This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
The Capacity of Multilevel Threshold Functions
March 1988 (vol. 10 no. 2)
pp. 277-281

Lower and upper bounds for the capacity of multilevel threshold elements are estimated, using two essentially different enumeration techniques. It is demonstrated that the exact number of multilevel threshold functions depends strongly on the relative topology of the input set. The results correct a previously published estimate and indicate that adding threshold levels enhances the capacity more than adding variables.

[1] T. M. Cover, "Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition,"IEEE Trans. Electron. Comput., vol. EC-14, pp. 326-334, June 1965.
[2] M. Minsky and S. Papert,Perceptrons. Cambridge, MA: M.I.T. Press, 1969.
[3] S. Muroga, "Lower bounds on the number of threshold functions and a maximum weight,"IEEE Trans. Electron. Comput., vol. EC-14, pp. 136-148, Apr. 1965.
[4] D. Haring, "Multi-threshold threshold elements,"IEEE Trans. Electron. Comput., vol. EC-15, pp. 45-65, June 1965.
[5] R. Takiyama, "The separating capacity of a multi-threshold threshold element,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-7, pp. 112-116, Jan. 1985.
[6] R. Takiyama, "Multiple threshold perceptron,"Pattern Recognition, vol. 10, pp. 27-30, 1978.
[7] J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities,"Proc. Nat. Acad. Sci., vol. 79, pp. 2554-2558, 1982.
[8] Y. S. Abu-Mostafa and J. St. Jacques, "Information capacity of the Hopfield model,"IEEE Trans. Inform. Theory, vol. IT-31, pp. 461-464, 1985.
[9] S. 'Olafsson, "Transpositions and Pascal's triangle," to be published.
[10] J. Pearl, "Capacity and error estimates for boolean classifiers with limited complexity,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-1, pp. 350-355, 1979.
[11] F. R. Krueger, "Comments on Takiyama's analysis of the multithreshold threshold element,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 760-761, Nov. 1986.

Index Terms:
lower bounds; information capacity; information theory; multilevel threshold functions; upper bounds; topology; input set; information theory; topology
Citation:
S. Olafsson, Y.S. Abu-Mostafa, "The Capacity of Multilevel Threshold Functions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 2, pp. 277-281, March 1988, doi:10.1109/34.3890
Usage of this product signifies your acceptance of the Terms of Use.