# 臺灣博碩士論文加值系統

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 Pattern recognition may be described as the process of making a decision based on data input. This is certainly a very huge domain with many practical applications in many fields of science. A specific distance measure which is invariant to different transformations, proposed by Simard et al. (1993) and called Tangent Distance (TD). It is to estimate the minimum distance between two patterns by using different direction of tangent vectors.In this research, we combine TD method with the new ideas. One iscalled Pseudo Missing Value. The key idea of it is to remove a certain region in the image to help classification. In experimental results for subset of Zip Code data, the best error rate is 0.197 that is slightly better than the result of TD method (0.206).Another idea is called local transformation. The main idea is to cut invariant transformations of TD method into two parts and give a new metric of distance. In experimental results, there are sixteen error rates of two classes recognition lower than it from TD method in the subset of Zip Code data. Furthermore, there are four error rates of two classes recognition lower than it from TD method in the Zip Code data.Here, we use one of typical handwritten digit recognition data set which is called Zip Code data set to demonstrate our methods. The digits were written by many different people with a great variety of writing styles and instruments. Two sets are available, one training set containing 7291 digits and one test set containing 2007 digits.Besides, classification problems in the wafer bin map is an important task. So we try to consider invariant transformations of TD method to the wafer map data.
 1. Introduction . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature Review . . . . . . . . . . .. . . . . . . . 21.3 Overview . . . . . . . . . . . . . . . . . . . . . . . 52. Data Sets . . . . . . . . . . . . . . . . . . . . . . . 62.1 Zip Code Data . . . . . . . . . .. . . . . . . . . . . 62.2 Wafer Map Data . . . . . . . . . . . . . . . . . . . . 82.3 Software Used . . . . . . . . . . . .. . . . . . . . . 93. Tangent Distance . . . . . . . . . . . . . . . . . . . 103.1 Implementation . . . . . . . . . . . . . . . . . . . 103.2 Tangent Vector . . . . . . . . . . . . . . . . . . . 123.3 Smooth Interpolating . . . . . . . . . . . . . . . . 143.4 Invariant Transformation Forms . . . . . . . . .. . . 154. New Methods . . . . . . . . . . . . . . . . . . . . . 224.1 Subset for Zip Code Data . . . . . . . . . . . . .. . 244.2 Pseudo Missing Value . . . . . . . . . . . . . . . . 254.3 Results of Pseudo Missing Value . . . . . . . . . . . 284.4 Local Transformation . . . . . . . . . . . . .. . . . 344.5 Results of Local Transformation . . . . . . . . . . . 355. Applications to Wafer Map Data . . . . . . . . . . . . 396. Conclusions and Further Researches . . . . . . . . . . 416.1 Conclusions . . . . . . . . . . . . . . . . . . . . . 416.2 Further Researches . . . . . . . . . . . . . . .. . . 42