Abstract
It is shown that the accuracy of chromosome classification constrained by class size can be improved over previously reported results by a combination of straightforward modifications to previously used methods. These are (i) the use of the logarithm of the Mahalanobis distance of an unknown chromosome's feature vector to estimated class mean vectors as the basis of the transportation method objective function, rather than the estimated likelihood; (ii) the use of all available features and full estimated covariance to compute the Mahalanobis distance, rather than a subset of features and the diagonal (variance) terms only; (iii) a modification to the way the transportation model deals with the constraint on the number of sex chromosomes in a metaphase cell; and (iv) the use of a newly discovered heuristic to weight off-diagonal elements of the covariance; this proved to be particularly valuable in cases where relatively few training examples were available to estimate covariance. The methods have been verified using 5 different sets of chromosome data.
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References
Anderson TW (1984) An introduction to multivariate statistical analysis, Second Edition. Wiley Series in Probability and Mathematical Statistics. Wiley
Duda RO, Hart PE (1973) Pattern classification and scene analysis. Wiley New York
Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall New York
Errington P, Graham J (1993) Neural network chromosome classification. Cytometry 14:627–639
Fahrmeir L, Hamerle A (eds) (1984) Multivariate statistische Verfahren. De Gruyter Berlin New York
Goodman MM (1972) Distance analysis in biology. Systematic Zoology 21(2): 174–186, reprinted in: Atchley WR, Bryant EH (eds) (1975) Multivariate statistical methods. Among-Group Covariation, Benchmark Papers in Systematic and Evolutionary Biology 1:377–389, Dowden Hutchinson & Ross
Granum E (1982) Application of statistical and syntactical methods of analysis and classification to chromosome data. In: Kittler J, Ku KS, Pau LF (eds) Pattern recognition theory and applications. NATO ASI (Oxford 1981) Reidel Dordrecht 373–398
Granum E, Thomason M (1990) Automatically inferred Markov network models for classification of chromosomal band pattern structures. Cytometry 11:26–39
Greon FCA, ten Kate TK, Smeulders AWM, Young IT (1989) Human chromosome classification based on local band descriptors. Pattern Recognition Letters 9:211–222
Habbema JDF (1979) Statistical methods for classification of human chromosomes. Biometrics 35:103–118
ISCN (1985) An international system for human cytogenetic nomenclature. Karger S Basel
Kirby SPJ, Theobald CM, Piper J, Carothers A (1991) Some methods of combining class information in multivariate normal discrimination for the classification of human chromosomes. Statistics in Medicine 10:141–149
Kleinschmidt P, Mitterreiter I, Rank C (1994) A hybrid method for automatic chromosome karyotyping. Pattern Recognition Letters 15:87–96
Lundsteen C, Gerdes T, Maahr J (1986) Automatic classification of chromosomes as part of a routine system for clinical analysis. Cytometry 7:1–7
Lundsteen C, Lind A-M, Granum E (1976) Visual classification of banded human chromosomes. I. Karyotyping compared with classification of isolated chromosomes. Annals of Human Genetics 40:87–97
Paton K (1969) Automatic chromosome identification by the maximum-likelihood method. Annals of Human Genetics 33:177–184
Piper J (1986) Classification of chromosomes constrained by expected class size pattern recognition letters 4:391–395
Piper J (1987) The effect of zero feature correlation assumption on maximum likelihood based classification of chromosomes. Signal Processing 12:49–57
Piper J (1990) A new approach to constrained maximum likelihood chromosome classification. Research Note, MRC Human Genetics Unit Edinburgh
Piper J (1982) Variability and bias in experimentally measured classifier error rates. Pattern Recognition Letters 13:685–692
Piper J, Breckon G (1989) An automated system for karyotyping mouse chromosomes. Cytogenetics and Cell Genetics 50:111–115
Piper J, Granum E (1989) On fully automatic feature measurement for banded chromosome classification. Cytometry 10:242–255
Piper J, Nickolls P, McLaren W, Rutovitz D, Chisholm A, Johnstone I (1981) The effect of digital image filtering on the performance of an automatic chromosome classifier. Signal Processing 4:361–373
Rohlf FJ (1971) Perspectives on the application of multivariate statistics to taxonomy. Taxon 20(1): 85–90. Reprinted in: Atchley WR, Bryant EH (eds) (1975) Multivariate statistical methods, among-group covariation. Benchmark Papers in Systematic and Evolutionary Biology 1:6–11, Dowden Hutchinson & Ross
Slot RE (1979) On the profit of taking into account the known number of objects per class in classification methods. IEEE Transactions on Information Theory IT-25:484–488
Sweeney W Classification of chromosomes using probabilistic neural network. Cytometry, submitted
Theobald CM, Kirby SPJ Discrimination using covariance selection models for the automated allocation of human chromosomes. Submitted
Tso M, Graham J (1983) The transportation algorithm as an aid to chromosome classification. Pattern Recognition Letters 1:489–496
Tso M, Kleinschmidt P, Mitterreiter I, Graham J (1991) An efficient transportation algorithm for automatic chromosome karyotyping. Pattern Recognition Letters 12:117–126
Zimmermann SO, Johnston DA, Arrighi FE, Rupp ME (1986) Automated homologue matching of human G-banded chromosomes. Computers in Biology and Medicine 16:223–233
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Kleinschmidt, P., Mitterreiter, I. & Piper, J. Improved chromosome classification using monotonic functions of mahalanobis distance and the transportation method. ZOR - Methods and Models of Operations Research 40, 305–323 (1994). https://doi.org/10.1007/BF01432971
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DOI: https://doi.org/10.1007/BF01432971