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CNN Week 4 (Neural style transfer (Find the generated image G (Initiate G…

- - - - Learning a "similarity" function
        d(img1, img2) = degree of difference between images
        if d(img1,img2) <= tau then "same persons"
        else "different persons"
      - d function can be learned by Siamese network
        input: x
        cnn, cnn, cnn, fc, fc (?)
        which output a vector f(x) of 128 elements
        you feed images x1 and x2 into it and get f(x1) and f(x2)
        then d(x1, x2) = (|| f(x1) - f(x2) ||) ^ 2 (not sure about square)
        (norm of difference of f1, f2)
        learn params so that
        if x1, x2 are same person, then d is small
        if x1, x2 are different, then d is large
      - Learning objective
        
        We can use the Triplet loss
        
        A img - anchor - original image of person 1
        P img - positive - different image of same person 1
        N img - negative - image of person 2
        
        what we want:
        || f(a) - f(p) || ^ 2 to be <= || f(a) - f(n) || ^ 2
        d(a, p) <= d(a, n)
        in other words
        (|| f(a) - f(p) || ^ 2) - (|| f(a) - f(n) || ^ 2) <= 0
        but to make sure NN don't just use 0 everywhere or make encodings of images to be identical for every face,
        we use 0 - alpha (margin parameter) in the right part of equation
        or
        (|| f(a) - f(p) || ^ 2) - (|| f(a) - f(n) || ^ 2) + alpha <= 0
        
        Triplet loss function
        Given A, P, N
        single set
        loss(a,p,n) = max( (|| f(a) - f(p) || ^ 2) - (|| f(a) - f(n) || ^ 2) + alpha, 0 )
        for all:
        J = sum of loss over all training examples
        
        How to choose triplets?
        If randomly, then constraint d(A, P) + alpha <= d(A, N) is easy to satisfy. As totally different people will likely have very different d
        Better select d(A, P) which is close to d(a, n)
      - Face verification and binary classification