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Abstract

Today’s analog IC sizing and optimization tools are mostly simulation based due to the results accuracy brought by commercial electrical simulators. Additionally, most of the optimization kernels, adopted by those tools, are based on evolutionary optimization algorithms or other metaheuristic techniques because of the large search space that must be explored to find the optimal solutions. The development of an accurate MC-based yield estimation technique that enables evolutionary-based analog IC sizing and optimization tools to search for more robust solutions is a challenging task that must be achieved. The early prediction of variability effect, particularly at the new nanometer technology nodes that are very sensitive to variability effects, is one of the keys to improve production costs. The addition of a large number of MC simulations, to accurately estimate the solutions yield, may increase, beyond an acceptable value, the search time for optimal IC solutions when evolutionary-based optimization algorithms are adopted. This chapter addresses this problem and presents a new MC-based yield estimation methodology with a reduced time impact in the overall optimization processes, which allows its adoption in today’s state-of-the-art evolutionary-based analog IC sizing tools.

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References

  1. N. García-Pedrajas, J. Pérez-Rodríguez, Multi-selection of instances: a straightforward way to improve evolutionary instance selection. Appl. Soft Comput. 12(11), 3590–3602 (2012)

    Article  Google Scholar 

  2. C. Ding, X. He, K-means clustering via principal component analysis, in Proc. 21st Int. Conf. Mach. Learn., Banff, Alberta, Canada, 2004

    Google Scholar 

  3. A. Fred, Similarity measures and clustering of string patterns, in Pattern Recognition and String Matching, (Springer, Boston, MA, 2003), pp. 155–193

    Chapter  Google Scholar 

  4. S. Theodoridis, K. Koutroumbas, Chapter 11—Clustering: basic concepts, in Pattern Recognition, 4th edn., (Academic Press, Boston, MA, 2009), pp. 595–625

    Chapter  MATH  Google Scholar 

  5. K.-L. Wu, J. Yu, M.-S. Yang, A novel fuzzy clustering algorithm based on a fuzzy scatter matrix with optimality tests. Pattern Recogn. Lett. 26(3), 639–652 (2005)

    Article  Google Scholar 

  6. T. Roughgarden, J.R. Wang, The complexity of the k-means method, in 24th Annual European Symposium on Algorithms (ESA 2016), Aarhus, Denmark, 2016

    Google Scholar 

  7. M. Masjed-Jamei, M.A. Jafari, H.M. Srivastava, Some applications of the stirling numbers of the first and second kind. J. Appl. Math. Comput. 47(1), 153–174 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Steinley, K-means clustering: a half-century synthesis. Br. J. Math. Stat. Psychol. 59(1), 1–34 (2006)

    Article  MathSciNet  Google Scholar 

  9. J. MacQueen, Some methods for classification and analysis of multivariate observations, in Proc. 5th Berkeley Symp. Math. Stat. Probability, 1967

    Google Scholar 

  10. S. Theodoridis, K. Koutroumbas, Chapter 5—Feature selection, in Pattern Recognition, 2nd edn., (Elsevier—Academic Press, San Diego, CA, 2003), pp. 163–205

    MATH  Google Scholar 

  11. C.D. Manning, P. Raghavan, H. Schütze, Introduction to Information Retrieval (Cambridge University Press, Cambridge, 2008)

    Book  MATH  Google Scholar 

  12. L. Kaufman, P.J. Rousseeuw, Finding Groups in Data: An Introduction to Cluster Analysis (Wiley, New York, 1990)

    Book  MATH  Google Scholar 

  13. R.T. Ng, J. Han, Efficient and effective clustering methods for spatial data mining, in Proc. 20th Int. Conf. Very Large Data Bases (VLDB’94), Santiago de Chile, Chile, 1994

    Google Scholar 

  14. J.C. Bezdek, R. Ehrlich, W. Full, FCM: the fuzzy c-means clustering algorithm. Comput. Geosci. 10(2), 191–203 (1984)

    Article  Google Scholar 

  15. A. Stetco, X.-J. Zeng, J. Keane, Fuzzy C-means++. Expert Syst. Appl. 42(21), 7541–7548 (2015)

    Article  Google Scholar 

  16. C.H. Li, B.C. Kuo, C.T. Lin, LDA-based clustering algorithm and its application to an unsupervised feature extraction. IEEE Trans. Fuzzy Syst. 19(1), 152–163 (2011)

    Article  Google Scholar 

  17. M.-S. Yang, A survey of fuzzy clustering. Math. Comput. Model. 18(11), 1–16 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  18. L. Bai, J. Liang, C. Dang, F. Cao, A novel fuzzy clustering algorithm with between-cluster information for categorical data. Fuzzy Sets Syst. 215, 55–73 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. V. Schwämmle, O.N. Jensen, A simple and fast method to determine the parameters for fuzzy c–means cluster analysis. Bioinformatics 26(22), 2841–2848 (2010)

    Article  Google Scholar 

  20. V. Torra, On the selection of m for Fuzzy c-Means, in 2015 Conf. Int. Fuzzy Syst. Assoc. European Soc. Fuzzy Logic Technol. (IFSA-EUSFLAT-15), 2015

    Google Scholar 

  21. K.-L. Wu, Analysis of parameter selections for fuzzy c-means. Pattern Recogn. 45(1), 407–415 (2012)

    Article  MATH  Google Scholar 

  22. S. Ghosh, S.K. Dubey, Comparative analysis of K-means and fuzzy C-means algorithms. Int. J. Adv. Comput. Sci. Appl. 4(4) (2013)

    Google Scholar 

  23. D.J. Ketchen, C.L. Shook, The application of cluster analysis in strategic management research: an analysis and critique. Strat. Manag. J. 17, 441–458 (1996)

    Article  Google Scholar 

  24. P.J. Rousseeuw, Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)

    Article  MATH  Google Scholar 

  25. D.T. Pham, S.S. Dimov, C.D. Nguyen, Selection of K in K-means clustering. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 219(1), 103–119 (2005)

    Article  Google Scholar 

  26. M. Halkidi, Y. Batistakis, M. Vazirgiannis, On clustering validation techniques. J. Intell. Inform. Syst. 17(2), 107–145 (2001)

    Article  MATH  Google Scholar 

  27. J.C. Bezdek, Numerical taxonomy with fuzzy sets. J. Math. Biol. 1, 57–71 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  28. J.C. Bezdek, Cluster validity with fuzzy sets. J. Cybernet. 3, 58–74 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  29. Y. Zhang, W. Wang, X. Zhang, Y. Li, A cluster validity index for fuzzy clustering. J. Inform. Sci. 178(4), 1205–1218 (2008)

    Article  MATH  Google Scholar 

  30. D. Campo, G. Stegmayer, D. Milone, A new index for clustering validation with overlapped clusters. Expert Syst. Appl. 64, 549–556 (2016)

    Article  Google Scholar 

  31. E. Lord, M. Willems, F.-J. Lapointe, V. Makarenkov, Using the stability of objects to determine the number of clusters in datasets. J. Inform. Sci. 393, 29–46 (2017)

    Article  Google Scholar 

  32. J. Wang, A linear assignment clustering algorithm based on the least similar cluster representatives, in Int. Conf. Syst. Man, Cybern., Orlando, FL, 1997

    Google Scholar 

  33. J. Fan, J. Wang, A two-phase fuzzy clustering algorithm based on neurodynamic optimization with its application for PolSAR image segmentation. IEEE Trans. Fuzzy. Syst. 26(1), 72–83 (2016). https://doi.org/10.1109/TFUZZ.2016.2637373

    Article  Google Scholar 

  34. K.L. Cheng, J. Fan, J. Wang, A two-pass clustering algorithm based on linear assignment initialization and k-means method, in 5th Int. Symp. Commun., Control Signal Process., Rome, 2012

    Google Scholar 

  35. D. Arthur, S. Vassilvitskii, k-means++: the advantages of careful seeding, in Proc. 18th Annu. ACM-SIAM Symp. Discrete Algorithms (SODA'07), New Orleans, Louisiana, 2007

    Google Scholar 

  36. M.E. Celebi, H.A. Kingravi, P.A. Vela, A comparative study of efficient initialization methods for the k-means clustering algorithm. Expert Syst. Appl. 40(1), 200–210 (2013)

    Article  Google Scholar 

  37. A.K. Jain, M.N. Murty, P.J. Flynn, Data clustering: a review. ACM Comput. Surv. 31(3), 264–323 (1999)

    Article  Google Scholar 

  38. K. Abirami, P. Mayilvahanan, Performance analysis of K-means and bisecting K-means algorithms in weblog data. Int. J. Emerg. Technol. Eng. Res. 4(8), 119–124 (2016)

    Google Scholar 

  39. R.R. Patil, A. Khan, Bisecting K-means for clustering web log data. Int. J. Comput. Appl. 116(19), 36–41 (2015)

    Google Scholar 

  40. P. Cimiano, A. Hotho, S. Staab, Comparing conceptual, partitional and agglomerative clustering for learning taxonomies from text, in Proc. 16th European Conf. Artificial Intell., Amsterdam, 2004

    Google Scholar 

  41. L. Sousa, J. Gama, The application of hierarchical clustering algorithms for recognition using biometrics of the hand. Int. J. Adv. Eng. Res. Sci. 1(7), 14–24 (2014)

    Google Scholar 

  42. F. Murtagh, P. Contreras, Algorithms for hierarchical clustering: an overview. WIREs Data Mining Knowl. Discov. 2(1), 86–97 (2012)

    Article  Google Scholar 

  43. G.W. Milligan, M.C. Cooper, An examination of procedures for determining the number of clusters in a data set. Psychometrika 50(2), 159–179 (1985)

    Article  Google Scholar 

  44. Y. Jung, H. Park, D.-Z. Du, B.L. Drake, A decision criterion for the optimal number of clusters in hierarchical clustering. J. Glob. Optim. 25(1), 91–111 (2003)

    Article  MathSciNet  Google Scholar 

  45. R. Jenssen, D. Erdogmus, K.E. Hild, J.C. Principe, T. Eltoft, Information force clustering using directed trees, in Energy Minimization Methods in Computer Vision and Pattern Recognition, Lisbon, 2003.

    Google Scholar 

  46. G. Karypis, E.-H. Han, V. Kumar, Chameleon: hierarchical clustering using dynamic modeling. Computer 32(8), 68–75 (1999)

    Article  Google Scholar 

  47. M. Ren, P. Liu, Z. Wang, J. Yi, A self-adaptive fuzzy c-means algorithm for determining the optimal number of clusters. Comput. Intell. Neurosci. 2016, 12 (2016)

    Article  Google Scholar 

  48. X.L. Xie, G. Beni, A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 13(8), 841–847 (1991)

    Article  Google Scholar 

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Canelas, A.M.L., Guilherme, J.M.C., Horta, N.C.G. (2020). Monte Carlo-Based Yield Estimation: New Methodology. In: Yield-Aware Analog IC Design and Optimization in Nanometer-scale Technologies. Springer, Cham. https://doi.org/10.1007/978-3-030-41536-5_4

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  • DOI: https://doi.org/10.1007/978-3-030-41536-5_4

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