Multivariate Relevance Vector Machines (MVRVM)
A relevance vector machine [Tipping 2001] provides a regression method in a Bayesian framework. It can be also adapted to perform classification tasks. Like Support Vector Machines (SVM) it learns a sparse representation of input basis functions. In its original form it only has a single dimensional output. This is a drawback in some regression tasks with multi-dimension outputs (e.g. human body pose estimation), since we have to use a separate relevance vector machine for each output dimension and will lead to separate sets of basis functions being selected for each output dimension, reducing the sparsity. To avoid this, we propose an extension which enables a single relevance vector machine to handle multiple output dimensions. We also extend the fast bottom-up basis function selection algorithm [Tipping 2003] to the multivariate output case. Details of these extensions can be found in the following documents.
Multivariate Relevance Vector Machines for Tracking [pdf]
A. Thayananthan, R. Navaratnam, B. Stenger, P.H.S. Torr and R. Cipolla, Proc. European Conference on Computer Vision, Graz, Austria, May 2006.
Template-based Pose Estimation and Tracking of 3D Hand Motion
(Chapter 6) [pdf]
A. Thayananthan, PhD Thesis, Department of Engineering, University of Cambridge, September 2005.
Matlab and C++ Code
C++ code : This c++ implementation uses the VNL numerical library, which can be downloaded from http://vxl.sourceforge.net/
Matlab code : This code contains a toy example (mvrvm_example.m) which creates the following figure. Note that the same examples are chosen for both output dimensions (sinc and linear).
Multi-class Relevance Vector Machine Classification
The following code extends Tipping's binary Relevance Vector Machine classification scheme [Tipping 2001] to a Multi-class Relevance Vector Machine classification algorithm. A bottom-up basis function selection algorithm [Tipping 2003] is used to select the sparse relevance vectors. Some of the details of this extension are explained in the following technical report.
Relevance Vector Machine based Mixture of Experts [pdf]
A. Thayananthan, Technical Report, Department of Engineering, University of Cambridge, September 2005.
Matlab code : This code contains a toy example (mcrvm_example.m) which creates the following figures.