scholarly journals Noise Reduction with Inference Based on Fuzzy Rule Interpolation at an Infinite Number of Activating Points: Toward Fuzzy Rule Learning in a Unified Inference Platform

2018 ◽  
Vol 22 (6) ◽  
pp. 883-899 ◽  
Author(s):  
Kiyohiko Uehara ◽  
Kaoru Hirota ◽  
◽  
Keyword(s):  
Noise Reduction ◽  
Infinite Number ◽  
Fuzzy Inference ◽  
Mathematical Proof ◽  
Rule Learning ◽  
Fuzzy Rule ◽  
Reduction Process ◽  
Global Smoothness ◽  
Fuzzy Rule Learning ◽  
Learning Data

In order to provide a unified platform for fuzzy inference and fuzzy rule learning with noise-corrupted data, a method is proposed for reducing noise in learning data on the basis of a fuzzy inference method called α-GEMINAS (α-level-set and generalized-mean-based inference with fuzzy rule interpolation at an infinite number of activating points). It is expected to prevent fuzzy rules from overfitting to noise in learning data, especially when there is less learning data available for fuzzy rule optimization. The proposed method is named α-GEMI-ES (α-GEMINAS-based local-evolution toward slight linearity for global smoothness) in this paper. α-GEMI-ES iteratively performs α-GEMINAS and reduces the noise in each iteration. This paper mathematically proves that α-GEMI-ES effectively reduces the noise. The noise-reduction process is decisive and thus relies less on trial-and-error-based progress. The noise is reduced by a large amount in the early iterations and the amount of its reduction is decelerated in the later iterations where the deviation in the learning data is suppressed to a great extent. This property makes it easy to determine the termination conditions for the iterative process. Simulation results demonstrate that α-GEMI-ES properly reduces noise as the mathematical proof suggests. The above-mentioned properties indicate that α-GEMI-ES is feasible in practice for the unified platform.

Noise Reduction with Fuzzy Inference Based on Generalized Mean and Singleton Input–Output Rules: Toward Fuzzy Rule Learning in a Unified Inference Platform

2019 ◽  
Vol 23 (6) ◽  
pp. 1027-1043
Author(s):  
Kiyohiko Uehara ◽  
Kaoru Hirota ◽  
Keyword(s):  
Noise Reduction ◽  
Level Set ◽  
Fuzzy Inference ◽  
Fuzzy Rule ◽  
Sampled Data ◽  
Input Output ◽  
Generalized Mean ◽  
Α Level ◽  
Rule Optimization ◽  
Learning Data

A method is proposed for reducing noise in learning data based on fuzzy inference methods called α-GEMII (α-level-set and generalized-mean-based inference with the proof of two-sided symmetry of consequences) and α-GEMINAS (α-level-set and generalized-mean-based inference with fuzzy rule interpolation at an infinite number of activating points). It is particularly effective for reducing noise in randomly sampled data given by singleton input–output pairs for fuzzy rule optimization. In the proposed method, α-GEMII and α-GEMINAS are performed with singleton input–output rules and facts defined by fuzzy sets (non-singletons). The rules are initially set by directly using the input–output pairs of the learning data. They are arranged with the facts and consequences deduced by α-GEMII and α-GEMINAS. This process reduces noise to some extent and transforms the randomly sampled data into regularly sampled data for iteratively reducing noise at a later stage. The width of the regular sampling interval can be determined with tolerance so as to satisfy application-specific requirements. Then, the singleton input–output rules are updated with consequences obtained in iteratively performing α-GEMINAS for noise reduction. The noise reduction in each iteration is a deterministic process, and thus the proposed method is expected to improve the noise robustness in fuzzy rule optimization, relying less on trial-and-error-based progress. Simulation results demonstrate that noise is properly reduced in each iteration and the deviation in the learning data is suppressed considerably.

scholarly journals On-The-Fly Syntheziser Programming with Fuzzy Rule Learning

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 969
Author(s):  
Iván Paz ◽  
Àngela Nebot ◽  
Francisco Mugica ◽  
Enrique Romero
Keyword(s):  
Real Time ◽  
Cross Validation ◽  
State Of The Art ◽  
Rule Learning ◽  
Fuzzy Rule ◽  
Feature Space ◽  
Maximum Volume ◽  
Time Variations ◽  
Fuzzy Rule Learning ◽  
Inductive Rule Learning

This manuscript explores fuzzy rule learning for sound synthesizer programming within the performative practice known as live coding. In this practice, sound synthesis algorithms are programmed in real time by means of source code. To facilitate this, one possibility is to automatically create variations out of a few synthesizer presets. However, the need for real-time feedback makes existent synthesizer programmers unfeasible to use. In addition, sometimes presets are created mid-performance and as such no benchmarks exist. Inductive rule learning has shown to be effective for creating real-time variations in such a scenario. However, logical IF-THEN rules do not cover the whole feature space. Here, we present an algorithm that extends IF-THEN rules to hyperrectangles, which are used as the cores of membership functions to create a map of the input space. To generalize the rules, the contradictions are solved by a maximum volume heuristics. The user controls the novelty-consistency balance with respect to the input data using the algorithm parameters. The algorithm was evaluated in live performances and by cross-validation using extrinsic-benchmarks and a dataset collected during user tests. The model’s accuracy achieves state-of-the-art results. This, together with the positive criticism received from live coders that tested our methodology, suggests that this is a promising approach.

Sign in / Sign up

Export Citation Format

Share Document