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Outliers Rejection Based On Repeated Medians. Author’s Name : Hanzi Wang Supervisor : David Suter Associate supervisor : Ray mond Jarvis. Introduction.

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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