A Study on Non-Metric Multidimensional Scaling Using A New Fitness Function

새로운 적합도 함수를 사용한 비계량형 다차원 척도법에 대한 연구

  • Lee, Dong-Ju (Dept. of Industrial and Systems Engineering, Kongju National University) ;
  • Lee, Chang-Yong (Dept. of Industrial and Systems Engineering, Kongju National University)
  • 이동주 (공주대학교 산업시스템공학과) ;
  • 이창용 (공주대학교 산업시스템공학과)
  • Received : 2011.05.16
  • Accepted : 2011.06.01
  • Published : 2011.06.30

Abstract

Since the non-metric Multidimensional scaling (nMDS), a data visualization technique, provides with insights about engineering, economic, and scientific applications, it is widely used for analyzing large non-metric multidimensional data sets. The nMDS requires a fitness function to measure fit of the proximity data by the distances among n objects. Most commonly used fitness functions are nonlinear and have a difficulty to find a good configuration. In this paper, we propose a new fitness function, an absolute value type, and show its advantages.

Keywords

References

  1. 김미향, 문형태, 신상희, 손명백, 변주영, 최휴창, 손민호; "월성원자력발전소 주변 해역 동물플랑크톤의 군집 특성", 환경생물학회지, 29 : 40-48, 2010.
  2. 노의경, 유효선; "면직물의 구성특성이 시지각에 미치는 영향과 이미지 스케일에 관한 연구", 한국의류학회지, 28 : 1142-1152, 2004.
  3. 박기용, 안성식, 정기용; "다차원척도법을 이용한 외식기업 경쟁요인 비교분석에 관한 연구", 외식경영학회, 9 : 93-114, 2006.
  4. 이창용, 이동주; "담금질을 사용한 비계량 다차원 척도법", 정보과학회 논문지 : 컴퓨팅의 실제 및 레터, 16 : 648-653, 2010.
  5. Abbiw-Jackson, R., Golden, B., Raghavan, S., and Wasil, E.; "A divide-and-conquer local search heuristic for data visualization," Computers and Operations Research, 33 : 3070-3087, 2006. https://doi.org/10.1016/j.cor.2005.01.020
  6. Groenen, P. J. F. and Heiser, W.; "The Tunneling Method For Global Optimization In Multidimensional Scaling," Psychometrika, 61 : 529-550, 1996. https://doi.org/10.1007/BF02294553
  7. Hiller, F. S. and Lieberman, G. J.; Introduction to Operations Research, 8th Ed,, McGraw-Hill, 2004.
  8. Kirkpatrick, S., Gelatt, C. D., and Vecchi. M. P.; "Optimization by simulated annealing," Science, 220 : 671-680, 1983. https://doi.org/10.1126/science.220.4598.671
  9. Klock, H. and Buhmann, J. M.; "Data Visualization by multidimensional scaling : a deterministic annealing approach," Pattern Recognition, 33 : 651-669, 2000. https://doi.org/10.1016/S0031-3203(99)00078-3
  10. Kruskal, J. B.; "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, 29 : 115-129, 1964. https://doi.org/10.1007/BF02289694
  11. Leung, P. L. and Lau, K.; "Estimating the city-block two-dimensional scaling model with simulated annealing," European Journal of Operaional Research, 158 : 518-524, 2004. https://doi.org/10.1016/S0377-2217(03)00357-6
  12. Leeuw, J. D.; "Differentiability of Kruskal's Stress At A Local Minimum," Psychometrika, 49 : 111-113, 1984. https://doi.org/10.1007/BF02294209
  13. Malone, S. W., Tarazaga, P., and Trosset, M. W.; "Better initial configurations for metric multidimensional scaling," Computational Statistics and Data Analysis, 41 : 143-156, 2002. https://doi.org/10.1016/S0167-9473(02)00145-7
  14. Muller, U. A., Dacorogna, M. M., Dave., R. D., Olsen, R. B., Pictet, O. V., and Weizsacker, J. E.; "Volatilities of different time resolutions-Analyzing the dynamics of market components," Journ. of Empirical Finance, 4 : 213-239, 1997. https://doi.org/10.1016/S0927-5398(97)00007-8
  15. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling W. T.; Numerical Recipes in C(3rd Editiion), Cambridge Univ Pr. N.Y., 2003.
  16. Taguchi, Y. h.; and Oono, Y.; "Relational patterns of gene expression via non-metric multidimensional scaling analysis," Bioinformatics, 21 : 730-740, 2005. https://doi.org/10.1093/bioinformatics/bti067
  17. Zilinskas A., Zilinskas, J.; "On Multidimensional Scaling with Euclidean and City Block Metrics," Okio Technologinis Ir Ekonominis Vystymas, 69-75, 2006.
  18. Newman, M.; "The structure and function of complex networks," SIAM Rev, 45 : 167-256, 2003. https://doi.org/10.1137/S003614450342480