Exact Indexing for Support Vector Machines

摘要

SVM (Support Vector Machine) is a well-established machine learning methodology popularly used for classification, regression, and ranking. Recently SVM has been actively researched for rank learning and applied to various applications including search engines or relevance feedback systems. A query in such systems is the ranking function F learned by SVM. Once learning a function F or formulating the query, processing the query to find top-k results requires evaluating the entire database by F. So far, there exists no exact indexing solution for SVM functions. Existing top-k query processing algorithms are not applicable to the machine-learned ranking functions, as they often make restrictive assumptions on the query, such as linearity or monotonicity of functions. Existing metric-based or reference-based indexing methods are also not applicable, because data points are invisible in the kernel space (SVM feature space) on which the index must be built. Existing kernel indexing methods return approximate results or fix kernel parameters. This paper proposes an exact indexing solution for SVM functions with varying kernel parameters. We first propose key geometric properties of the kernel space - ranking instability and ordering stability - which is crucial for building indices in the kernel space. Based on them, we develop an index structure iKernel and processing algorithms. We then present clustering techniques in the kernel space to enhance the pruning effectiveness of the index. According to our experiments, iKernel is highly effective overall producing 1 ～5% of evaluation ratio on large data sets. According to our best knowledge, iKernel is the first indexing solution that rinds exact top-k results of SVM functions without a full scan of data set.