bagging predictors, Machine Learning 24: 123-140, 1996.
    10. Brown, S., Barraclough, B., and Inskip, H., Causes of the excess mortality of schizophrenia, Br. J. Psychiatry 177: 212-217, 2000.
    11. Bucklew, James A., An Introduction to Rare Event Simulation, Spring, Inc., 2004.
    12. Buja, A., and Stuetzle W., The effect of bagging on variance, bias, and mean squared error, Preprint, AT& T Labs-Research, 2000.
    13. Cavallini Fabio and Alessandro Rebez, Representing earthquake intensity-magnitude relationship with a nonlinear function, Bulletin of the Seismological Society of America 86(1A): 73-78, 1996.
    14. Chen L.-W., Zuo Z., Medoff D., Holcomb H.H., Lahti A.C., and Tamminga C.A., How many subjects? A Monte Carlo bootstrap simulation for functional imaging, Schizophrenia Research 24: 164-164, 1997.
    15. Chernick, Michael R., Bootstrap Methods: A practitioner's guide, Wiley Series in Probability and Statistics, 1999.
    16. Deng, J.L., Control problems of grey systems, Systems Control Letter 1: 288-294, 1982.
    17. Diaconis, P., and Efron, B., Computer-intensive methods in statistics, Scientific American, 116-130, 1983.
    18. Docherty, J.P., Van Kammen, D.P., Siris, S.G., and Marder, S.R., Stages of onset of schizophrenic psychosis, Am. J. Psychiatry 135: 420-426, 1978.
    19. Du Timon C., Fu-Kwun Wang, and Jen-Chuan Ro, The effect of the bootstrap method on additive fixed data perturbation in statistical database, Omega 30: 367-379, 2002.
    20. Efron B., Bootstrap methods; another look at the jackknife, Annals of Statistics 7: 1-26, 1979.
    21. Efron, B., Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods, Biometrika 63: 589-599, 1981.
    22. Efron B., The jackknife, the bootstrap, and other resampling plans, SIAM Monograph 38, 1982.
    23. Efron B., G. Gong, A leisurely look at the boot strap, the jackknife and cross-validation, American Statistician 37: 36-48, 1983.
    24. Efron B., R.J. Tibshirani, Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Statistical Science 1: 54-77, 1986.
    25. Efron B., Better bootstrap confidence intervals, Journal of the American Statistical Association 82: 171-200, 1987.
    26. Efron Bradley and Tibshirani, R. J., An Introduction of the Bootstrap, Chapman & Hall, Inc., 1993.
    27. Fisher Gordon and Ah Boon Sim, Some finite sample theory for bootstrap regression estimates, Journal of Statistical Planning and Inference 43: 289-300, 1995.
    28. Fitzgerald B.P., The role of early warning symptoms in the detection and prevention of relapse in schizophrenia, Aust. N. Z. J. Psychiatry 35: 758-764, 2001.
    29. Foulds, G., and Bedford, A., A hierachy of classes of personal illness, Psychol. Med. 5: 181-192, 1975.
    30. Frederick S. Hiller and Gerald J. Liberman, Introduction to Operations Research, Sixth Edition. McGraw-Hill, Inc., 1995.
    31. Gaebel, W., and Pietzcker, A., One year outcome of schizophrenic patients: the interaction of chronicity and neuroleptic treatment, Pharmacopsychiatry 18: 235-239, 1985.
    32. Girosi Federico, and Nicholas Tung Chan, Prior knowledge and the creation of "virtual" examples for RBF networks, Proceedings of the IEEE Workshop on Neural Networks for Signal Processing, September 1995, Cambridge, MA.
    33. Graham Alexander, Kronecker Products and Matrix Calculus with Applications, Halsted Press, John Wiley & Sons, Inc., 1981.
    34. Harris R.I.D. and G. Judge, Small sample testing for cointegration using the bootstrap approach. Economics Letters 58: 31-37, 1998.
    35. Hennekens, C.H., Hennekens, A.R., Hollar, D., and Casey, D.E., Schizophrenia and increased risks of cardiovascular disease, Am. Heart J. 150: 1115-1121, 2005.
    36. Herz, M.I., Lamberti, J.S., Mintz, J., Scott, R., O'Dell, S.P., McCartan, L., and Nix, G., A Program for Relapse Prevention in Schizophrenia: A Controlled Study, Arch. Gen. Psychiatry 57: 277-283, 2000.
    37. Hornick, K., Stinchcombe, M., and White, H., Universal Approximation of an Unknown Mapping and its Derivatives Using Multilayer Feedforward Networks, Neural Networks 3: 551-560, 1990.
    38. Huang C.F., Principle of information diffusion, Fuzzy Sets and Systems 91, 69-90, 1997.
    39. Huang C.F., Y. Leung, Estimating the relationship between isoseismal area and earthquake magnitude by a hybrid fuzzy-neural-network method, Fuzzy Sets and Systems 107, 131-146, 1999.
    40. Huang C.F., Information diffusion techniques and small-sample problem, International Journal of Information Technology and Decision Making 1: 229-249, 2002.
    41. Huang C.F., Y. Shi, Towards Efficient Fuzzy Information Processing–Using the Principle of Information Diffusion, Physica-Verlag, Heidelberg, 2002.
    42. Huang C.F. and Claudio Moraga, A diffusion-neural-network for learning from small samples, International Journal of Approximate Reasoning 35: 137-161, 2004.
    43. Huang C.F. and Claudio Moraga, Extracting fuzzy if-then rules by using the information matrix technique, Journal of Computer and System Sciences 70, 26-52, 2005.
    44. Huang Chun-Jung and Hsiao-Fan Wang, Possibility Distribution of Earthquakes in Taiwan, APRU/AEARU Research Symposium, San Francisco, USA, 21-23 April, 2006.
    45. Huang Chun-Jung and Hsiao-Fan Wang, Resolution of rare event by set division, Proceedings from the 36th International Conference on Computers and Industrial Engineering, Taipei, Taiwan, R.O.C., 20-23 June, 2006.
    46. Huang Chun-Jung and Hsiao-Fan Wang, Data Construction Method for Basis Selection in RBF Networks, IEEE International Conference on Industrial Engineering and Engineering Management, Singapore, 2-5 December, 2007.
    47. Huang Chun-Jung and Hsiao-Fan Wang, Virtual sampling with Data Construction Method, in Intelligent Data Analysis: Developing New Methodologies through Pattern Discovery and Recovery, Chapter XVIII, 300-308, Information Science Reference, Hershey, New York, USA, 2008.
    48. Huang Chun-Jung, Hsiao-Fan Wang, Hsien-Jane Chiu, Tsuo-Hung Lan, Tsung-Ming Hu, and El-Wui Loh, Prediction of the Period of Psychotic Episode in Individual Schizophrenics by Simulation-Data Construction Approach, Journal of Medical System, 2009. (in print)
    49. Huber, G., and Gross, G., The concept of basic symptoms in schizophrenia and schizoaffective psychoses, Recenti Prog. Med. 80: 646-652, 1989.
    50. Hudson, T.J., Owen, R.R., Lancaster, A.E., and Mason, L., The Feasibility of Using Automated Data to Assess Guideline-Concordant Care for Schizophrenia, Journal of Medical System 23: 299-307, 1999.
    51. Jae H. Kim, Bootstrap prediction intervals for auto-regression using asymptotically mean-unbiased estimators, International Journal of Forecasting 20: 85-97, 2004.
    52. Jhun Myoungshic and Hueong-Chul Jeong,Applications of bootstrap methods for categorical data analysis, Computational Statistics & Data Analysis 35: 83-91, 2000.
    53. Jia Yanbing and Teresa B. Culver, Bootstrapped artificial neural networks for synthetic flow generation with a small data sample, Journal of Hydrology 33: 580-590, 2006.
    54. Jun Kanda, Ryoji Iwasaki, Hajime Kobayashi, and Bruce R. Ellingwood, Probability-based seismic safety evaluation of existing buildings, Engineering Structures 19(9): 708-717, 1997.
    55. Kamil Kayabali, Modeling of seismic hazard for Turkey using the recent neotectonic data, Engineering Geology 63: 221-232, 2002.
    56. Kaufmann A., and M.M. Gupta, Introduction to fuzzy arithmetic: theory and applications, Van Nostrand Reinhold Company, 1985.
    57. Kim, K.H., J.M. Chiu, H. Kao, Q. Liu, Y.H. Yeh, A preliminary study of crustal structure in Taiwan region using receiver function analysis, Geophysical Journal International 159: 146-164, 2004.
    58. Kracke Dieter W. and Roswitha Heinrich, Local seismic hazard assessment in areas of weak to moderate seismicity-case study from Eastern Germany, Tectonophysics 390: 45-55, 2004.
    59. Krus, D. J., and Fuller, E. A., Computer-assisted multicross-validation in regression analysis” Educational and Psychological Measurement 42: 187-193, 1982.
    60. Kurtz, A. K., A research test of Rorschach test, Personnel Psychology 1: 41-53, 1948.
    61. Law, A.M., and Kelton, W.D., Simulation Modeling and Analysis. 3rd edition, McGraw-Hill International Series, 2000.
    62. Lewis, M. Marshall, S., Lockwood, A., Drake, R., Jones, P., Croudace, T., Association between Duration of Untreated Psychosis and Outcome in Cohorts of First-Episode Patients: A Systematic Review, Arch. Gen. Psychiatry 62: 975-983, 2005.
    63. Leydecker Günter, and Jürgen R. Kopera, 1999. Seismological hazard assessment for a site in Northern Germany, an area of low seismicity, Engineering Geology 52, 293-304.
    64. Li D.-C., Chen L.-S., and Lin Y.S., Using functional virtual population as assistance to learn scheduling knowledge in dynamic manufacturing environments, International Journal of Production Research 41, 4011-4024, 2003.
    65. Li D.-C., Wu C.-S., and Chang F.M., Using data-fuzzification technology in small data set learning to improve FMS scheduling accuracy, International Journal of Advanced Manufacturing Technology 27, 321-328, 2005.
    66. Li Der-Chang and Yao-San Lin, Using virtual sample generation to build up management knowledge in the early manufacturing stages, European Journal of Operational Research 175: 413-434, 2006.
    67. Lin, L.L., Li, W.T., Hwu, H.G., Chen, W.J., Estimating life expectancy of schizophrenic patient: application of trend surface analysis. Presented at the XI Congress of National Public Health Association of the Republic of China, Taipei, October 9, 1999.
    68. Lunneborg, C. E., Data analysis by resampling: Concepts and Applications, Pacific Grove, CA: Duxbury, 2000.
    69. Miguel Mendez, Multiset and the Combinatorics of Symmetric Functions, Advances in Mathematics 102: 95-125, 1993.
    70. Mosier, C. I., Problems and designs of cross-validation, Educational and Psychological Measurement 11: 5-11, 1951.
    71. Muralidhar Krishnamurty, Gary Adna Ames, and Rathindra Sarathy, Bootstrap confidence intervals for estimating audit value from skewed populations and small samples, Simulation 56(2): 119-127, 1991.
    72. Muto Yoshihiko and Yoshihiko Hamamoto, Improvement of the Parzen classifier in small training sample size situations, Intelligent Data Analysis 5: 477–490, 2001.
    73. Neter, J. and J. K. Loebbecke, Behavior of major statistical estimators in sampling accounting populations: An empirical study, AICPA, 1975.
    74. NeuralWorks Professional Ⅱ/PLUS (tm) Win32, NeuralWare, Inc.
    75. Niyogi, P., Girosi, F., and Tomaso, P., Incorporating prior information in machine learning by creating virtual examples, Proceedings of the IEEE 86: 275-298, 1998.
    76. Peddada S.D., Confidence interval estimation of population means subject to order restrictions using resampling procedures, Statistics and Probability Letters 31: 255-262, 1997.
    77. Porter P.S., Rao S.T., Ku J.Y., Poirot R.L., Dakins M., Small sample properties of nonparametric bootstrap t confidence intervals, Journal of the Air and Waste Management Association 47: 1197-1203, 1997.
    78. Quenouille, M., Approximate tests of correlation in time series, Journal of the Royal Statistical Society, Soc. Series B 11: 18-84, 1949.
    79. Quigley John, Tim Bedford, and Lesley Walls, Estimating rate of occurrence of rare events with empirical bayes: A railway application, Reliability Engineering and System Safety 92(5): 619-627, 2007.
    80. Ross M. Sheldon, Introduction to Probability and Statistics for Engineers and Scientists, John Wiley & Sons, Inc., 1987.
    81. Rumelhart, D. E., Hinton, G. E., and Williams, R. J., Learning representations by back-propagating errors, Nature 323: 533-536, 1986.
    82. Saw G. John, Mark C. K. Yang, and Tse Chin Mo, Chebyshev Inequality with Estimated Mean and Variance, The American Statistician 38(2): 130-132, 1984.
    83. Scholz H. Christopher, A Further Note on Earthquake Size Distributions, Bulletin of the Seismological Society of America 88(5): 1325-1326, 1998.
    84. Sheldon M. Ross, 1987. Introduction to Probability and Statistics for Engineers and Scientists. John Wiley & Sons, Inc.
    85. Silver A. Carl, Statistical analysis of rare events in groundwater, Journal of Hazardous Materials 18(1): 17-24, 1998.
    86. Silverman B. W., Using Kernel Density Estimates to Investigate Multimodality, Journal of the Royal Statistical Society Series B 43(1): 97-99, 1981.
    87. Tak K. Mak, Estimating variances for all sample sizes by the bootstrap, Computational Statistics & Data Analysis 46 459-467, 2004.
    88. Tsou Ming-Cheng and Chin-Hong Sun, A comparative and integrated study of a predictive model in spatial data mining-The case of Chi-Chi Earthquake-induced landslide spatial database, Journal of Geographical Science 38: 93-109, 2004.
    89. Tukey, J. W., Bias and confidence in not quite large samples, Annals of Mathematical Statistics 29: 614, 1958.
    90. Wang F. K., Confidence interval for the mean of non-normal data, Quality and Reliability Engineering International 17: 257-267, 2001.
    91. Wang Hsiao-Fan and Chun-Jung Huang, Data Construction Method for the analysis of the spatial distribution of disastrous earthquakes in Taiwan, International Transactions in Operational Research 16: 189-212, 2009.
    92. Wang Hsiao-Fan and Chun-Jung Huang, Multi-dimensional Data Construction Method with its application to learning from small-sample-sets. Intelligent Data Analysis, 2009. (in print)
    93. Weiden, P.J., and Olfson, M., Cost of relapse in schizophrenia, Schizophr. Bull. 21: 419-429, 1995.
    94. Wiersma, D., Nienhuis, F.J., Slooff, C.J., Giel, R., Natural course of schizophrenic disorders: a 15-year follow-up of a Dutch incidence cohort, Schizophr. Bull. 24: 75-85. 1998.
    95. Zhang Jie, Inferential estimation of polymer quality using bootstrap aggregated neural networks, Neural Networks 12: 927-938, 1999.
    96. Zhang Jie, Developing robust non-linear models through bootstrap aggregated neural networks, Neurocomputing 25: 93-113, 1999.
    97. http://fault.moeacgs.gov.tw/, Central Geological Survey, MOEA, Taiwan, Republic of China. (Online available)
    98. http://www.itl.nist.gov/div898/handbook/index.htm. e-Handbook of Statistical Methods. (Online available)

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