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Model-based clustering has many advantages over other nonparametric clustering methods that cluster aggregated local defects, by simultaneously identifying defect clusters and obtaining spatial pattern information in the ICs yield model. In the model-based clustering, observations are assumed to reflect a mixture distribution, and all of the mixing components (clusters) are usually described by identical types of models, i.e., multivariate normal distribution [1-2]. Examples of model-based clustering are:
         i) Considered mixtures of principal curves (PCs) [3]. For instance, two-step clustering strategy using model-based clustering that applies PCs to the local defects on wafer map data. [4]
         ii) Amorphous/linear and curvilinear patterns of local defect clusters are considered simultaneously, and then are modeled using multivariate normal distributions (MVNs) and PCs, respectively, which extended the traditional model-based clustering approach by considering the mixture of two different probability densities. [5-6] However, this approach is mainly based on simulation results and lacks the capability to detect closed-ring shaped patterns that have been widely observed in IC manufacturing processes. In addition, this approach is also computationally intensive when the number of defect clusters is relatively large.
         iii) Multiple step approach. (page4264)

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[1] J. D. Banfield and A. E. Raftery, “Model-based Gaussian and non-Gaussian clustering,” Biometrics, vol. 49, pp. 803–821, Sep. 1993.
[2] H. Bensmail, G. Celeux, A. E. Raftery, and C. P. Robert, “Inference in model-based cluster analysis,” Stat. Comp., vol. 7, no. 1, pp. 1–10, 1997.
[3] D. C. Stanford and A. E. Raftery, “Finding curvilinear features in spatial point patterns: Principal curve clustering with noise,” IEEE Trans. Pattern Mach. Intell., vol. 22, no. 6, pp. 601–609, Jun. 2000.
[4] J. Y. Hwang and W. Kuo, “Model-based clustering for integrated circuits yield enhancement,” Eur. J. Oper. Res., vol. 178, no. 1, pp. 143–153, 2007.
[5] T. Yuan and W. Kuo, “A model-based clustering approach to the recognition of spatial defect patterns produced during semiconductor fabrication,” IIE Trans., vol. 40, no. 2, pp. 93–101, 2008.
[6] T. Yuan and W. Kuo, “Spatial defect pattern recognition in semiconductor manufacturing using model-based clustering and Bayesian inference,” Eur. J. Oper. Res., vol. 190, no. 1, pp. 228–240, 2008.