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Some functions are identical between systems, for example nearest neighbour analysis. It would be unusual to have nearest neighbour implemented differently as appears in academic papers.

Is it the same with maximum likelihood (supervised classification)? How likely is it that the same input imagery raster and same training polygons result a different classified image in ERDAS, ENVI, ArcGIS and IDRISI?

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  • $\begingroup$ Cross-posted as gis.stackexchange.com/q/222491/115 $\endgroup$
    – PolyGeo
    Dec 30, 2016 at 23:21
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    $\begingroup$ @PolyGeo yep where it's been open for a while with no useful answers then closed as too broad, where as here answered in less than an hour! $\endgroup$
    – Rudolf O
    Dec 30, 2016 at 23:23
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    $\begingroup$ Rudolf, the GIS site focuses more on details of particular software programs and GIS platforms. Some members of its community are experts in image processing and statistics, but it's a tiny group. Here on CV we focus on concepts and methods while trying to be software agnostic (but we will often supply working software examples). I am very pleased you got a quick answer here, especially such a good one by @Gregor. $\endgroup$
    – whuber ♦
    Dec 30, 2016 at 23:30
  • $\begingroup$ Questions are not equally suited to all sites. Rather than cross-post (which is against SE protocols), if the first site does not answer your question, and you become aware of another that might, then delete it from the first and ask it on the second. I'm glad you got an answer to your question even though in its current form I think it was unsuited for the Geographic Information Systems Stack Exchange. $\endgroup$
    – PolyGeo
    Dec 30, 2016 at 23:54

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You should not expect the same results using different software. "Maximum likelihood" is a general term for a common way of estimating parameters for a statistical model: attempt to find the values of the parameters that maximize the likelihood function for the model.

Different software packages may run different models for classification, and may also parameterize them differently. This means they are likely starting with different likelihood functions and will have different results.

Furthermore, in most cases, there is not a closed-form solution to the likelihood maximization, so the problem is a numerical optimization problem. Different algorithms will find different solutions (though hopefully they will be quite close to each other - this will be true if the likelihood function is "well-behaved" which is not always the case). For example, even starting with the same model, one piece of software may use L-BFGS and another Nelder-Mead.

There could be other differences as well, maybe some of the algorithms use bootstrapping for robustness, or cross-validation to improve predictive accuracy. And for classification, your software may be automatically choosing an operating point. All of these, if implemented, are probably implemented differently in different software packages.

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    $\begingroup$ There are situations where a particular likelihood function may not have a unique solution. In other cases depending on the parameter space the likelihood function could have no solution because it increases with no bound. $\endgroup$
    – Michael R. Chernick
    Dec 30, 2016 at 23:21

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