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Neighborhood Counting Measure and Minimum Risk Metric
April 2010 (vol. 32 no. 4)
pp. 766-768
Hui Wang, University of Ulster, Jordanstown, Newtownabbey, Co. Antrim
The neighborhood counting measure (NCM) is a similarity measure based on the counting of all common neighborhoods in a data space [5]. The minimum risk metric (MRM) [2] is a distance measure based on the minimization of the risk of misclassification. The paper by Argentini and Blanzieri [1] refutes a remark in [5] about the time complexity of MRM, and presents an experimental comparison of MRM and NCM. This paper is a response to the paper by Argentini and Blanzieri [1]. The original remark is clarified by a combination of theoretical analysis of different implementations of MRM and experimental comparison of MRM and NCM using straightforward implementations of the two measures.

[1] A. Argentini and E. Blanzieri, "About Neighborhood Rounting Measure Metric and Minimum Risk Metric," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 32, no. 4, pp. , Apr. 2010.
[2] E. Blanzieri and F. Ricci, "Probability Based Metrics for Nearest Neighbor Classification and Case-Based Reasoning," Lecture Notes in Computer Science, vol. 1650, pp. 14-29, 1999.
[3] C. Elzinga, S. Rahmann, and H. Wang, "Algorithms for Subsequence Combinatorics," Theoretical Computer Science vol. 409, no. 3, pp. 394-404, 2008.
[4] Z. Lin, H. Wang, S. McClean, and C. Liu, "All Common Embedded Subtrees for Measuring Tree Similarity," Proc. Int'l Symp. Computational Intelligence and Design, pp. 29-32, 2008.
[5] H. Wang, "Nearest Neighbors by Neighborhood Counting," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 6, pp. 942-953, June 2006.
[6] H. Wang, "All Common Subsequences," Proc. Int'l Joint Confs. Artificial Intelligence, pp. 63-640, 2007.
[7] H. Wang and Z. Lin, "A Time Weighted Neighbourhood Counting Similarity for Time Series Analysis," Proc. Int'l Conf. Rough Set and Knowledge Technology 2008.

Index Terms:
Minimum risk metric, neighborhood counting measure, k-nearest neighbor.
Citation:
Hui Wang, "Neighborhood Counting Measure and Minimum Risk Metric," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 4, pp. 766-768, April 2010, doi:10.1109/TPAMI.2010.16
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