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Auto-tools/Projects/OrangeFactor/Statistics: Difference between revisions
Auto-tools/Projects/OrangeFactor/Statistics (view source)
Revision as of 21:08, 2 November 2010
, 2 November 2010→Smoothing: explain random data
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It can be seen that unweighted (w=1) smoothing converged rapidly even with three iterations. With ten smoothing passes, the results are mostly the same, though the weighted (w=0.25) smoothing has better results along the edges. The endpoints are hard to get accurate with this type of filter as you only have information coming from one direction. Note that the results towards the endpoints are worse for ten passes at w=1 than at three passes. The results are over-smooth and would get even worse with more passes, eventually trending to a constant. This illustrates that the choice of number of passes and weight appropriate to given data is a function of the data. This may be automatically controlled if desired. | It can be seen that unweighted (w=1) smoothing converged rapidly even with three iterations. With ten smoothing passes, the results are mostly the same, though the weighted (w=0.25) smoothing has better results along the edges. The endpoints are hard to get accurate with this type of filter as you only have information coming from one direction. Note that the results towards the endpoints are worse for ten passes at w=1 than at three passes. The results are over-smooth and would get even worse with more passes, eventually trending to a constant. This illustrates that the choice of number of passes and weight appropriate to given data is a function of the data. This may be automatically controlled if desired. | ||
To give an example more illustrative of real noise, we take the same basis curve (linear rise from 3-13) and for each point add a random value from -6 to 6 to it. A high amount of noise was chosen both to be illustrative and because oranges are also very noisy. Note the small number of data points (11) hurts us in identifying the trend but is good for illustration. | |||
[[File:Random-three.png]] | [[File:Random-three.png]] | ||