|
Eigenanalysis is a powerful mathematical technique for analyzing matrices of data. With the data matrix constructed from a digitized image of a chromosome, this technique can be used to extract the features of the image, such as the chromosome banding pattern. The study of chromosome banding patterns represented by their pixel values in the images is based on eigenanalysis of the correlation or covariance matrix. Since the resulting eigenvectors are orthogonal, the information in each vector is excluded from all other vectors. Alternatively, the singular value decomposition method can be used to represent the data matrix as sum of its outer products, thereby avoiding the construction of a correlation/covariance matrix. Both procedures allow the sorting of information according to its significance, because the most significant information is associated with highest eigenvalues and corresponding eigenvectors. Consequently, the original data can be reconstituted using only the significant information. The advantage of this processing is that the preparatory artifacts and noise in the image are removed from the data before a recognition procedure is begun. An additional feature of this technique is that multiple data sets can be combined and processed simultaneously to establish, using objective statistical criteria, prototypes for each chromosome. Accumulative analysis improves the prototypes, and consequently the classification procedure. Features from prophase human chromosome number four have been to illustrate the eigenanalysis. Chromosomes from different spreads and individuals were used. Comparison of our statistically determined prototype with schematic idiotype from the literature shows significant improvement in recognition for all chromosomes, reconstituted at the level of only the most significant eigenvector. This type of analysis can be used for objective comparison of the various chromosomal banding patterns created by Giemsa, fluorescent dyes, monoclonal antibodies, and restriction enzymes. The ultimate objective is to relate various banding patterns, identified by eigenanalysis, to the genome structure.
|
