Kaushik Chakrabarti and Sharad Mehrotra. Local dimensionality reduction: A new approach to indexing high dimensional spaces. In Proceedings of the 26th VLDB Conference, Cairo, Egypt, 2000. Home/Search Document Details and Download
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....and compute all the lower and some upper bounds on the distance to the query point. 3. PRINCIPAL COMPONENT ANALYSIS The Principal Component Analysis (PCA) 12] is a widely used method for transforming points in the original (highdimensional) space into another (usually lower dimensional) space [5, 11]. It examines the variance structure in the dataset and determines the directions along which the data exhibits high variance. The first principal component (or dimension) accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the ....
....points of P projected on k1andk2dimen sions respectively (after applying PCA) 0 k1 k2 D. Qk1 and Qk2 are similarly defined. The PCA method has several nice properties: 1. dist(Pk1,Q k1 ) dist(Pk2,Q k2 )0 k1 k2 D,wheredist(p, q) denotes the distance between two points p and q (See [5] for a proof) 2. Because the first few dimensions of the projection are the most important, dist(Pk,Q k ) can be very near to the actual distance between P and Q for k D [5] 3. The above properties also hold for new points that are added into the dataset (despite the fact that they do not ....
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K. Chakrabarti and S. Mehrotra. Local dimensionality reduction: A new approach to indexing high dimensional spaces. In Proc. 26th VLDB Conference, pages 89--100, 2000.
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K. Chakrabarti and S. Mehrotra. Local dimensionality reduction: A new approach to indexing high dimensional spaces. In Proceedings of the 26th VLDB Conference, Cairo, Egypt, 2000.
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....are averaged over the 100 queries. The performance gap between our technique and the other techniques was even greater with SR tree [77] as the index structure due to higher dimensionality curse [23] We do not report those results here but can be found in the full version of the LDR paper [25]. 58 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 Skew (z) LDR GDR Figure 4.6: Sensitivity of precision to skew. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 7 8 9 10 Precision Number of Clusters (n) LDR GDR Figure 4.7: Sensitivity of precision to number of ....
K. Chakrabarti and S. Mehrotra. Local dimensionality reduction: A new approach to indexing high dimensional spaces. Technical Report, TR-MARS-00-04, University of California at Irvine, http://wwwdb. ics.uci.edu/pages/publications/, 2000.
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K. Chakrabarti and S. Mehrotra. Local dimensionality reduction: A new approach to indexing high dimensional spaces. In A. E. Abbadi, M. L. Brodie, S. Chakravarthy, U. Dayal, N. Kamel, G. Schlageter, and K.-Y. Whang, editors, Proc. of 26th International Conference on Very Large Data Bases, pages 89-100. Morgan Kaufmann, September 2000.
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