When QSAR models are fitted, it is important to validate any fitted model-to check that it is plausible that its predictions will carry over to fresh data not used in the model fitting exercise. There are two standard ways of doing this-using a separate hold-out test sample and the computationally much more burdensome leave-one-out cross-validation in which the entire pool of available compounds is used both to fit the model and to assess its validity. We show by theoretical argument and empiric study of a large QSAR data set that when the available sample size is small-in the dozens or scores rather than the hundreds, holding a portion of it back for testing is wasteful, and that it is much better to use cross-validation, but ensure that this is done properly.
In this article we (1) outline the construction of a 3-D "graphical" representation of DNA primary sequences, illustrated on a portion of the human beta globin gene; (2) describe a particular scheme that transforms the above 3-D spatial representation of DNA into a numerical matrix representation; (3) illustrate construction of matrix invariants for DNA sequences; and (4) suggest a data reduction based on statistical analysis of matrix invariants generated for DNA. Each of the four contributions represents a novel development that we hope will facilitate comparative studies of DNA and open new directions for representation and characterization of DNA primary sequences.
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