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On Distributional Assumptions and Whitened Cosine Similarities
June 2008 (vol. 30 no. 6)
pp. 1114-1115
Recently, an interpretation of the whitened cosine similarity measure as a Bayes decision rule was proposed (C. Liu, "The Bayes Decision Rule Induced Similarity Measures,'' IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 1086-1090, June 2007. This communication makes the observation that some of the distributional assumptions made to derive this measure are very restrictive and, considered simultaneously, even inconsistent.

[1] C. Liu, “The Bayes Decision Rule Induced Similarity Measures,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 1086-1090, June 2007.
[2] G.J. McLachlan, Discriminant Analysis and Statistical Pattern Recognition. John Wiley & Sons, 1992.
[3] K. Fukunaga, Introduction to Statistical Pattern Recognition. Academic Press, 1990.
[4] M. Loog, R.P.W. Duin, and R. Haeb-Umbach, “Multiclass Linear Dimension Reduction by Weighted Pairwise Fisher Criteria,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 7, pp. 762-766, July 2001.

Index Terms:
Statistical, Classifier design and evaluation
Citation:
Marco Loog, "On Distributional Assumptions and Whitened Cosine Similarities," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 6, pp. 1114-1115, June 2008, doi:10.1109/TPAMI.2007.70838
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