title: Graphical Representation of Proximity Measures for Multidimensional Data: Classical and Metric Multidimensional Scaling.
abstract: We describe the use of classical and metric multidimensional scaling methods for graphical representation of the proximity between collections of data consisting of cases characterized by multidimensional attributes. These methods can preserve metric differences between cases, while allowing for dimensional reduction and projection to two or three dimensions ideal for data exploration. We demonstrate these methods with three datasets for: (i) the immunological similarity of influenza proteins measured by a multidimensional assay; (ii) influenza protein sequence similarity; and (iii) reconstruction of airport-relative locations from paired proximity measurements. These examples highlight the use of proximity matrices, eigenvalues, eigenvectors, and linear and nonlinear mappings using numerical minimization methods. Some considerations and caveats for each method are also discussed, and compactMathematicaprograms are provided.
authors.affiliation: University of Rochester Medical Center, 601 Elmwood Avenue - Box 675, Rochester, NY 14618.
authors.forename: Martin S
authors.initials: MS
authors.lastname: Zand
authors.affiliation: University of Rochester Medical Center, 601 Elmwood Avenue - Box 675, Rochester, NY 14618.
authors.forename: Jiong
authors.initials: J
authors.lastname: Wang
authors.affiliation: University of Rochester Medical Center, 601 Elmwood Avenue - Box 675, Rochester, NY 14618.
authors.forename: Shannon
authors.initials: S
authors.lastname: Hilchey