Why pdf value of gaussian Mixture Model (GMM) is greater than 1?

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Eman Elkhateeb
Eman Elkhateeb 2018-5-1
回答： Jeff Miller 2018-6-21
I use GMM to built two prior models for sea_samples and land_samples. what is the probability of the data point (xi) belongs to sea_samples? i utilize pdf method but, the value is greater than 1
example:
GMM_sea=fitgmdist(RGB_sea_samples,2);
GMM_land=fitgmdist(RGB_land_samples,5);
pdf(GMM_sea,RGB_sea_samples);
pdf(GMM_land,RGB_land_samples);

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回答（2 个）

Walter Roberson
Walter Roberson 2018-5-1
Remember that pdf is probability density, not probability. It is the integral of the pdf over the range that must be one, which means that the pdf can be up to 1/(width of interval)
  2 个评论
Eman Elkhateeb
Eman Elkhateeb 2018-6-20
what can I do when computing the likelihood that the pixel i belongs to class sea or land
Walter Roberson
Walter Roberson 2018-6-20
Unfortunately I have not used GMM, so I do not know how you would compute that.

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Jeff Miller
Jeff Miller 2018-6-21
As I understand the question, the answer only depends on the pdf's, not on where they came from (here, GMM).
GMM_sea=fitgmdist(RGB_sea_samples,2);
GMM_land=fitgmdist(RGB_land_samples,5);
pdf_sea = pdf(GMM_sea,RGB_sea_samples);
pdf_land = pdf(GMM_land,RGB_land_samples);
Pr_sea = pdf_sea*prior_sea / (pdf_sea*prior_sea + pdf_land*prior_land);
Pr_land = 1 - Pr_sea;
I think that Pr_sea and Pr_land are the probabilities you are after. prior_sea and prior_land are the overall proportions of sea and land creatures of whatever type you are studying.

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