Decomposition of multiple-valued functions

Perkowski, Marek; Marek-Sadowska, Malgorzata; Jóźwiak, L.; Łuba, T.; Grygiel, Stanislaw; Nowicka, M.; Malvi, Rahul; Wang, Z.; Zhang, J.S.

doi:10.1109/ismvl.1995.513540

Cited by 50 publications

(14 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Curtis published in 1976 an important paper: "Simplified decomposition of Boolean functions," [44]. The new problem representation introduced in this paper influenced the very successful line of research represented recently by Luba et al [58,90,107,99]. The same year M.G.…”

Section: -8mentioning

confidence: 96%

“…• The approach can-be easily expanded to multiple-valued [66,91,107,33], fuzzy [57,45] and continuous [110] logic.…”

Section: -4mentioning

confidence: 99%

“…The most important aspect of a successful Functional Decomposer is the representation of data. From all representations in the literature, the most successful programs use Binary Decision Diagrams and Edge-Valued Decision Diagrams [89], lists of disjoint ON and OFF cubes [111] and variablepartitions on ON and OFF minterms [107]. The last representation has very interesting properties and allows to define, on incompletely specified functions, several operators, that have not been defined before, allowing thus for efficient variable partitioning and column compaction algorithms, as well as for formulating new kinds of decompositions, including a new method of "variable re-using".…”

Section: -13mentioning

confidence: 99%

See 2 more Smart Citations

USAF Summer Research Program - 1994 Summer Faculty Research Program Final Reports, Volume 5B, Wright Laboratory

Moore¹

1994

View full text Add to dashboard Cite

Section: -8mentioning

confidence: 96%

“…• The approach can-be easily expanded to multiple-valued [66,91,107,33], fuzzy [57,45] and continuous [110] logic.…”

Section: -4mentioning

confidence: 99%

Section: -13mentioning

confidence: 99%

See 1 more Smart Citation

USAF Summer Research Program - 1994 Summer Faculty Research Program Final Reports, Volume 5B, Wright Laboratory

Moore¹

1994

View full text Add to dashboard Cite

“…Much later, the interest in the algorithm has been renewed. Perkowski et al [5] improved the original algorithm to handle incompletely specified functions, and Luba [4] proposed to decompose multi-valued functions by representing a multi-valued variable by a set of Boolean variables. Zupan and Bohanec [7] developed an algorithm that induces a hierarchy of multi-valued variables without the need to represent them as Boolean.…”

Section: Introductionmentioning

confidence: 99%

Constructing intermediate concepts by decomposition of real functions

Demšar

Zupan

Bohanec

et al. 1997

Machine Learning: ECML-97

View full text Add to dashboard Cite

Abstract.In learning from examples it is often useful to expand an attribute-vector representation by intermediate concepts. The usual advantage of such structuring of the learning problem is that it makes the learning easier and improves the comprehensibility of induced descriptions. In this paper, we develop a technique for discovering useful intermediate concepts when both the class and the attributes are real-valued. The technique is based on a decomposition method originally developed for the design of switching circuits and recently extended to handle incompletely specified multi-valued functions. It was also applied to machine learning tasks. In this paper, we introduce modifications, needed to decompose real functions and to present them in symbolic form. The method is evaluated on a number of test functions. The results show that the method correctly decomposes fairly complex functions. The decomposition hierarchy does not depend on a given repertoir of basic functions (background knowledge).

show abstract

“…Several papers written on decomposition of multi-valued networks have shown an interest in using their decomposers in the field of machine learning [7,16,14,13]. Each of these papers had a slight twist to the decomposition process and the type of data that they were able to handle.…”

Section: Introductionmentioning

confidence: 99%

An error reducing approach to machine learning using multi-valued functional decomposition

Files

Perkowski²

Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)

View full text Add to dashboard Cite

This paper considers minimization of incompletely specified multi-valued functions using functional decomposition. While functional decomposition was originally created for the minimization of logic circuits, this paper uses the decomposition process for both machine learning and logic synthesis of multi-valued functions. As it turns out, the minimization of logic circuits can be used in the concept of "learning" in machine learning, by reducing the complexity of a given data set. A main difference is that machine learning problems normally have a large number of output don't cares. Thus, the decomposition technique presented in this paper is focused on functions with a large number of don't cares. There have been several papers that have discussed the topic of using multi-valued functional decomposition for functions with a large number of don't cares.The novelty brought with this paper is that the proposed method is structured to reduce the resulting "error" of the functional decomposer, where "error" is a measure of how well a machine learning algorithm approximates the actual, or true function.

show abstract

Decomposition of multiple-valued functions

Cited by 50 publications

References 11 publications

USAF Summer Research Program - 1994 Summer Faculty Research Program Final Reports, Volume 5B, Wright Laboratory

USAF Summer Research Program - 1994 Summer Faculty Research Program Final Reports, Volume 5B, Wright Laboratory

Constructing intermediate concepts by decomposition of real functions

An error reducing approach to machine learning using multi-valued functional decomposition

Contact Info

Product

Resources

About