Data-Driven Compression and Efficient Learning of the Choquet Integral
| Autor: | Timothy C. Havens, Muhammad Aminul Islam, Anthony J. Pinar, Derek T. Anderson |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Lossless compression
Mathematical optimization 021103 operations research Computational complexity theory Applied Mathematics 0211 other engineering and technologies Monotonic function 02 engineering and technology Lossy compression Fuzzy logic Computational Theory and Mathematics Choquet integral Artificial Intelligence Control and Systems Engineering 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Imputation (statistics) Algorithm Mathematics Parametric statistics |
| Zdroj: | IEEE Transactions on Fuzzy Systems. 26:1908-1922 |
| ISSN: | 1941-0034 1063-6706 |
| DOI: | 10.1109/tfuzz.2017.2755002 |
| Popis: | The Choquet integral (ChI) is a parametric nonlinear aggregation function defined with respect to the fuzzy measure (FM). To date, application of the ChI has sadly been restricted to problems with relatively few numbers of inputs; primarily as the FM has $2^N$ variables for $N$ inputs and $N(2^{N-1}-1)$ monotonicity constraints. In return, the community has turned to density-based imputation (e.g., Sugeno $\lambda$ -FM) or the number of interactions (FM variables) are restricted (e.g., $k$ -additivity). Herein, we propose a new scalable data-driven way to represent and learn the ChI, making learning computationally manageable for larger $N$ . First, data supported variables are identified and used in optimization. Identification of these variables also allows us recognize future ill-posed fusion scenarios; ChIs involving variable subsets not supported by data. Second, we outline an imputation function framework to address data unsupported variables. Third, we present a lossless way to compress redundant variables and associated monotonicity constraints. Finally, we outline a lossy approximation method to further compress the ChI (if/when desired). Computational complexity analysis and experiments conducted on synthetic datasets with known FMs demonstrate the effectiveness and efficiency of the proposed theory. |
| Databáze: | OpenAIRE |
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