Kernel-based online machine learning and support vector reduction Sumeet Agarwal, V. Vijaya Saradhi and Harish Karnick 1,2 Abstract We apply kernel-based machine learning methods to online learning situations, and look at the related requirement of reducing the complexity of the learnt classifier. Online methods are particularly useful in situations which involve streaming data, such as medical or financial applications. We show that the concept of span of support vectors can be used to build a classifier that performs reasonably well while satisfying given space and time constraints, thus making it potentially suitable for such online situations. 1 Introduction Kernel-based learning methods [16] have been successfully applied to a wide range of problems. The key idea behind these methods is to implicitly map the input data to a new feature space, and then find a suitable hypothesis in this space. The mapping to the new space is defined by a function called the kernel function. Due to promising generalization performance, kernel methods have been widely used in many applications. However, they may not always be the most efficient technique; training and classification times are the two main is- sues which concern researchers and practitioners. Many techniques have been proposed to speed up training time of (offline) SVMs. Sequential minimal op- timization (SMO) [15], modified SMO [11], decomposition method [9] and low rank kernel matrix construction method [8] are some of the methods proposed towards speeding up the training time. Email address: lawraga.teemus@gmail.com, {saradhi, hk}@cse.iitk.ac.in (Sumeet Agarwal, V. Vijaya Saradhi and Harish Karnick). 1 IBM India Research Lab, New Delhi, India 2 Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, Kanpur, India Preprint submitted to Elsevier 25 June 2007