Unsupervised Image Classification - Expectation-Maximization

[doomdiglet]

Around 4:12, where you showed the 3 equations in the M-step, can you please explain further on how to calculate the covariance matrix? Am I correct that it involves dot product of 3 matrices and the result is a square covariance matrix?

[tkorting]

@doomdiglet Explaining the terms:

Numerator, P(Cj|xk) is the probability of the element xk to belong to class Cj (one value)

Numerator, (xk-uj(t)), xk is the input vector (X has N vectors), and uj(t) is the mean of the matrix for class 'j'

Numerator, (xk-uj(t))T is the same, but transposed, which will result in a square matrix

Denominator, the sum of all probabilities for class 'j'

The result will be a matrix of covariance for class 'j'

[doomdiglet]

@tkorting Thank you for your helpful reply. I misunderstood P(Cj|xk) to be a matrix representing each pixel.

Again, thank you for posting this video. It really helps me understand how to implement EM algorithm for image classification. =D

[TheRightOfReplyDZ]

Good job , thank you but can you told me where is the difference between GMM and EM ? i dont see it .

thank you again

[tkorting]

@TheRightOfReplyDZ EM is just a technique to estimate the probabilities of a dataset, assuming it behaves as a Gaussian Mixture Model, then to apply it to data.

[TheRightOfReplyDZ]

@tkorting

thank you for your reply

so , we assume that the dataset follow a GMM, and we try to apply EM to estimate its probability !

and i have an other question , you say " there is not a training stage " , what about GMM !

i think that " the training step in GMM " is when we apply EM !!! but is the same in "test step"  ! no !

have you an other video explain this method ( GMM ) !

[tkorting]

@TheRightOfReplyDZ

as EM is a unsupervised algorithm, we use to say there is no training stage, but a step that estimates the GMM's present in the data.

after this, we can classify each point in the dataset as one of the estimated GMM's.

No, unfortunately I have no other video about GMM.

Best regards,

Thales

[modelmark]

I do not understand what the attributes are (pixel color/brightness ?). You have 3 graphs under the 2 pictures (red green and blue) What is on the axis of these graphs?

[tkorting]

Yes, the attributes are pixel intensity for each band, R,G and B. The axis mean intensity for R and G, in the first graph, R and B for the second and G and B for the third.

e.g. if a pure red pixel is present in the image, its RGB vector will be (255, 0, 0) right? So it is going to mean a point in the graph R/G in the position (255, 0) and in the graph B/R in the position (0, 255).

More information in the paper "Expectation-Maximization x Self-Organizing Maps for Image classification"

[jenpai]

can this be applied in classifying land use on satellite images?

[tkorting]

Yes, check the paper called "Expectation-Maximization x Self-Organizing Maps for Image classification" where I show EM for satellite imagery.

Regards.