Kernel Logistic Regression and the Import Vector Machine

• Activity Number: 201
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Graphics*
• Author(s): Ji Zhu*+ and Trevor Hastie
• Affiliation(s): Stanford University and Stanford University
• Keywords: classification ; kernel methods ; logistic regression ; multi-class learning ; radial basis ; reproducing kernal Hilbert space (RKHS) ; support vector machines

Abstract

The support vector machine (SVM) is known for its good performance in binary classification, but its extension to multi-class classification is still an on-going research issue. In this paper, we propose a new approach for classification, called the import vector machine (IVM), which is built on kernel logistic regression (KLR). We show that the IVM not only performs as well as the SVM in binary classification, but also can naturally be generalized to the multi-class case. Furthermore, the IVM provides an estimate of the underlying probability. Similar to the `"support points'' of the SVM, the IVM model uses only a fraction of the training data to index kernel basis functions, typically a much smaller fraction than the SVM. This gives the IVM a computational advantage over the SVM, especially when the size of the training data set is large.