tailieunhanh - Báo cáo hóa học: " Modified Kernel Functions by Geodesic Distance"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Modified Kernel Functions by Geodesic Distance | EURASIP Journal on Applied Signal Processing 2004 16 2515-2521 2004 Hindawi Publishing Corporation Modified Kernel Functions by Geodesic Distance Quan Yong Institute of Image Processing Pattern Recognition Shanghai Jiaotong University Shanghai 200030 China Email quanysjtu@ Yang Jie Institute of Image Processing Pattern Recognition Shanghai Jiaotong University Shanghai 200030 China Email jieyang@ Received 20 August 2003 Revised 9 March 2004 When dealing with pattern recognition problems one encounters different types of prior knowledge. It is important to incorporate such knowledge into the classification method at hand. A common prior knowledge is that many datasets are on some kinds of manifolds. Distance-based classification methods can make use of this by a modified distance measure called geodesic distance. We introduce a new kind of kernels for a support vector machine SVM which incorporates geodesic distance and therefore is applicable in cases where such transformation invariance is known. Experiments results show that the performance of our method is comparable to that of other state-of-the-art methods such as SVM-based Euclidean distance. Keywords and phrases support vector machine geodesic distance kernel function. 1. INTRODUCTION Support vector machine SVM is a new promising pattern classification technique proposed recently by Vapnik and coworkers 1 2 . Unlike traditional methods which minimize the empirical training error SVM aims at minimizing an upper bound of the generalization error through controlling the margin between the separating hyperplane and the data. This can be regarded as an approximate implementation of the structure risk minimization principle. What makes SVM attractive is the property of condensing information in the training data and providing a sparse representation by using a very small number of data points. SVM is a linear classifier in the parameter space but it is easily extended to a nonlinear classifier

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