Publication 2005 Issue No. 4 - April Abstract - Feature Space Interpretation of SVMs with Indefinite Kernels
Feature Space Interpretation of SVMs with Indefinite Kernels
April 2005 (vol. 27 no. 4)
pp. 482-492
 ASCII Text x Bernard Haasdonk, "Feature Space Interpretation of SVMs with Indefinite Kernels," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 4, pp. 482-492, April, 2005.
 BibTex x @article{ 10.1109/TPAMI.2005.78,author = {Bernard Haasdonk},title = {Feature Space Interpretation of SVMs with Indefinite Kernels},journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},volume = {27},number = {4},issn = {0162-8828},year = {2005},pages = {482-492},doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2005.78},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Pattern Analysis and Machine IntelligenceTI - Feature Space Interpretation of SVMs with Indefinite KernelsIS - 4SN - 0162-8828SP482EP492EPD - 482-492A1 - Bernard Haasdonk, PY - 2005KW - Support vector machineKW - indefinite kernelKW - pseudo-Euclidean spaceKW - separation of convex hullsKW - pattern recognition.VL - 27JA - IEEE Transactions on Pattern Analysis and Machine IntelligenceER -
Kernel methods are becoming increasingly popular for various kinds of machine learning tasks, the most famous being the support vector machine (SVM) for classification. The SVM is well understood when using conditionally positive definite (cpd) kernel functions. However, in practice, non-cpd kernels arise and demand application in SVMs. The procedure of "plugging” these indefinite kernels in SVMs often yields good empirical classification results. However, they are hard to interpret due to missing geometrical and theoretical understanding. In this paper, we provide a step toward the comprehension of SVM classifiers in these situations. We give a geometric interpretation of SVMs with indefinite kernel functions. We show that such SVMs are optimal hyperplane classifiers not by margin maximization, but by minimization of distances between convex hulls in pseudo-Euclidean spaces. By this, we obtain a sound framework and motivation for indefinite SVMs. This interpretation is the basis for further theoretical analysis, e.g., investigating uniqueness, and for the derivation of practical guidelines like characterizing the suitability of indefinite SVMs.

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Index Terms:
Support vector machine, indefinite kernel, pseudo-Euclidean space, separation of convex hulls, pattern recognition.
Citation:
Bernard Haasdonk, "Feature Space Interpretation of SVMs with Indefinite Kernels," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 4, pp. 482-492, April 2005, doi:10.1109/TPAMI.2005.78