Kernel methods in machine learning

Hofmann, Thomas; Schölkopf, Bernhard; Smola, Alexander J.

doi:10.1214/009053607000000677

Cited by 1,803 publications

(1,257 citation statements)

References 110 publications

Supporting

Mentioning

1,245

Contrasting

Unclassified

Order By: Relevance

“…It can be shown that even in the infinite dimensional case, this norm can be evaluated using the kernel. For more details see (Jäkel et al, 2007;Hofmann et al, 2008;Schölkopf & Smola, 2002).…”

Section: Box 2 Kernel Methods and Exemplar Modelsmentioning

confidence: 99%

“…Here, we will focus on a different set of techniques from machine learning, called kernel methods (Jäkel, Schölkopf, & Wichmann, 2007;Hofmann, Schölkopf, & Smola, 2008;Schölkopf & Smola, 2002). Contrary to multilayer neural networks, kernel methods are linear methods, in a way we will describe in more detail below.…”

Section: Learning In Humans and Machinesmentioning

confidence: 99%

“…However, polynomial kernels have some plausibility, too (Jäkel et al, 2007) and they can potentially be used for identifying critical features via Wiener and Volterra Theory (Franz & Schölkopf, 2006). There are also kernels that can deal with non-vectorial stimuli, like strings, trees or graphs (Hofmann et al, 2008). Such kernels might be useful for modelling categorization of interestingly structured stimuli, like sentences or visual objects.…”

Section: Box 3 Questions For Future Researchmentioning

confidence: 99%

See 2 more Smart Citations

Does Cognitive Science Need Kernels?

Jäkel

Schölkopf

Wichmann

2009

Trends in Cognitive Sciences

Self Cite

View full text Add to dashboard Cite

Section: Box 2 Kernel Methods and Exemplar Modelsmentioning

confidence: 99%

Section: Learning In Humans and Machinesmentioning

confidence: 99%

Section: Box 3 Questions For Future Researchmentioning

confidence: 99%

See 1 more Smart Citation

Does Cognitive Science Need Kernels?

Jäkel

Schölkopf

Wichmann

2009

Trends in Cognitive Sciences

Self Cite

View full text Add to dashboard Cite

“…However, evaluating and choosing a kernel function is often done experimentally. There exist different types of kernel functions that can be used in SVMs [25,6,28].…”

Section: Constructionmentioning

confidence: 99%

Decisions: Algebra and Implementation

Danylenko

Lundberg

Löwe

2011

Machine Learning and Data Mining in Pattern Recognition

View full text Add to dashboard Cite

Processing decision information is a constitutive part in a number of applications in Computer Science fields. In general, decision information can be used to deduce the relationship between a certain context and a certain decision. Decision information is represented by a decision model that captures this information. Frequently used examples of decision models are decision tables and decision trees. The choice of an appropriate decision model has an impact on application performance in terms of memory consumption and execution time. High memory expenses can possibly occur due to redundancy in a decision model; and high execution time is often a consequence of an unsuitable decision model. Applications in different domains try to overcome these problems by introducing new data structures or algorithms for implementing decision models. These solutions are usually domain-specific and hard to transfer from one domain to another.Different application domains of Computer Science often process decision information in a similar way and, hence, have similar problems. We should thus be able to present a unifying approach that can be applicable in all application domains for capturing and manipulating decision information. Therefore, the goal of this thesis is (i) to suggest a general structure (Decision Algebra) which provides a common theoretical framework that captures decision information and defines operations (signatures) for storing, accessing, merging, approximating, and manipulating such information along with some general algebraic laws regardless of the used implementation. Our Decision Algebra allows defining different construction strategies for decision models and data structures that capture decision information as implementation variants, and it simplifies experimental comparisons between them.Additionally, this thesis presents (ii) an implementation of Decision Algebra capturing the information in a non-redundant way and performing the operations efficiently. In fact, we show that existing decision models that originated in the field of Data Mining and Machine Learning and variants thereof as exploited in special algorithms can be understood as alternative implementation variants of the Decision Algebra by varying the implementations of the Decision Algebra operations. Hence, this work (iii) will contribute to a classification of existing technology for processing decision information in different application domains of Computer Science.

show abstract

“…Kernel density estimation (KDE) is an established non-parametric approach that is widely used in pattern analysis, computer vision, dimensionality reduction, and clustering [68,69,70,71]. In the KDE literature, methods that tackle overall computational complexity primarily approach from the perspective of reducing pairwise kernel evaluations; examples include Nystrom approximation [72], Fast Gauss Transform [73,74] and sparse dictionary learning methods [75].…”

Section: Introductionmentioning

confidence: 99%

Manifold learning and unwrapping using density ridges

Shaker¹

View full text Add to dashboard Cite

xii 3.6 Unwrapped mnist-0 digits with a selection of images of the actual digits on top. Orientation and thickness of digits smoothly vary across horizontal and vertical directions, respectively. . 34 3.7 Unfolding mnist-0 digits using two benchmark manifold learning methods. Unlike the proposed method, no smooth variation of structure is preserved using these methods. . . . . 35 3.8 Unfolding mnist-2 digits using the proposed method and t-SNE. Similar to Figure 3.7(b) for mnist-0, no smooth variation of structure is preserved using t-SNE, while proposed method shows smooth change of thickness and shape in horizontal and vertical coordinates, respectively. 36 3.9 Unfolding mnist-9 digits using the proposed method, which shows smooth change of thickness Sylvain Bouix, who were also my mentors, for all of their guidance through this process; your discussion, ideas, and feedback have been absolutely invaluable.

show abstract

Kernel methods in machine learning

Cited by 1,803 publications

References 110 publications

Does Cognitive Science Need Kernels?

Does Cognitive Science Need Kernels?

Decisions: Algebra and Implementation

Manifold learning and unwrapping using density ridges

Contact Info

Product

Resources

About