The Significant and Profound Impacts of Chou’s Invariance Theorem


In this short review paper, the significant and profound impacts of the Chou’s “invariance theorem” have been briefly presented with crystal clear convincingness.

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Chou, K. (2020) The Significant and Profound Impacts of Chou’s Invariance Theorem. Natural Science, 12, 659-660. doi: 10.4236/ns.2020.129055.

The Chou’s invariance theorem was originally proposed by Kuo-Chen Chou [1] in 1995 to address the problem often encountered in bioinformatics and cheminformatics. The issue is that the Mahalanobis distance [2] cannot be defined because its covariance matrix is singular. One effective approach to solve this problem is to reduce its Dimension (vector space) until the covariance matrix concerned is well defined. This can be done by removing one or more components until the matrix concerned is no longer singular. The “Chou’s invariance theorem” says that it does not matter at all to remove which components because exactly the same final outcome will be remained.

Ever since it was proposed, the “Chou’s invariance theorem” has been widely and increasingly used by many follow-up scientists (see, e.g., [3-7]).

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Chou, K.C. (1995) A Novel Approach to Predicting Protein Structural Classes in a (20-1)-D Amino Acid Composition Space. Proteins: Structure, Function & Genetics, 21, 319-344.
[2] Mahalanobis, P.C. (1936) On the Generalized Distance in Statistics. Proceedings of the National Academy of Sciences, India, 2, 49-55.
[3] Pillai, K.C.S. and Mahalanobis, D. (1985) Encyclopedia of Statistical Sciences. In: Kotz, S. and Johnson, N.L., Eds., John Wiley & Sons. (This Reference Also Presents a Brief Biography of Mahalanobis Who Was a Man of Great Originality and Who Made Considerable Contributions to Statistics, New York, 176-181.)
[4] Liu, W. and Chou, K.C. (1998) Prediction of Protein Structural Classes by Modified Mahalanobis Discriminant Algorithm. Journal of Protein Chemistry, 17, 209-217.
[5] Lin, H. and Li, Q.Z. (2007) Predicting Conotoxin Superfamily and Family by Using Pseudo Amino Acid Composition and Modified Mahalanobis Discriminant. Biochemical and Biophysical Research Communications, 354, 548-551.
[6] Lin, H. (2008) The Modified Mahalanobis Discriminant for Predicting Outer Membrane Proteins by Using Chou’s Pseudo Amino Acid Composition. Journal of Theoretical Biology, 252, 350-356.
[7] Ding, H., Liu, L., Guo, F.B., Huang, J. and Lin, H. (2011) Identify Golgi Protein Types with Modified Mahalanobis Discriminant Algorithm and Pseudo Amino Acid Composition. Protein & Peptide Letters, 18, 58-63.

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