Semantic spaces: Measuring the distance between different subspaces

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

Volumn 5494, Issue , 2009, Pages 225-236

  Zuccon, Guido ^a   Azzopardi, Leif A ^a   Van Rijsbergen, C J ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

HERMITIAN OPERATORS; MINKOWSKI DISTANCE; NUMERICAL REPRESENTATION; QUANTUM COLLAPSE; SEMANTIC ASSOCIATIONS; SEMANTIC SPACE; SUBSPACE DISTANCE; VECTOR REPRESENTATIONS;

INFORMATION SERVICES; SEMANTICS;

HILBERT SPACES;

EID: 67049159636     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-00834-4_19     Document Type: Conference Paper

References (22)

1. Bruza, P.D., Cole, R.J.: Quantum Logic of Semantic Space: An Exploratory Investigation of Context Effects in Practical Reasoning. In: We Will Show Them: Essay in Honour of Dov Gabbay, vol. 1, pp. 339-361. College Publications (2005)
2. Bruza, P.D., Woods, J.: Quantum Collapse in Semantic Space: Interpreting Natural Language Argumentation. In: Proceedings of the 2nd QI Symposium, pp. 141-147 (2008)
3. Lund, K., Burgess, C.: Producing High-dimensional Semantic Spaces from Lexical Co-occurrence. Behavior Research Methods 28(2), 203-208 (1996)
4. Osgood, C., Suci, G., Tannenbaum, P., Date, P.: The Measurement of Meaning. University of Illinois Press, US (1957)
5. Burgess, C., Livesay, K., Lund, K.: Explorations in Context Space: Words, Sentences, Discourse. Discourse Processes 25(2,3), 211-257 (1998)
6. Landauer, T.K., Foltz, P.W., Laham, D.: An Introduction to Latent Semantic Analysis. Discourse Processes 25(2,3), 259-284 (1998)
7. Song, D., Bruza, P.D.: Discovering Information Flow Using High Dimensional Conceptual Space. In: Proceedings of the 24th ACM SIGIR, pp. 327-333 (2001)
8. Gardenfors, P.: Conceptual Spaces: The Geometry of Thought. MIT Press, US (2000)
9. Bowman, G.E.: Essential Quantum Mechanics. Oxford University Press, UK (2008)
10. Sahlgren, M.: The Word-Space Model. Ph.D thesis. Stockholm University (2006)
11. Ipsen, I.C.F., Meyer, C.D.: The Angle Between Complementary Subspaces. American Mathematical Monthly 102(10), 904-914 (1995)
12. Wong, Y.C.: Differential Geometry of Grassmann Manifolds. In: Proceedings of the National Academy of Science, vol. 57, pp. 589-594 (1967)
13. Bengtsson, I., Bruzda, W., Ericsson, A., Larsson, J.A., Tadej, W., Zyczkowski, K.: Mubs and Hadamards of Order Six (2006), ArXiv Quantum Physics e-prints
14. Wang, L., Wang, X., Feng, J.: Subspace Distance Analysis with Application to Adaptive Bayesian Algorithm for Face Recognition. Pat. Rec. 39(3), 456-464 (2006)
15. Sun, X., Wang, L., Feng, J.: Further Results on the Subspace Distance. Pat. Rec. 40(1), 328-329 (2007)
16. Sun, X., Cheng, Q.: On subspace distance. In: Campilho, A., Kamel, M.S. (eds.) ICIAR 2006. LNCS, vol. 4142, pp. 81-89. Springer, Heidelberg (2006)
17. Conway, J.H., Hardin, R.H., Sloane, N.J.A.: Packing Lines, Planes, etc.: Packings in Grassmannian Spaces. Experimental Mathematics 5(2), 139-159 (1996)
18. Bengtsson, I., Bruzda, W., Ericsson, A., Larsson, J.A., Tadej, W., Zyczkowski, K.: Mutually Unbiased Bases and Hadamard Matrices of Order Six. Journal of Mathematical Physics 48(5) (2007)
19. Wootters, W.K.: Statistical Distance and Hilbert Space. Phys. Rev. D 23(2), 357-362 (1981)
20. Braunstein, S.L., Caves, C.M.: Statistical Distance and the Geometry of Quantum States. Phys. Rev. Lett. 72(22), 3439-3443 (1994)
21. Uhlmann, A.: The "Transition Probability" in the State Space of a algebra. Reports on Mathematical Physics 9, 273-279 (1976)
22. Huertas-Rosero, A.F., Azzopardi, L.A., van Rijsbergen, C.J.: Characterising through Erasing: A theoretical framework for representing documents inspired by quantum theory. In: Proceedings of the 2nd QI Symposium, pp. 160-163 (2008)