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Furthermore, they also proposed a novel approach based on RP for clustering, which was compared with PCA. Kaski (Kaski, 1998) used RP in the WEBSOM system for document clustering. RP was compared to PCA for reducing the dimensionality of the data in order to construct Self-Organized Maps. 5 Outex Concluding remarks We have compared the use of PCA and RP for reducing dimensionality of data to be used by a nearest neighbor classifier on five image data sets and two micro array data sets. It was observed that for all data sets, the use of PCA resulted in a higher accuracy compared to using RP.

Therefore, all image data sets contain 1024 attributes. The number of attributes for the micro array data sets and the number of instances for all data sets are shown in Table 1. The Waikato Environment for Knowledge Analysis (WEKA) (Witten and Frank, 2005) implementation of the nearest neighbor classifier was used for this study. PCA was done using MATLAB whereas WEKA’s RP filter implementation was used for RP. The accuracies were estimated using ten-fold crossvalidation, and the results for RP is the average from 30 runs to account for its random nature.

Dasgupta and A. Gupta. An elementary proof of the Johnson-Lindenstrauss lemma. Technical Report TR-99-006, International Computer Science Institute, Berkeley, CA, 1999. X. Z. Fern and C. E. Brodley. Random projection for high dimensional data clustering: A cluster ensemble approach. In Proceedings of the Twentieth International Conference of Machine Learning, 2003. D. Fradkin and D. Madigan. Experiments with Random Projections for Machine Learning. In KDD ’03: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, pages 517–522, 2003.

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A Coll. of Diophantine Probs. With Solns. by J. Matteson

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