Random projection towards the Baire metric for high dimensional clustering

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 9047, Issue , 2015, Pages 424-431

  Murtagh, Fionn ^a   Contreras, Pedro ^b  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b ThinkingSafe Ltd   (United Kingdom)

Author keywords

Big data; Binary rooted tree; Computational complexity; Hierarchical clustering; Ultrametric topology

Indexed keywords

BINARY TREES; COMPUTATIONAL COMPLEXITY; TREES (MATHEMATICS);

DIVISIVE HIERARCHICAL CLUSTERING; HIER-ARCHICAL CLUSTERING; HIGH-DIMENSIONAL CLUSTERING; LINEAR COMPUTATIONS; ORTHOGONAL PROJECTION; RANDOM PROJECTIONS; ROOTED TREES; ULTRAMETRIC TOPOLOGY;

BIG DATA;

EID: 84949776887     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-319-17091-6_37     Document Type: Conference Paper

References (23)

1. Achlioptas, D.: Database-friendly random projections: Johnson-Lindenstrauss with binary coins. Journal of Computer and System Sciences 66(4), 671–687 (2003)
2. Bingham, E., Mannila, H.: Random projection in dimensionality reduction: applications to image and text data. In: Proceedings of the Seventh International Conference on Knowledge Discovery and Data Mining, pp. 245–250. ACM, New York (2001)
3. Contreras, P., Murtagh, F.: Fast, linear time hierarchical clustering using the Baire metric. Journal of Classification 29, 118–143 (2012)
4. Dasgupta, S., Gupta, A.: An elementary proof of a theorem of Johnson and Lindenstrauss. Random Structures and Algorithms 22(1), 60–65 (2003)
5. Dasgupta, S.: Experiments with random projection. In: Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence, pp. 143–151. Morgan Kaufmann, San Francisco (2000)
6. Deegalla, S., Boström, H.: Reducing high-dimensional data by principal component analysis vs. random projection for nearest neighbor classification. In: ICMLA 2006: Proceedings of the 5th International Conference on Machine Learning and Applications, pp. 245–250. IEEE Computer Society, Washington DC (2006)
7. Fern, X.Z., Brodly, C.: Random projection for high dimensional data clustering: a cluster ensemble approach. In: Proceedings of the Twentieth International Conference on Machine Learning. AAAI Press, Washington DC (2007)
8. Fradkin, D., Madigan, D.: Experiments with random projections for machine learning. In: KDD 2003: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 517–522. ACM, New York (2003)
9. Johnson, W.B., Lindenstrauss, J.: Extensions of Lipschitz maps into a Hilbert space. In: Conference in Modern Analysis and Probabilities. Contemporary Mathematics, vol. 26, pp. 189–206. American Mathematical Society, Providence (1984)
10. Hall, P., Marron, J.S., Neeman, A.: Geometric representation of high dimension, low sample size data. Journal of the Royal Statistical Society Series B 67, 427–444 (2005)
11. Critchley, F., Heiser, W.: Hierarchical trees can be perfectly scaled in one dimension. Journal of Classification 5, 5–20 (1988)
12. Kaski, S.: Dimensionality reduction by random mapping: fast similarity computation for clustering. In: Proceedings of the 1998 IEEE International Joint Conference on Neural Networks, pp. 413–418 (1998)
13. Li, P., Hastie, T., Church, K.: Very sparse random projections. In: KDD 2006: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, vol. 1, pp. 287–296. ACM, New York (2006)
14. Lin, J., Gunopulos, D.: Dimensionality reduction by random projection and latent semantic indexing. In: 3rd SIAM International Conference on Data Mining. SIAM, San Francisco (2003)
15. Murtagh, F.: Correspondence Analysis and Data Coding with R and Java. Chapman and Hall (2005)
16. Murtagh, F., Contreras, P.: Algorithms for hierarchical clustering: an overview. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 2(1), 86–97 (2012)
17. Murtagh, F., Contreras, P.: Fast, linear time, m-adic hierarchical clustering for search and retrieval using the Baire metric, with linkages to generalized ultrametrics, hashing, Formal Concept Analysis, and precision of data measurement. p-Adic Numbers, Ultrametric Analysis and Applications 4, 45–56 (2012)
18. Murtagh, F., Contreras, P.: Linear storage and potentially constant time hierarchical clustering using the Baire metric and random spanning paths. In: Proceedings, European Conference on Data Analysis. Springer (forthcoming, 2015)
19. Murtagh, F., Contreras, P.: Search and retrieval in massive data: sparse p-adic coding for linear time hierarchical clustering and linear space storage (in preparation, 2015)
20. Starck, J.L., Murtagh, F., Fadili, J.M.: Sparse Image and Signal Processing: Wavelets, Morphological Diversity. Cambridge University Press, Curvelets (2010)
21. Terada, Y.: Clustering for high-dimension, low-sample size data using distance vectors, 16 p. (2013). http://arxiv.org/abs/1312.3386
22. Urruty, T., Djeraba, C., Simovici, D.A.: Clustering by random projections. In: Perner, P. (ed.) ICDM2007. LNCS (LNAI), vol. 4597, pp. 107–119. Springer, Heidelberg (2007)
23. Vempala, S.S.: The Random Projection Method, DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, vol.65. American Mathematical Society, Providence (2004)