Skip to main content Accessibility help
×
Home
Hostname: page-component-99c86f546-cxxrm Total loading time: 0.517 Render date: 2021-12-01T03:04:40.314Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Part IV - Kernel ridge regressors and variants

Published online by Cambridge University Press:  05 July 2014

S. Y. Kung
Affiliation:
Princeton University, New Jersey
Get access

Summary

This part contains three chapters, covering learning models closely related to the kernel ridge regressor (KRR).

  1. (i) Chapter 7 discusses applications of the kernel ridge regressor (KRR) to regularization and approximation problems.

  2. (ii) Chapter 8 covers a broad spectrum of conventional linear classification techniques, all related to ridge regression.

  3. (iii) Chapter 9 extends the linear classification to kernel methods for nonlinear classifiers that are closely related to the kernel ridge regressor (KRR).

Chapter 7 discusses the role of ridge regression analysis in regularization problems. The optimization formulation for the kernel ridge regressor (KRR), in the intrinsic space, obviously satisfies the LSP condition in Theorem 1.1, implying the existence of a kernelized KRR learning model, see Algorithm 7.1.

If a Gaussian RBF kernel is adopted, the KRR learning model is intimately related to several prominent regularization models:

  1. (i) the RBF approximation networks devised by Poggio and Girosi [207];

  2. (ii) Nadaraya–Watson regression estimators [191, 293]; and

  3. (iii) RBF-based back-propagation neural networks [198, 226, 294].

The chapter also addresses the role of the multi-kernel formulation in regression/classification problems. It shows that, if the LSP condition is satisfied, then some multi-kernel problems effectively warant a mono-kernel solution.

Chapter 8 covers a family of linear classifiers. The basic linear regression analysis leads to the classical least-squares-error (LSE) classifiers, see Algorithm 8.1.The derivation of Fisher's conventional linear discriminant analysis is based on finding the best projection direction which can maximize the so-called signal-to-noise ratio; see Algorithm 8.2.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Send book to Kindle

To send this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Send book to Dropbox

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.

Available formats
×

Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

Available formats
×