Electrical and Computer Systems Engineering Postgraduate Student Research Forum 2001

1. Outliers Rejection Based On Repeated Medians Author’s Name: Hanzi Wang Supervisor: David Suter Associate supervisor: Raymond Jarvis Introduction Regression analysis has been used as an important tool for computer vision. But many regression techniques adopted ordinary least squares(OLS) method, which has a low breakdown point and is very vulnerable to the distortion by outliers. The aim of this research is to provide a new estimator, we called it as ORRM, which can resist large numbers of outliers and has higher breakdown points and convergence speed. Fig. 2 Bad initial fit by ORS with outliers Fig. 3 The result by RRD with clustered outliers Types of Data There are three types of data existing in the observed data: A. Inliers, i..e. good observations. B.Leverage points which can potentially affect the results. - Good leverage points - Bad leverage points C. Outliers that are far away from the majority of data. They are showed as below: Fig. 4 The points excluded by RRD Fig. 5 The points remained by RRD Outliers rejection based on repeated medians This algorithm is based on repeated medians (RM) method. ♬Advantages of RM method:  High breakdown point ( 50%) which is perhaps the highest  It can resist large numbers of outliers ORRM procedures:  Using RM to produce an initial fit  Check the residual of each point, when it is greater than gate value G, remove the point.  Reduce the gate value G by a certain percentage, and when it is smaller than specified value, stop and get the final results; otherwise continuing Fig. 1 Three Types of Data Previous Method and Their Limits • Ordinary regression diagnostics (ORS) • An initial fit is acquiredby OLS • Computing the residual of each datum, if no data exceed the • threshold, then stop. • Deleting the pointswith large residuals • Acquiring a new fit by the remaining data • Disadvantages: Sensitive to outliers If the initial fit is bad, it will fail to reject badobservations. 2. A refinement of regression diagnostics (RRD) Computing the initial fit θ by OLD Omitting a datum i from the data and computing the new fit θii by OLD. Finding the change in the new fit ∆ θi = θ- θii Finding the datum i for which ∆ θi is the biggest, if ∆ θi is smaller than a predetermined value, then stop; Otherwise, deleting datum i and continuing. ♬Advantages: It has a better breakdown point. It work well in some uniformly distributed outliers • Disadvantage: Very sensitive to clustered outliers. Convergence speed is low. Experimental Results Fig.6 Results by OLS, RM and ORRM Fig. 7 Results of ORRM Conclusion ♬This estimator has followed advantages: High breakdown value Robust to both clustered and uniformly distributed outliers  Higher convergence speed It is nonbiased Further Work Optimize the computational efficiency and improve calculation speed.  Extend the application to multivariate parameters estimate. Electrical and Computer Systems Engineering Postgraduate Student Research Forum 2001