A cluster based approach to robust regression and outlier detection

We consider the simultaneous estimation of the inlier set and the regression parameter using the contaminated data set, A, which has many members obey the linear model, but some do not. The single link clustering algorithm is used to partition the data set into inlier and outlier subsets. The subset having the least mean sum of squares of residuals is chosen to be the best subset among all subsets of A for a fixed link distance, λ. By assuming that the outliers also obey the same type of density as the inliers but different parameters, we develop a negative log likelihood expression for all the observations in terms of λ. By minimizing the negative log likelihood function with respect to λ we get the required λ* and the regression parameters. We apply the theory developed here to two data sets, and show our method correctly estimates the regression parameters and the inlier set for the given data set