Abstract
The Mahalanobis distance, or quadratic form distance, is a distance measure commonly used for feature-based similarity search in scenarios where features are correlated. For efficient query processing on such data effective distance-based spatial pruning techniques are required. In this work we investigate such pruning techniques by means of distance bounds of the Mahalanobis distance in the presence of rectangular spatial approximations. Specifically we discuss how to transform the problem of computing minimum and maximum distance approximations between two minimum bounding rectangles (MBRs) into a quadratic optimization problem. Furthermore, we show how the recently developed concept of spatial domination can be solved under the Mahalanobis distance by a quadratic programming approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Warrens, M.J.: N-way metrics. Journal of Classification 27(2), 173–190 (2010)
Beecks, C., Uysal, M.S., Seidl, T.: Signature quadratic form distance. In: Proc. CIVR, pp. 438–445 (2010)
Beecks, C., Uysal, M.S., Seidl, T.: Similarity matrix compression for efficient signature quadratic form distance computation. In: Proc. SISAP, pp. 109–114 (2010)
Emrich, T., Kriegel, H.-P., Kröger, P., Renz, M., Züfle, A.: Boosting spatial pruning: On optimal pruning of MBRs. In: Proc. SIGMOD, pp. 39–50 (2010)
Gath, E.G., Hayes, K.: Bounds for the largest mahalanobis distance. Linear Algebra Appl. 419(1), 93–106 (2006)
Lokoc, J., Hetland, M.L., Skopal, T., Beecks, C.: Ptolemaic indexing of the signature quadratic form distance. In: Proc. SISAP, pp. 9–16 (2011)
Roussopoulos, N., Kelley, S., Vincent, F.: Nearest neighbor queries. In: Proc. SIGMOD, pp. 71–79 (1995)
Seidl, T., Kriegel, H.-P.: Efficient user-adaptable similarity search in large multimedia databases. In: Proc. VLDB, pp. 506–515 (1997)
Skopal, T., Bartos, T., Lokoc, J.: On (not) indexing quadratic form distance by metric access methods. In: Proc. EDBT, pp. 249–258 (2011)
Yang, L.: An overview of distance metric learning. Technical report, Department of Computer Science and Engineering, Michigan State University (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Emrich, T. et al. (2013). Optimal Distance Bounds for the Mahalanobis Distance. In: Brisaboa, N., Pedreira, O., Zezula, P. (eds) Similarity Search and Applications. SISAP 2013. Lecture Notes in Computer Science, vol 8199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41062-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-41062-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41061-1
Online ISBN: 978-3-642-41062-8
eBook Packages: Computer ScienceComputer Science (R0)