Lee, Y., Lin, Y. & Wahba, G. (2002) Multicategory support vector machines, theory, and application to the classi cation of microarray data and satellite radiance data. Journal of American Statistical Association. To appear. Home/Search Document Details and Download
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Ranking with Large Margin Principle: Two Approaches - Shashua, Levin (2003) (4 citations) (Correct)
....equal to twice the number of training examples precisely N =2l;i 1 ;i k where l is the number of training examples. This favorably compares to the O(l ) required by the recent SVM approach to ordinal regression introduced in [7] or the kl required by the general multi class approach to SVM [4, 8]. Further note that since the entries of Q Q are the inner products of the training examples, they can be represented by the kernel inner product in the input space dimension rather than by inner products in the feature space dimension. The decision rule, in this case, given a new instance ....
Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines. Technical Report 1043, Univ. of Wisconsin, Dept. of Statistics, Sep. 2001.
Bound on the Risk for M-SVMs - Guermeur, Elisseeff, Zelus (Correct)
....expression of the guaranteed risk . Recently, two new models became available. The rst one, described in [4] uses an original expression of the empirical risk. The bound on the generalization error provided is directly borrowed from a tree based decomposition approach called DAGSVM [10] In [9], the machine is devised to asymptotically implement the Bayes rule. To sum up, numerous solutions, based on di erent principles, are currently available to compute polychotomies with SVMs. They are still to be compared in the very framework to which they belong, i.e. with respect to their ....
Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines. Technical Report 1043, University of Wisconsin, Madison, Department of Statistics, 2001.
Taxonomy of Large Margin Principle Algorithms for Ordinal.. - Shashua, Levin (2002) (Correct)
....classes. As in conventional SVM, the margin is pre scaled to be equal to 2=jwj thus maximizing the margin is achieved by minimizing w Delta w. The support vectors lie on the boundaries between the two closest classes. training set of size 2l) Likewise, the multi class SVMs proposed in [4, 11, 12, 8] would also ignore the ordering of the class labels and use a training set of size kl. In this paper we adopt the notion of maintaining a totally ordered set via projections in the sense of projecting the instances x i onto the reals f(x) w Delta x [7, 5] and show how this could be implemented ....
Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines. Technical Report 1043, Univ. of Wisconsin, Dept. of Statistics, Sep. 2001.
Optimal Properties and Adaptive Tuning of Standard and.. - Wahba, Lin, Lee, Zhang (2002) (2 citations) Self-citation (Lin Wahba) (Correct)
....case. We describe the nonstandard SVM, and show how both the GACV and the ## method can be generalized in that case, from [31] A modest simulation shows that they behave similarly. Finally, we briefly mention that we have generalized the (standard and nonstandard) SVM to the multicategory case [15]. 1.2 Optimal Classification and Penalized Likelihood Let hA ( hB ( be densities of x for class A and class B, and let #A = probability the next observation (Y ) is an A, and let #B = 1 #A = probability that the next observation is a B. Then p(x) # prob Y = A x = #AhA (x) ....
Y. Lee, Y. Lin, and G. Wahba.Multicategory support vector machines (preliminary long abstract).Technical Report 1040, Department of Statistics, University of Wisconsin, Madison WI, 2001.
Optimal Properties and Adaptive Tuning of Standard and.. - Wahba, Lin, Lee, Zhang (2002) (2 citations) Self-citation (Lin Wahba) (Correct)
....to the k category case, which solves a single optimization problem to obtain a vector f # (x) f 1# (x) f k# (x) where the category classifier is the component of f that is 1. Optimal Properties and Adaptive Tuning of Standard and Nonstandard Support Vector Machines 15 largest, see [14]. Usual muticategory classification schemes do one vs many or # k 2 # pairwise comparisons, and the multicategory SVM has advantages in certain examples. The GACV has been been extended to the nonstandard multicategory SVM case and it appears that the BRXA can also be extended. Penalized ....
Y. Lee, Y. Lin, and G. Wahba.Multicategory support vector machines.Technical Report 1043, Department of Statistics, University of Wisconsin, Madison WI, 2001.
Kernel Logistic Regression and the Import Vector Machine - Ji Zhu Department (Correct)
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Lee, Y., Lin, Y. & Wahba, G. (2002) Multicategory support vector machines, theory, and application to the classi cation of microarray data and satellite radiance data. Journal of American Statistical Association. To appear.
An Approach to Automatic Recognition of Spontaneous.. - Braathen Bartlett.. (2002) (Correct)
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Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines. Technical Report TR 1040, U. Wisconsin, Madison, Dept. of Statistics, 2001.
Ranking with Large Margin Principle: Two Approaches - Shashua, Levin (2003) (4 citations) (Correct)
No context found.
Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines. Technical Report 1043, Univ. of Wisconsin, Dept. of Statistics, Sep. 2001.
Ranking with Large Margin Principle: Two Approaches - Shashua, Levin (2002) (4 citations) (Correct)
No context found.
Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines. Technical Report 1043, Univ. of Wisconsin, Dept. of Statistics, Sep. 2001.
An Approach to Automatic Recognition of Spontaneous.. - Braathen Bartlett.. (Correct)
No context found.
Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines. Technical Report TR 1040, U. Wisconsin, Madison, Dept. of Statistics, 2001.
Topological Fields Chunking for German with SVM's: Optimizing.. - Liepert (2003) (Correct)
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Y. Lee, Y. Lin, and G. Wahba. Multicategory support vector machines. Technical Report 1043, Department of Statistics, University of Wisconsin, Madison WI, 2001. Proceedings of the 33rd Symposium on the Interface, 2001.
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