Optimal Least-Squares Unidimensional Scaling: Improved Branch-and-Bound Procedures and Comparison to Dynamic Programming

Brusco, Michael J.; Stahl, Stephanie

doi:10.1007/s11336-002-1032-6

Cited by 21 publications

(28 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Accordingly, two-mode KL-means clustering and nonnegative matrix factorization can be applied for analyzing these data. Since their original publication, these lipread consonant data have been reanalyzed using clustering or seriation methods (Brusco & Stahl, 2005b;. However, the latter studies analyzed the data subsequent to transforming the asymmetric confusion proportions to a symmetric matrix.…”

Section: Example 1 Lipread Consonant Datamentioning

confidence: 99%

“…For any given pair of objects (i, j), asymmetry can potentially occur because a presented stimulus i could be mistaken more frequently for j than stimulus j would be mistaken for i, or vice versa. Likewise, for brand-switching applications in consumer psychology, where x ij (for i ≠ j) is a measure reflecting the Brusco, 2001;Brusco & Stahl, 2005b;DeCani, 1972;Flueck & Korsh, 1974;Hubert, 1976;Hubert et al, 2001, chap. 4;Ranyard, 1976).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Biclustering methods for one-mode asymmetric matrices

2015

Self Cite

View full text Add to dashboard Cite

An asymmetric one-mode data matrix has rows and columns that correspond to the same set of objects. However, the roles of the objects frequently differ for the rows and the columns. For example, in a visual alphabetic confusion matrix from an experimental psychology study, both the rows and columns pertain to letters of the alphabet. Yet the rows correspond to the presented stimulus letter, whereas the columns refer to the letter provided as the response. Other examples abound in psychology, including applications related to interpersonal interactions (friendship, trust, information sharing) in social and developmental psychology, brand switching in consumer psychology, journal citation analysis in any discipline (including quantitative psychology), and free association tasks in any subarea of psychology. When seeking to establish a partition of the objects in such applications, it is overly restrictive to require the partitions of the row and column objects to be identical, or even the numbers of clusters for the row and column objects to be the same. This suggests the need for a biclustering approach that simultaneously establishes separate partitions of the row and column objects. We present and compare several approaches for the biclustering of one-mode matrices using data sets from the empirical literature. A suite of MATLAB m-files for implementing the procedures is provided as a Web supplement with this article.

show abstract

Section: Example 1 Lipread Consonant Datamentioning

confidence: 99%

mentioning

confidence: 99%

Biclustering methods for one-mode asymmetric matrices

2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Robinson (anti-Robinson) patterning of a dissimilarity matrix, which is named for the pioneering work of Robinson (1951), is characterized by never-increasing (never-decreasing) elements in the rows and columns of the matrix when moving away from the main diagonal. The importance of anti-Robinson structures stems from a variety of important applications in combinatorial data analysis, including: (a) anti-Robinson patterning is a necessary, although not sufficient, condition for a perfect unidimensional scaling of objects (see Brusco & Stahl, 2005a for a discussion), (b) anti-Robinson patterning enables representation of a dissimilarity matrix via subsets of increasing diameter (Hubert, Arabie, & Meulman, 1998a, 1998b, 2006, and (c) anti-Robinson patterning is instrumental in the fitting of ultrametric trees (Hubert & Arabie, 1995;Hubert et al, 2006, chapter 5).…”

Section: Inducing Anti-robinson Structure On Symmetric Matricesmentioning

confidence: 99%

“…Although we could have opted to use a branch-and-bound method to attempt to improve locally-optimal permutations (Brusco & Stahl 2005a, 2005b, chapters 8 and 10), we selected the dynamic programming approach because its CPU time is less affected by the structural properties of the proximity matrix. For example, in their comparison of various branch-and-bound methods to dynamic programming, Brusco and Stahl (2005a) found comparable CPU times when the symmetric dissimilarity matrices exhibited structural properties that were conducive to a unidimensional scale.…”

Section: Introductionmentioning

confidence: 99%

“…For example, in their comparison of various branch-and-bound methods to dynamic programming, Brusco and Stahl (2005a) found comparable CPU times when the symmetric dissimilarity matrices exhibited structural properties that were conducive to a unidimensional scale. However, for problems where this structure was not present, even the best performing branch-and-bound method consumed two to four times the CPU time required by the dynamic programming algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation