Orthogonality considerations for library searching Nth-order data

Identification of chemicals from multi-order (Nth-order) instruments is typically carried out with only first-order library searches. Simultaneous library searches for all orders of Nth-order data enhances identification of chemicals. Three methods are presented for simultaneous Nth-order library searches based on measuring the angle between the unknown and reference chemicals present in a library. The first method, called first-order limited (FOL), consists of unfolding Nth-order data to first-order and using the standard dot product function to compute the angle. The second approach, second-order limited (SOL), unfolds Nth-order data to second-order and uses singular value decomposition to obtain the angle. The third method, Nth-order (NO), computes the angle directly without unfolding. Performance evaluations show the advantages of SOL in search time for large libraries while FOL and NO appear to have a higher degree of selectivity. The methods of FOL and NO are shown to be the same measures but NO has a computational advantage. Computer memory usage for all three methods is also addressed.