Assessment of two-dimensional separative systems using nearest-neighbor distances approach. Part 1: orthogonality aspects.

We propose here a new approach to the evaluation of two-dimensional and, more generally, multidimensional separations based on topological methods. We consider the apex plot as a graph, which could further be treated using a topological tool: the measure of distances between the nearest neighbors (NND). Orthogonality can be thus defined as the quality of peak dispersion in normalized separation space, which is characterized by two factors describing the population of distances between nearest neighbors: the lengths (di(o)) of distances and the degree of similarity of all lengths.

Assessment of two-dimensional separative systems using the nearest neighbor distances approach. Part 2: separation quality aspects.

In this paper we propose a method for the evaluation of real separation quality in multidimensional separations based on the nearest neighbor distances (NND). This approach allows us to overcome the principal drawback of the orthogonality measurement which does not evaluate how good the real separation obtained with one system is, especially when compared to another one. Separation quality evaluation takes into account the distances (di(s)) between peaks in whole separation space.