Nonlinear Dimensionality Reduction by Isomap and MLEdim as Applied to Amino-Acid Distribution in Yeast ORFs

We consider the multivariate distribution of amino-acids coding for proteins in Open Reading Frames (ORFs). An appropriate statistical model of this distribution might throw some light on the interdependency of the 20 amino-acids and contribute to the problem of verification of known ORFs (At the date 3. April 2008 only 71.02% of known ORFs were verified). From a graphical analysis od the data we deduce that the data cloud mightbe modelled by a curvilinear manifold of smaller dimension embedded in a larger, 20-dimensional space. To check that assumption we have applied to the recorded data (containing frequency of appearing 20 amino-acids in ORFs found in the 7th yeast chromosome) two nonlinear methods referred to as the Isomap (Tennenbaum et al., 2000 ) and MLEdim (Levina and Bickel, 2005). These two methods, based on complete different principles, gave similar results: the true ´intrinsic´ dimension of the investigated data appears several dimensions smaller as originally supposed.