Abstract
The theory of machine learning in Banach space is a new research topic and has drawn much attention in recent years. The theoretical foundation of this topic is that under what conditions two sample sets can be separated in Banach space. In this paper, motivated by developing new support vector machine (SVM) in Banach space, we present a necessary and sufficient condition of separating two finite classes of samples by a hyper-plane in Banach space. We also present an attainable expression of maximal margin of the separating hyper-planes which includes some cases of the classes of infinite samples in Banach space.
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Acknowledgments
This work is partly supported by National NSFCs (61070242), by the Natural Science Foundation of Hebei Province (F2010000323), by the Scientific Research Project of Department of Education of Hebei Province (2009410), by Scientific Research Project of Hebei University (09265631D-2), and by 2010 Baoding science Research and Development Project (10ZG008).
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He, Q., Wu, C. Separating theorem of samples in Banach space for support vector machine learning. Int. J. Mach. Learn. & Cyber. 2, 49–54 (2011). https://doi.org/10.1007/s13042-011-0013-4
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DOI: https://doi.org/10.1007/s13042-011-0013-4