Constructing ultrametric and additive trees based on the L1 norm

Journal of Classification

Volumn 18, Issue 2, 2001, Pages 185-207

  Smith, Thomas J ^a  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Additive tree; Cluster analysis; Optimization; Structural representation; Ultrametric

Indexed keywords

EID: 0035540984     PISSN: 01764268     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00357-001-0015-0     Document Type: Article

References (21)

1. ARABIE, P., and HUBERT, L. J. (1992), "Combinatorial Data Analysis," Annual Review of Psychology, 43, 169-203.
2. BARTHÉLEMY, J. P, and GUÉNOCHE, A. (1991), Tree and Proximity Representations, West Sussex: Wiley.
3. CARROLL, J. D., and PRUZANSKY, S. (1980), "Discrete and Hybrid Scaling Models," in Similarity and Choice, Eds. E. D. Lantermann and H. Feger, Bern: Huber 108-139.
4. CORTER, J. E. (1982), "ADDTREE/P: A PASCAL Program for Fitting Additive Trees Based on Sattath and Tversky's ADDTREE Algorithm," Behavior Research Methods and Instrumentation, 14, 353-354.
5. CUNNINGHAM, J. P. (1978), "Free Trees and Bidirectional Trees as Representations of Psychological Distance," Journal of Mathematical Psychology, 17, 165-188.
6. DAY, W. H. E. (1987), "Computational Complexity of Inferring Phylogenies from Dissimilarity Matrices," Bulletin of Mathematical Biology, 49, 461-467.
7. DAY, W. H. E. (1996), "Complexity Theory: an Introduction for Practitioiners of Classification," in Clustering and Classification, Eds. P. Arabie, L. J. Hubert, and G. De Soete, Singapore: World Scientific Publishing, 199-233.
8. DE SOETE, G. (1983), "A Least-squares Algorithm for Fitting Additive Trees to Proximity Data," Psychometrika, 48, 621-626.
9. HUBERT, L. J., and ARABIE, P. (1994), "The Analysis of Proximity Matrices through Sums of Matrices having (Anti-)Robinson Forms," British Journal of Mathematical and Statistical Psychology, 47, 1-40.
10. HUBERT, L. J., and ARABIE, P. (1995a), "Iterative Projection Strategies for the Least-squares Fitting of Tree Structures to Proximity Data," British Journal of Mathematical and Statistical Psychology, 48, 281-317.
11. HUBERT, L., and ARABIE, P. (1995b), "The Approximation of Two-mode Proximity Matrices by Sums of Order-constrained Matrices," Psychometrika, 60, 57-605.
12. HUBERT, L., ARABIE, P., and MEULMAN, J. (1997), "Linear and Circular Unidimensional Scaling for Symmetric Proximity Matrices," British Journal of Mathematical and Statistical Psychology, 50, 253-284.
13. HUBERT, L., ARABIE, P., and MEULMAN, J. (2001), "Modeling Dissimilarity: Generalizing Ultrametric and Additive Tree Representations," British Journal of Mathematical and Statistical Psychology, 54.
14. KŘIVÁNEK, M., and MORÁVEK, J. (1986), "NP-hard Problems in Hierarchical-tree Clustering," Acta Informatica, 23, 311-323.
15. ROSS, B. H., and MURPHY, G. L. (1999), "Food for Thought: Cross-classification and Category Organization in a Complex Real-world Domain," Cognitive Psychology, 38, 495-553.
16. SATTATH, S., and TVERSKY, A. (1977), "Additive Similarity Trees," Psychometrika, 42, 319-345.
17. SMITH, T. J. (1998), "A Comparison of Three Additive Tree Algorithms that Rely on a Least-squares Loss Criterion," British Journal of Mathematical and Statistical Psychology, 51, 269-288.
18. 1 Optimization under Linear Inequality Constraints," Journal of Classification, 17, 225-242.
19. SOKAL, R. R., and SNEATH, P. H. A. (1963), Principles of Numerical Taxonomy, San Francisco: W. H. Freeman.
20. SPÄTH, H. (1992), Mathematical Algorithms for Linear Regression, San Diego: Academic Press.
21. U. S. DEPARTMENT OF LABOR EMPLOYMENT AND TRAINING ADMINISTRATION (1998), O*NET 98 Data Dictionary, Orono, ME: Trefoil Corporation.