Kernel Machines: Introduction

Kernels are a type of similarity measures between observed patterns. By exploiting an important mathematical property, they provide new pattern representation and, at the same time, new perspectives to solve many machine learning problems. In this article, we will describe and motivate the main idea of the kernel approach. Notice that, while the usage of kernels is based on well founded theoretical arguments, we will confine our discussion to the main intuitive functional concepts and definitions.

[1]  Lawrence K. Saul,et al.  Kernel Methods for Deep Learning , 2009, NIPS.

[2]  Avrim Blum,et al.  Correlation Clustering , 2004, Machine Learning.

[3]  Thomas Gärtner,et al.  On Graph Kernels: Hardness Results and Efficient Alternatives , 2003, COLT.

[4]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[5]  O Mason,et al.  Graph theory and networks in Biology. , 2006, IET systems biology.

[6]  Stephen R. Marsland,et al.  Machine Learning - An Algorithmic Perspective , 2009, Chapman and Hall / CRC machine learning and pattern recognition series.

[7]  Giancarlo Mauri,et al.  Copy-Number Alterations for Tumor Progression Inference , 2013, AIME.

[8]  Alexander Gammerman,et al.  Sequence alignment kernel for recognition of promoter regions , 2003, Bioinform..

[9]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[10]  Juho Rousu,et al.  Efficient Computation of Gapped Substring Kernels on Large Alphabets , 2005, J. Mach. Learn. Res..

[11]  Thorsten Joachims,et al.  Text Categorization with Support Vector Machines: Learning with Many Relevant Features , 1998, ECML.

[12]  J. Mercer.  Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations , 1909 .

[13]  L. Watson,et al.  Reverse engineering dynamic temporal models of biological processes and their relationships , 2010, Proceedings of the National Academy of Sciences.

[14]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[15]  Giancarlo Mauri,et al.  Clustering Dependencies with Support Vectors , 2008 .

[16]  Rong Jin,et al.  Understanding bag-of-words model: a statistical framework , 2010, Int. J. Mach. Learn. Cybern..

[17]  Yee Whye Teh,et al.  A Fast Learning Algorithm for Deep Belief Nets , 2006, Neural Computation.

[18]  André Raspaud,et al.  Recursive graphs with small-world scale-free properties. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Yoshua. Bengio,et al.  Learning Deep Architectures for AI , 2007, Found. Trends Mach. Learn..

[20]  G. Mauri,et al.  Urinary Signatures of Renal Cell Carcinoma Investigated by Peptidomic Approaches , 2014, PloS one.

[21]  Giancarlo Mauri,et al.  An application of kernel methods to gene cluster temporal meta-analysis , 2010, Comput. Oper. Res..

[22]  Ben Taskar,et al.  Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning) , 2007 .

[23]  Michael I. Jordan,et al.  Kernel independent component analysis , 2003 .

[25]  Lipo Wang.  Support vector machines : theory and applications , 2005 .

[26]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[27]  Alex Smola,et al.  Kernel methods in machine learning , 2007, math/0701907.

[28]  Bernhard Schölkopf,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2005, IEEE Transactions on Neural Networks.

[29]  Gunnar Rätsch,et al.  Kernel PCA and De-Noising in Feature Spaces , 1998, NIPS.

[30]  Dong Yu,et al.  Deep Learning: Methods and Applications , 2014, Found. Trends Signal Process..

[31]  Ian H. Witten,et al.  Data mining: practical machine learning tools and techniques, 3rd Edition , 1999 .

[32]  Nello Cristianini,et al.  Classification using String Kernels , 2000 .

[33]  Yunqian Ma,et al.  Practical selection of SVM parameters and noise estimation for SVM regression , 2004, Neural Networks.

[34]  Giancarlo Mauri,et al.  Combined analysis of chromosomal instabilities and gene expression for colon cancer progression inference , 2014, Journal of Clinical Bioinformatics.