Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 634165, 15 pages
Research Article

Multiple Subject Barycentric Discriminant Analysis (MUSUBADA): How to Assign Scans to Categories without Using Spatial Normalization

1School of Behavioral and Brain Sciences, University of Texas at Dallas, MS: GR4.1, 800 West Campbell Road, Richardson, TX 75080-3021, USA
2The Rotman Institute at Baycrest, 3560 Bathurst Street, Toronto, ON, Canada M6A 2E1
3Psychological Brain Sciences, Dartmouth College, 6207 Moore Hall, Hanover, NH 03755, USA
4Dipartimento di Psicologia, Universitá di Bologna, Viale Berti Pichat 5, 40127 Bologna, Italy

Received 30 September 2011; Revised 20 December 2011; Accepted 21 December 2011

Academic Editor: Michele Migliore

Copyright © 2012 Hervé Abdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a new discriminant analysis (DA) method called Multiple Subject Barycentric Discriminant Analysis (MUSUBADA) suited for analyzing fMRI data because it handles datasets with multiple participants that each provides different number of variables (i.e., voxels) that are themselves grouped into regions of interest (ROIs). Like DA, MUSUBADA (1) assigns observations to predefined categories, (2) gives factorial maps displaying observations and categories, and (3) optimally assigns observations to categories. MUSUBADA handles cases with more variables than observations and can project portions of the data table (e.g., subtables, which can represent participants or ROIs) on the factorial maps. Therefore MUSUBADA can analyze datasets with different voxel numbers per participant and, so does not require spatial normalization. MUSUBADA statistical inferences are implemented with cross-validation techniques (e.g., jackknife and bootstrap), its performance is evaluated with confusion matrices (for fixed and random models) and represented with prediction, tolerance, and confidence intervals. We present an example where we predict the image categories (houses, shoes, chairs, and human, monkey, dog, faces,) of images watched by participants whose brains were scanned. This example corresponds to a DA question in which the data table is made of subtables (one per subject) and with more variables than observations.