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I have sparse overdefined system of linear equations.

For example I have n variables, m equations(m>n) and k equations from m are "bad" equations that represent outliers.

Is there any methods to solve this problem?

I already found techniques such as iterative reweighred least squares,LMeds,M-estimator but I'm not sure which is my case?

Here is my task in detail:

I want to solve computer vision problem which seems to be called "panorama global registration" like described here (they use weighted least squares).

Main problem is that when I calculate pairwise relations between images (which is then become equations in my system) even if I prune weak connections by threshold I have some bogus connections, so I need robust algorithm that can handle outliers.

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    $\begingroup$ Here's a start: stats.stackexchange.com/search?tab=relevance&q=irls. $\endgroup$
    – whuber
    Jun 5 '13 at 12:32
  • $\begingroup$ I already found techniques such as iterative reweighred least squares,LMeds,M-estimator but i'm not sure which is my case? $\endgroup$
    – mrgloom
    Jun 5 '13 at 12:41
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    $\begingroup$ To get that answered, you will need to describe your data and your data analysis objectives. $\endgroup$
    – whuber
    Jun 5 '13 at 12:42
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    $\begingroup$ Ok, I update question and add some details. $\endgroup$
    – mrgloom
    Jun 5 '13 at 13:16
  • $\begingroup$ If it's robust to outliers, it isn't actually least squares. You'd really need to identify what kinds of compromises or optimality you seek. $\endgroup$
    – Glen_b
    Oct 4 '13 at 4:18
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Your equations relate inputs to outputs. Machine learning methods (universal function approximators) do the same and in fact have been used to solve systems of equations.

I have seen random forests do the tasks that your words describe. They can be used to rank the value of the inputs in describing the outputs in an ensemble sense. You can then use your judgement to discard some of the less informative values and continue.

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