Abstract
The paper shows the application of the multidimensional scaling to discover the intrinsic dimensionality of the substitution matrices. These matrices are used in Bioinformatics to compare amino acids in the alignment procedures. However, the methodology can be used in other applications to discover the intrinsic dimensionality of a wide class of symmetrical matrices. The discovery of the intrinsic dimensionality of substitutions matrices is a data processing problem with applications in chemical evolution. The problem is related with the number of relevant physical, chemical and structural characteristic involved in these matrices. Many studies have dealt with the identification of relevant characteristic sets for these matrices, but few have concerned with establishing an upper bound of their cardinality. The methodology of multidimensional scaling is used to map the substitution matrix information in a virtual low dimensional space. The relationship between the quality of this process and the dimensionality of the mapping provides clues about the number of characteristics which better represents the matrix. To avoid the local minima problem, a genetic algorithm is used to minimize the objective function of the multidimensional scaling procedure. The main conclusion is that the number of effective characteristics involved in substitution matrices is small.
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References
Dayhoff, M., Schwartz, R., Orcutt, B.: Atlas of Protein Sequence and Structure. Volume 5. Nat. Biomed. Res. Found. (1978)
Henikoff, S., Henikoff, J.: Amino acid substitution matrices from protein blocks. Proc. Natl. Acad. Sci. 89 (1992) 10915–10919
Fukunaga, K.: Introduction to Statistical Pattern Recognition. Morgan Kaufmann (1990)
Chakrabarti, K., Mehrotra, S.: Local dimensionality reduction: A new approach to indexing high dimensional spaces. In: The VLDB Journal. (2000) 89–100
Kanth, K.V.R., Agrawal, D., Abbadi, A.E., Singh, A.: Dimensionality reduction for similarity searching in dynamic databases. Computer Vision and Image Understanding: CVIU 75(1–2) (1999) 59–72
Aggarwal, C.C.: On the effects of dimensionality reduction on high dimensional similarity search. In: Symposium on Principles of Database Systems. (2001)
Kawashima, S., Ogata, H., Kanehisa, M.: Aaindex: amino acid index database. Nucleic Acids Res. 27 (1999) 368–369
Venkatarajan, M.S., Braun, W.: New quantitative descriptors of amino acids based on multidimensional scaling of a large number of pysical-chemical properties. J. Mol. Model 7 (2001) 445–453
Cox, T., Cox, M.A.: Multidimensional Scaling. Chapman and Hall (1994)
Duda, R., Hart, P., Stork, D.: Pattern Classification. John Wiley and Sons (2001)
Sammon, J.: A nonlinear mapping for data structure analysis. IEEE Trans. Computers 18 (1969) 401–409
Li, S., de Vel, O., Coomans, D.: Comparative performance analysis of non-linear dimensionality reduction methods. Technical report, James Cook Univ. (1995)
Backer, S.D., Naud, A., Scheunders, P.: Nonlinear dimensionality reduction techniques for unsupervised feature extraction. Pattern Recognition Letters 19 (1998) 711–720
Scheunders, P., Backer, S.D., Naud, A.: Non-linear mapping for feature extraction. Lecture notes in computer science 1451 (1998) 823–830
Hagerty, C., Kulikowski, C., Muchnik, I., Kim, S.: Two indeces can approximate 402 amino acid properties. In: Proc. IEEE Int. Symp. Intelligent Control, Intelligent Systems and Semiotics. (1999) 365–369
Gerstein, M., Levitt, M.: Simulating water and the molecules of life. Scientific American (1998) 100–105
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Méndez, J., Falcón, A., Hernández, M., Lorenzo, J. (2007). Discovering the Intrinsic Dimensionality of BLOSUM Substitution Matrices Using Evolutionary MDS. In: Corchado, E., Corchado, J.M., Abraham, A. (eds) Innovations in Hybrid Intelligent Systems. Advances in Soft Computing, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74972-1_48
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DOI: https://doi.org/10.1007/978-3-540-74972-1_48
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