Separating points by parallel hyperplanes--characterization problem.
This paper deals with partitions of a discrete set S of points in a d-dimensional space, by h parallel hyperplanes. Such partitions are in a direct correspondence with multilinear threshold functions which appear in the theory of neural networks and multivalued logic. The characterization (encoding) problem is studied. We show that a unique characterization (encoding) of such multilinear partitions of S = {0, 1,..., m-1}d is possible within theta(h x d2 x log m) bit rate per encoded partition. The proposed characterization (code) consists of (d + 1) x (h + 1) discrete moments having the order no bigger than 1. The obtained bit rate is evaluated depending on the mutual relations between h, d, and m. The optimality is reached in some cases.
Ghilezan
Silvia
S
Faculty of Engineering, University of Novi Sad, 21000 Novi Sad, Serbia. gsilvia@uns.ns.ac.yu
Pantović
Jovanka
J
Zunić
Jovisa
J
D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D008962:Models, Theoretical; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted