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Nonparametric Transforms of Graph Kernels for Semi-Supervised Learning
2004
Neural Information Processing Systems
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We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. ...
We evaluate the kernels on real datasets using support vector machines, with encouraging results. ...
The well-known linear programming problem can be generalized to a semi-definite optimization by replacing the vector of variables with a symmetric matrix, and replacing the non-negativity constraints with ...
dblp:conf/nips/ZhuKGL04
fatcat:5p33ng3izbdztmb73xkiwhas3e
Unsupervised and Semi-supervised Lagrangian Support Vector Machines
[chapter]
2007
Lecture Notes in Computer Science
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But the problems have difficulty to compute, we will find their semi-definite relaxations that can approximate them well. ...
Experimental results show that our new unsupervised and semi-supervised classification algorithms often obtain almost the same accurate results as the unsupervised and semi-supervised methods [4] [11], ...
Semi-definite Programming (SDP) has showed its utility in machine learning. Lanckreit et al show how the kernel matrix can be learned from data via semi-definite programming techniques [3] . ...
doi:10.1007/978-3-540-72588-6_140
fatcat:abtclimzbfer7cot7zlh4yfth4
Deploying SDP for machine learning
2007
The European Symposium on Artificial Neural Networks
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We discuss the use in machine learning of a general type of convex optimisation problem known as semi-definite programming (SDP) [1] . ...
We intend to argue that SDP's arise quite naturally in a variety of situations, accounting for their omnipresence in modern machine learning approaches, and we provide examples in support. ...
We had to omit discussions of other uses, such as for approximate inference in graphical models [16] , distance metric learning [17] , sparse PCA [18] , kernel matrix completion [19] , nonlinear dimensionality ...
dblp:conf/esann/Bie07
fatcat:6hfbdzjbbvczlkk3g4zpbylxm4
Non-Parametric Kernel Learning with robust pairwise constraints
2011
International Journal of Machine Learning and Cybernetics
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Keywords Kernel learning · semi-definitive programming · graph embedding · pairwise constraint · semi-supervised learning 1 Introduction Semi-supervised clustering based on kernel learning is a popular ...
We generalized the graph embedding framework into kernel learning, by reforming it as a semi-definitive programming (SDP) problem, smoothing and avoiding over-smoothing the functional Hilbert space with ...
[15] proposed a kernel learning algorithm by formulating it into a semi-definite programming (SDP) problem. ...
doi:10.1007/s13042-011-0048-6
fatcat:2nao4vg4f5eezkifccwzrys2bu
Graph Kernels by Spectral Transforms
[chapter]
2006
Semi-Supervised Learning
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Many graph-based semi-supervised learning methods can be viewed as imposing smoothness conditions on the target function with respect to a graph representing the data points to be labeled. ...
The central quantity in such regularization is the spectral decomposition of the graph Laplacian, a matrix derived from the graph's edge weights. ...
Since K is the non-negative sum of outer products, it is positive semi-definite, i.e., a kernel matrix. ...
doi:10.7551/mitpress/9780262033589.003.0015
fatcat:5nkrwjfkzbf4vl73w6hr7gjce4
Evolutionary Kernel Learning
[chapter]
2011
Encyclopedia of Machine Learning
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Definition Evolutionary kernel learning stands for using evolutionary algorithms to optimize the kernel function for a kernel-based learning machine. ...
A function k : X × X → C, X = ∅, is positive (semi-) definite if for all m ∈ IN and all x 1 , . . . , x m ∈ X the m × m matrix K with elements K ij := k (x i , x j ) is positive (semi-) definite. ...
In general, kernel methods assume that the kernel (or at least the Gram matrix in the training process) is positive semi-definite (psd). ...
doi:10.1007/978-0-387-30164-8_284
fatcat:n757tyeoevcorg7vu7stvrblyq
Robust Kernel Approximation for Classification
[chapter]
2017
Lecture Notes in Computer Science
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Keywords: robust kernel approximation, indefinite kernel learning, support vector machine Corresponding author. 1 The kernel matrix K associated to a positive definite kernel K is PSD. ...
It aims to tackle the issue that the indefinite kernel is contaminated by noises and outliers, i.e. a noisy observation of the true positive definite (PD) kernel. ...
The corresponding robust kernel learning problem can be solved by an alternate iterative algorithm with a semi-definite programming and a soft-threshold operator with theoretical guarantees. ...
doi:10.1007/978-3-319-70087-8_31
fatcat:wpzdv73fbjeiplgtju5wcxp43u
Learning a Distance Metric for Object Identification Without Human Supervision
[chapter]
2006
Lecture Notes in Computer Science
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The metric learning is formulated using only dissimilar example pairs as a convex quadratic programming problem that can be solved much faster than a semi-definite programming problem, which generally ...
must be solved to learn a distance metric matrix. ...
Grant-in-Aid for Scientific Research (No. 16700097) from MEXT of Japan, by a MEXT project titled "Software Technologies for Search and Integration across Heterogeneous-Media Archives," and by a 21st Century COE Program ...
doi:10.1007/11871637_62
fatcat:cjmeswxwwzf5ndip3jleqtvuyi
Learning SVM Classifiers with Indefinite Kernels
2021
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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Recently, training support vector machines with indefinite kernels has attracted great attention in the machine learning community. ...
We first reformulate the kernel principal component analysis as a general kernel transformation framework, and then incorporate it into the SVM classification to formulate a joint optimization model. ...
This positive semi-definite property of the kernel matrix ensures the SVMs can be efficiently solved using convex quadratic programming. ...
doi:10.1609/aaai.v26i1.8293
fatcat:fzio42eqvfatfdgkfjpdzxixc4
Learning a Kernel Matrix Using Some Similar and Dissimilar pairs
2014
International Journal of Combinatorial Optimization Problems and Informatics
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Traditional distance metric learning approaches are based on Mahanalobis distance which result in optimizing a positive semi definite problem. ...
This paper proposed a new algorithm in order to learn kernel matrix which is based on distance metric learning. It is implemented and applied to several standard data sets and the results are shown. ...
The kernel function which is used should satisfy several conditions known as Mercer's conditions. K ij = ϕ(x i ) T ϕ(x j ) Matrix K is symmetric semi positive definite. ...
dblp:journals/ijcopi/Hajiabadi14
fatcat:rzi3wypxmzcsrj5ttz5vtwfbdm
Maximum Margin based Semi-supervised Spectral Kernel Learning
2007
Neural Networks (IJCNN), International Joint Conference on
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However, the kernel designing process does not involve the bias of a kernel-based learning algorithm, the deduced kernel matrix cannot necessarily facilitate a specific learning algorithm. ...
One of the most well-known semi-supervised kernel learning approaches is the spectral kernel learning methodology which usually tunes the spectral empirically or through optimizing some generalized performance ...
The authors would like to thank Dr. Steven Hoi for his fruitful discussion and providing the code of the Unified Kernel Machines. ...
doi:10.1109/ijcnn.2007.4370993
dblp:conf/ijcnn/XuZLK07
fatcat:mnoo2eij7nflvpyjmdyhkl3kay
Solving Semi-infinite Linear Programs Using Boosting-Like Methods
[chapter]
2006
Lecture Notes in Computer Science
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I show that it can be reduced to a semi-infinite linear program [7] that is equivalent to a semi-definite programming formulation proposed in [8] . ...
In the finite case the constraints can be described by a matrix with m rows and n columns that can be used to directly solve the LP. ...
I show that it can be reduced to a semi-infinite linear program [7] that is equivalent to a semi-definite programming formulation proposed in [8] . ...
doi:10.1007/11894841_2
fatcat:fiqbhebvnvhx3aptogivefriaa
A comparison of graph- and kernel-based –omics data integration algorithms for classifying complex traits
2017
BMC Bioinformatics
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Seven different integration algorithms, including graph-based semisupervised learning, graph sharpening integration, composite association network, Bayesian network, semi-definite programming-support vector ...
Well-studied algorithms mostly deal with single data source, and cannot fully utilize the potential of these multi-omics data sources. ...
The Starr County data were generated with support by National Institutes of Health grants R01 DK073541 and R01 HL102830. H. ...
doi:10.1186/s12859-017-1982-4
pmid:29212468
fatcat:buvnw75ksvf57lpavfjjdnd6x4
Enhanced protein fold recognition through a novel data integration approach
2009
BMC Bioinformatics
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One of the most appealing properties of this approach is that it can easily cope with multi-class classification and multi-task learning by an appropriate choice of the output kernel matrix. ...
We propose a novel information-theoretic approach based on a Kullback-Leibler (KL) divergence between the output kernel matrix and the input kernel matrix so as to integrate heterogeneous data sources. ...
Acknowledgements We would like to thank the referees for their constructive comments and suggestions which greatly improve the paper. We also thank Prof. Mark Girolami, Dr. Theodoros Damoulas and Dr. ...
doi:10.1186/1471-2105-10-267
pmid:19709406
pmcid:PMC2761901
fatcat:pdzn3gsns5e7bki5k2jh5swpye
Inner Product Laplacian Embedding Based on Semidefinite Programming
2011
Journal of Signal and Information Processing
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The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. ...
This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. ...
Acknowledgements The authors would like to thank the anonymous reviewers for their help. This work was supported by the Na- ...
doi:10.4236/jsip.2011.23027
fatcat:giqwz27rgfgnpmiaxypgdwn3by
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