Three-Way Nonmetric Multidimensional Scaling for Fusing Heterogeneous Data Sources

• Activity Number: 347
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Brent S. Castle*+ and Michael Trosset
• Companies: Indiana University and Indiana University
• Keywords: three-way multidimensional scaling ; nonmetric multidimensional scaling ; data fusion ; multi-view learning ; raw stress criterion ; partial ordering

Abstract

We consider the problem of classification given several heterogeneous sources of data. For example, images on the popular image hosting website Flickr are often accompanied by captions, comments, and tags. One might be able to improve classification performance by using the images as well as the various text sources. A popular approach to classification in this context is to form classifiers using pairwise comparisons from each of the data types and to combine the resulting predictions. In this work we propose a three-way nonmetric multidimensional scaling formulation as a means to combine proximity measures constructed from each data type. We first embed the objects into a single low-dimensional Euclidean representation and subsequently perform classification using the resulting configuration. This nonmetric multidimensional scaling algorithm uses only ordinal properties of each of the proximity measures so one can remain agnostic to the measure itself while adhering to its ordinal properties.