최소 절대 편차 근사를 이용한 퍼지 변환 = Fuzzy transform based on least absolute deviation approximation

다국어 초록 (Multilingual Abstract)

Least-squares fuzzy transform, which applied a least-squares estimation method that minimizes the error between original data and reconstructed data to fuzzy transform, has been proposed, but has the disadvantage of being very sensitive to outlier. To overcome it, the paper proposes Least Absolute Deviation Fuzzy Transform fuzzy transform algorithm, applied Least Absolute Deviation Approximation method that is robust to outlier to Fuzzy transform. Iterative Reweighted Least Squares method is used to implement Least Absolute Deviation Fuzzy Transform fuzzy transform algorithm. Experiments show that Least Absolute Deviation Fuzzy Transform fuzzy transform outperforms than other fuzzy transform method in terms of reconstruction and is robust to outlier.

국문 초록 (Abstract)

본 논문은 데이터 압축과 복원을 위한 퍼지 변환 기법과 최소 절대 편차 방법을 새롭게 결합한 최소 절대 편차 퍼지 변환을 위한 새로운 알고리즘을 제안한다. 기존 퍼지 변환에 원본데이터와 재구성된 데이터의 오차를 최소화하는 최소 제곱 추정방법을 적용한 최소 제곱 퍼지 변환기법이 제시되었다. 그러나 최소 제곱 퍼지 변환은 데이터 복원에는 효과적이지만이상치에 매우 민감하다는 단점이 있다. 따라서 본 논문은 이상치에 강건한 최소 절대 편차방법을 적용한 최소 절대 편차 퍼지 변환 알고리즘을 제안한다. 이를 위해 반복 가중치 최소제곱을 사용했으며, 실험의 결과를 통해 최소 절대 편차 퍼지 변환이 데이터 복원 성능이 높고, 이상치에 강건하다는 것을 확인했다.

참고문헌 (Reference)

1 MJ Ebadi, "Video Data Compression by Progressive Iterative Approximation" 6 (6): 2021

2 Zhang, Yu, "MI3:Machine-initiated Intelligent Interaction for Interactive Classification and Data Reconstruction" 11 (11): 1-34, 2021

3 S. Tomasiello, "Least-Squares Fuzzy Transforms and Autoencoders: Some Remarks and Application" 29 : 129-136, 2020

4 I. Perfilieva, "Fuzzy transforms: theory and applications" 157 : 993-1023, 2006

5 G. PatanN, "Fuzzy transform and least-squares approximation:analogies, differences, and generalizations" 180 (180): 41-54, 2011

6 Seok-Beom Roh, "Design of face recognition system based on fuzzy transform and radial basis function neural networks" 23 (23): 4969-4985, 2019

7 V NovNk, "Analysis of seasonal time series using fuzzy approach" 39 (39): 305-328, 2010

8 Schlossmacher, E. J., "An iterative technique for absolute deviations curve fitting" 68 (68): 857-859, 1973

9 Barrodale, Ian, "An improved algorithm for discrete l_1 linear approximation" 10 (10): 839-848, 1973

10 Woo-Joo Lee, "A novel forecasting method based on F-transform and fuzzy time series" 19 (19): 1793-1802, 2017

11 Chandra, S., "A comparative analysis of performance of several wavelet based ECG data compression methodologies" 42 (42): 227-244, 2021

12 Di Martino, "A color image reduction based on fuzzy transforms" 266 : 101-111, 2014