TAILIEUCHUNG - Pattern Recognition Techniques, Technology and Applications_2

Tham khảo sách 'pattern recognition techniques, technology and applications_2', công nghệ thông tin, kỹ thuật lập trình phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 13 Manifold Matching for High-Dimensional Pattern Recognition Seiji Hotta Tokyo University of Agriculture and Technology Japan 1. Introduction In pattern recognition a kind of classical classifier called k-nearest neighbor rule kNN has been applied to many real-life problems because of its good performance and simple algorithm. In kNN a test sample is classified by a majority vote of its k-closest training samples. This approach has the following advantages 1 It was proved that the error rate of kNN approaches the Bayes error when both the number of training samples and the value of k are infinite Duda et al. 2001 . 2 kNN performs well even if different classes overlap each other. 3 It is easy to implement kNN due to its simple algorithm. However kNN does not perform well when the dimensionality of feature vectors is large. As an example Fig. 1 shows a test sample belonging to class 5 of the MNIST dataset LeCun et al. 1998 and its five closest training samples selected by using Euclidean distance. Because the selected five training samples include the three samples belonging to class 8 the test sample is misclassified into class 8. Such misclassification is often yielded by kNN in highdimensional pattern classification such as character and face recognition. Moreover kNN requires a large number of training samples for high accuracy because kNN is a kind of memory-based classifiers. Consequently the classification cost and memory requirement of kNN tend to be high. Fig. 1. An example of a test sample leftmost . The others are five training samples closest to the test sample. For overcoming these difficulties classifiers using subspaces or linear manifolds affine subspace are used for real-life problems such as face recognition. Linear manifold-based classifiers can represent various artificial patterns by linear combinations of the small number of bases. As an example a two-dimensional linear manifold spanned by three handwritten digit images 4 is shown in Fig. 2. .

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