A least square approach for the detection and removal of outliers for fuzzy linear regressions

Mashinchi, M.; Orgun, Mehmet A.

doi:10.1109/nabic.2010.5716374

Cited by 6 publications

(2 citation statements)

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“…The proposal introduced by Nasrabadi et al [54] discusses ways to apply linear programming and fuzzy least squares to the outlier detection in fuzzy regression analysis. The importance of outlier detection was also raised by Mashinchi et al [48], where the authors developed two stage LS approach with no user defined variables. The first stage detects outliers, while the second stage uses the purged sample to fit a regression model with the model fitting measure minimized with a hybrid optimization technique.…”

Section: Linear Regression Analysis Problem Over Fuzzy Datamentioning

confidence: 99%

Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

Nikolova

Rodríguez

Symes

et al. 2021

Int. J. Fuzzy Syst.

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In the classical leave-one-out procedure for outlier detection in regression analysis, we exclude an observation, then construct a model on the remaining data. If the difference between predicted and observed value is high we declare this value an outlier. As a rule, those procedures utilize single comparison testing. The problem becomes much harder when the observations can be associated with a given degree of membership to an underlying population and the outlier detection should be generalized to operate over fuzzy data. We present a new approach for outlier that operates over fuzzy data using two inter-related algorithms. Due to the way outliers enter the observation sample, they may be of various order of magnitude. To account for this, we divided the outlier detection procedure into cycles. Furthermore, each cycle consists of two phases. In Phase 1 we apply a leave-one-out procedure for each nonoutlier in the data set. In Phase 2, all previously declared outliers are subjected to Benjamini-Hochberg step-up multiple testing procedure controlling the false discovery rate, and the non-confirmed outliers can return to the data set. Finally, we construct a regression model over the resulting set of non-outliers. In that way we ensure that a reliable and high-quality regression model is obtained in Phase 1 because the leaveone-out procedure comparatively easily purges the dubious observations due to the single comparison testing. In the same time, the confirmation of the outlier status in relation to the newly obtained high-quality regression model is much harder due to the multiple testing procedure applied hence only the true outliers remain outside the data sample. The two phases in each cycle are a good trade-off between the desire to construct a high-quality model (i.e. over informative data points) and the desire to use as much data points as possible (thus leaving as much observations as possible in the data sample). The number of cycles is user-defined, but the procedures can finalize the analysis in case a cycle with no new outliers is detected. We offer one illustrative example and two other practical case studies (from real-life thrombosis studies) that demonstrate the application and strengths of our algorithms. In the concluding section, we discuss several limitations of our approach and also offer directions for future research. Keywords: regression analysis, leave-one-out method, degree of membership, multiple testing, Benjamini-Hochberg step-up multiple testing, false-discovery rate Highlights: -We develop algorithms for outlier rejection over fuzzy samples using weighted least squares that operate in a given number of cycles -Each cycle has two phases -use single testing leave-one-out procedure for initial purging of data, then confirm the previous outlier status with multiple testing -We offer one illustrative example and two examples from a case study in thrombosis research to show the strength of our cycle-based approach

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Section: Linear Regression Analysis Problem Over Fuzzy Datamentioning

confidence: 99%

Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

Nikolova

Rodríguez

Symes

et al. 2021

Int. J. Fuzzy Syst.

View full text Add to dashboard Cite

show abstract

“…In the second stage of proposed GBRs, we obtain the clean data set [34] by applying Algorithm 1 to instances confined in each box. To compute the distance of each instance, we measure the average distance of all data to the median point.…”

Section: Second Stage: Elimination Of Outliersmentioning

confidence: 99%