Conformal Transformation of Kernel Functions: A Data-Dependent Way to Improve Support Vector Machine Classifiers

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Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “…kernels through a conformal mapping—i.e., a transformation that preserves angles locally—given by k̃(x,y) := f(x)k(x,y)f(y) for any bounded continuous function f such that f(x) > 0 for all x ∈ X and k(x,x)|f(x)|2 is bounded (Fukumizu et al. 2009b; Lemma 2), see, also Wu and Amari (2002).”
Characteristic Kernels on Groups and Semigroups (2008, background): “The following result shows that the characteristic propert y is invariant under some conformal mappings introduced in [17] and provides a construction to gene rate new characteristic kernels.”
Beyond the point cloud: from transductive to semi-supervised learning (2005, background): “Finally, ( Wu & Amari, 2002 ) produced a family of data dependent kernels with some interesting geometric interpretations.”
Class-Boundary Alignment for Imbalanced Dataset Learning (2003, methodology): “We conduct the transformation based on the spatial distribution of the support vectors in feature space F , instead of in input space I (Wu & Amari, 2002).”
Support Vector Machines with Applications (2006, methodology): “For instance, Wu and Amari [83] proposed the use of diﬀerential geometry methods [2] to derive kernels that improve class separation in classiﬁcation problems.”