Linear Decompositions for Multi-Valued Input Classification Functions

In a multi-valued input classification function, each input combination represents properties of an object, while the output represents the class of the object. Each variable may have different radix. In most cases, the functions are partially defined. To represent multi-valued variables, both one-hot and minimum-length encoding are considered. Experimental results using University of California Irvine (UCI) benchmark functions show that the one-hot approach results in fewer variables than the minimum-length approach with linear decompositions.

[1]  Alan Mishchenko,et al.  Implicit Algorithms for Multi-Valued Input Support Manipulation , 2001 .

[2]  Tsutomu Sasao Index Generation Functions , 2019, Synthesis Lectures on Digital Circuits and Systems.

[3]  Ivan Bratko,et al.  Function Decomposition in Machine Learning , 2001, Machine Learning and Its Applications.

[4]  Tsutomu Sasao On the numbers of variables to represent sparse logic functions , 2008, 2008 IEEE/ACM International Conference on Computer-Aided Design.

[5]  Tsutomu Sasao Totally undecomposable functions: applications to efficient multiple-valued decompositions , 1999, Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329).

[6]  Toshihide Ibaraki,et al.  Finding Essential Attributes from Binary Data , 2003, Annals of Mathematics and Artificial Intelligence.

[7]  Tsutomu Sasao Linear decomposition of index generation functions , 2012, 17th Asia and South Pacific Design Automation Conference.

[8]  Tsutomu Sasao,et al.  Switching Theory for Logic Synthesis , 1999, Springer US.

[9]  Tsutomu Sasao Memory-Based Logic Synthesis , 2011 .

[10]  Bernd Steinbach,et al.  Bi-Decomposition of Function Sets in Multiple-Valued Logic for Circuit Design and Data Mining , 2004, Artificial Intelligence Review.

[11]  Tsutomu Sasao Multiple-Valued Index Generation Functions: Reduction of Variables by Linear Transformation , 2013, J. Multiple Valued Log. Soft Comput..

[12]  矢島 脩三,et al.  Harmonic Analysis of Switching Functions (情報科学の数学的理論) , 1973 .

[13]  Tsutomu Sasao,et al.  An algorithm to find optimum support-reducing decompositions for index generation functions , 2017, Design, Automation & Test in Europe Conference & Exhibition (DATE), 2017.

[14]  Sze-Tsen Hu ON THE DECOMPOSITION OF SWITCHING FUNCTIONS , 1961 .

[15]  Tsutomu Sasao Multiple-Valued Input Index Generation Functions: Optimization by Linear Transformation , 2012, 2012 IEEE 42nd International Symposium on Multiple-Valued Logic.

[16]  Tsutomu Sasao On a Minimization of Variables to Represent Sparse Multi-Valued Input Decision Functions , 2019, 2019 IEEE 49th International Symposium on Multiple-Valued Logic (ISMVL).