Addendum to: An Approach to Hierarchical Clustering via Level Surfaces and Convexity

References

[1] R. Holley, J. Malitz and S. Malitz, “An Approach to Hierarchical Clustering via Level Surfaces and Convexity,” Discrete and Computational Geometry, Vol. 25, No. 2, 2001, pp. 221-233.

[2]
J. Hartigan, “Clustering Algorithms,” Wiley, 1975.

[3]
K. Fukunaga and L. Hostler, “The Estimation of the Gradient of a Density Function with Application in Pattern Recognition,” IEEE Transactions on Information Theory, Vol. 21, No. 1, 1975, pp. 32-40.

[4]
P. Schnell, “A Method to Find Point-Groups,” Biometrika, Vol. 6, 1964, pp. 47-48.

[5]
M. Halkidi, Y. Batistakis and M. Vazirgiannis, “On Clustering Validation Techniques,” Journal of Intelligent Information Systems, Academic Publishers, Vol. 17, No. 2-3, 2001, pp. 107-145.

[6]
S. Kotsiantis and P. Pintelas, “Recent Advances in Clustering: A Brief Survey,” WSEAS Transactions on Information Science and Applications, Vol. 1, No. 1, 2004, pp. 73-81.

[7]
A. Hinneburg and D. Keim, “An Efficient Approach to Clustering in Large Multimedia Databases with Noise,” Proceedings of 4th International Conference on Knowledge Discovery and Data Mining, AAAI Press, 1998, pp. 58-65.

[8]
Y. J. Oyang, C. Y. Chen and T. W. Yang, “A Study on the Hierarchical Data Clustering Algorithm Based on Gravity Theory,” Principles of Data Mining and Knowledge Discovery, Lecture Notes in Computer Science, Springer, Berlin/Heidelberg, 2001, pp. 350-361.

[9]
C. Y. Chen, S. C. Hwang and Y. J. Oyang, “An Incremental Hierarchical Data Clustering Algorithm Based on Gravity Theory,” Advances in Knowledge Discovery and Data Mining, Lecture Notes in Computer Science, Sprin- ger, Berlin/Heidelberg, 2002, pp. 237-250.

[10]
G. Strang, “Introduction to Applied Mathematics,” Wellesley- Cambridge Press, Wellesley, 1985.

[11]
J. Sethian, “Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Scien- ce,” Cambridge University Press, Cambridge, 2002.

[12]
Y. W. Teh, M. Jordan, M. Beal and D. Blei, “Hierarchical Dirichlet Processes,” Journal of the American Statistical Association, Vol. 101, No. 476, 2006, pp. 1566-1581.

[13]
S. Axler, P. Bourdon and W. Ramey, “Harmonic Function Theory,” Springer-Verlag, New York, 2001.

[14]
M. Kass, A. Witkin and D. Terzopolous, “Snakes: Active Contour Models,” International Journal of Computer Vision, Kluwer Academic Publishers, Norwell, 1988, pp. 321-331.

[15]
L. Hyafil and R. Rivest, “Constructing Optimal Binary Decision Trees is NP-Complete,” Information Processing Letters, Vol. 5, No. 1, 1976. pp. 15-17.

[16]
M. Garey and D. Johnson, “The Rectilinear Steiner Tree Problem is NP-Complete,” SIAM Journal on Applied Mathematics, Vol. 32, No. 4, 1977, pp. 826-834.

[17]
L. Foulds and R. Graham, “The Steiner Problem in Phylogeny is NP-Complete,” Advances in Applied Mathematics, Vol. 3, No. 1, 1982, pp. 43-49.

[18]
B. Chor and T. Tuller, “Finding a Maximum Likelihood Tree is Hard,” Journal of the ACM, Vol. 53, No. 5, September 2006, pp. 722-744.

[19]
W. Day, “Computationally Difficult Parsimony Problems in Phylogenetics Systematics,” Journal of Theoretical Biology, Vol. 103, No. 3, 1983, pp. 429-438.

[20]
C. Aggarwal, A. Hinneburg and D. Keim, “On the Surprising Behavior of Distance Metrics in High Dimensional Space,” Database Theory — ICDT 2001, Lecture Notes in Computer Science, Springer, Berlin/Heidelberg, Vol. 1973, 2001, pp. 420-434.