zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Error bounds of multi-graph regularized semi-supervised classification. (English) Zbl 1192.68509
Summary: We investigate the generalization performance of the multi-graph regularized semi-supervised classification algorithm associated with the hinge loss. We provide estimates for the excess misclassification error of multi-graph regularized classifiers and show the relations between the generalization performance and the structural invariants of data graphs. Experiments performed on real database demonstrate the effectiveness of our theoretical analysis.
MSC:
68T05Learning and adaptive systems
68T10Pattern recognition, speech recognition
References:
[1]Argyriou, A.; Herbster, M.; Pontil, M.: Combining graph Laplacians for semi-supervised learning, Nips 18 (2006)
[2]Aronszajn, N.: Theory of reproducing kernels, Transactions of the American mathematical society 68, 337-404 (1950) · Zbl 0037.20701 · doi:10.2307/1990404
[3]Bartlett, P. L.; Mendelson, S.: Rademacher and Gaussian complexities: risk bounds and structural results, Journal of machine learning research 3, 463-482 (2002) · Zbl 1084.68549 · doi:10.1162/153244303321897690
[4]Belkin, M.; Matveeva, I.; Niyogi, P.: Regularization and semi-supervised learning on large graphs, Proceedings of the 17th annual conference on learning theory, Banff, Albert, 624-638 (2004) · Zbl 1078.68685 · doi:10.1007/b98522
[5]Belkin, M.; Niyogi, P.: Semi-supervised learning on Riemannian manifolds, Machine learning 56, 209-239 (2004) · Zbl 1089.68086 · doi:10.1023/B:MACH.0000033120.25363.1e
[6]Belkin, M.; Niyogi, P.; Sindhwani, V.: Manifold regularizaion: a geometric framework for learning from labeled and unlabeled examples, Journal of machine learning research 7, 2399-2434 (2006) · Zbl 1222.68144 · doi:http://www.jmlr.org/papers/v7/belkin06a.html
[7]C.L. Blake, C.J. Merz, UCI repository of machine learning databases, Irvine, CA, University of California, Department of Information and Computer Science, 1998, lt;http://www.ics.uci.edu/mlearn/MLRepository.htmlgt;.
[8]A. Blum, T. Mitchell, Combining labeled and unlabeled data with co-training, in: Proceedings of the Workshop on Computational Learning Theory, 1998.
[9]Chen, D. R.; Wu, Q.; Ying, Y.; Zhou, D. X.: Support vector machine soft margin classifiers: error analysis, Journal of machine learning research 5, 1143-1175 (2004) · Zbl 1222.68167 · doi:http://www.jmlr.org/papers/v5/chen04b.html
[10]Chung, F. R. K.: Spectral graph theory, Regional conference series in mathematics 92 (1997) · Zbl 0867.05046
[11]Cucker, F.; Smale, S.: On the mathematical foundations of learning, Bulletin of the American mathematical society 39, 1-49 (2002) · Zbl 0983.68162 · doi:10.1090/S0273-0979-01-00923-5
[12]Cucker, F.; Zhou, D. X.: Learning theory: an approximation theory viewpoint, (2007)
[13]R. El-Yaniv, D. Pechyony, Stable transductive learning, in: G. Lugosi, H.U. Simon (Eds.), Proceedings of the 19th Annual Conference on Learning Theory, Pittsburgh, PA, USA, 2006, pp. 35 – 49.
[14]Johnson, R.; Zhang, T.: On the effectiveness of Laplacian normalization for graph semi-supervised learning, Journal of machine learning research 8, 1489-1517 (2007) · Zbl 1222.68227 · doi:http://www.jmlr.org/papers/v8/johnson07a.html
[15]Johnson, R.; Zhang, T.: Graph-based semi-supervised learning and spectral kernel design, IEEE transactions on information theory 54, 275-288 (2008)
[16]Koprinska, I.; Poon, J.; Clark, J.; Chan, J.: Learning to classify e-mail, Information sciences 177, 2167-2187 (2007)
[17]Lafferty, J.; Wasserman, L.: Challenges in statistical machine learning, Statistica sinica 16, 307-323 (2006)
[18]Lanckriet, G.; Cristianini, N.; Bartlett, P. L.; Ghaoui, L.; Jordan, M. I.: Learning the kernel matrix with semidefinite programming, Journal of machine learning research 5, 27-72 (2004) · Zbl 1222.68241 · doi:http://www.jmlr.org/papers/v5/lanckriet04a.html
[19]Lee, C. -H.; Zaı&uml, O. R.; Ane; Park, H. -H.; Huang, J.; Creiner, R.: Clustering high dimensional data: a graph-based relaxed optimization approach, Information sciences 178, 4501-4511 (2008)
[20]Lingras, P.; Butz, C.: Rough set based 1-v-1 and 1-v-r approaches to support vector machine multi-classification, Information sciences 177, 3782-3798 (2007)
[21]Mcdiarmid, C.: On the method of bounded differences, Surveys in combinatorics 1989 (1989)
[22]Micchelli, C. A.; Pontil, M.: Learning the kernel function via regularization, Journal of machine learning research 6, 1099-1125 (2005) · Zbl 1222.68265 · doi:http://www.jmlr.org/papers/v6/micchelli05a.html
[23]Vapnik, V.: Statistical learning theory, (1998) · Zbl 0935.62007
[24]Wu, Q.; Ying, Y.; Zhou, D. X.: Multi-kernel regularized classifiers, Journal of complexity 23, 108-134 (2007) · Zbl 1171.65043 · doi:10.1016/j.jco.2006.06.007
[25]X. Zhu, Semi-supervised learning literature survey, Technical Report 1530, Computer Sciences, University of Wisconsin – Madison, 2005.