Question about shift trick

Thanks for your work! I find the shifting skill simple and interesting, however, it seems that the implementation in the code is different from what is in the paper.

Paper

Code

GraphLearning/graphlearning/graphlearning.py

Lines 2335 to 2344 in a137e30

    
           def mean_shifted_laplace_learning(W,I,g,norm='none'): 
        
               #Laplace learning 
        
               u = laplace_learning(W,I,g,norm=norm) 
        
               #Mean shift 
        
               c = np.mean(u,axis=1) 
        
               u = u -  c[:,np.newaxis] 
        
               return u

You subtract mean of output u, which is

I have tried subtracting the y_w described in the paper but can't get satisfying results ( accuracy below 15% for 1 labeled sample per class). Could you help explain the difference?

Also, could you provide some thought on the stopping condition ' v --> vinf '? I have no idea where it comes from. It seems that it's not mentioned in the paper.

GraphLearning/graphlearning/graphlearning.py

Line 2562 in a137e30

while (T < min_iter or np.max(np.absolute(v-vinf)) > 1/n) and (T < 1000):

Regarding the shift trick, we had an error in our code that always shifted by the mean value after shifting by y_w. We will correct this in the next journal version of the paper. Indeed, you need to shift by the mean and not y_w. The difference is possibly quite small, since y_w should be close to the mean of u, but the scoring function u is so flat that even a small difference can be significant. The arguments later in the paper connecting to Poisson learning are equally valid in both cases.

Regarding your second question, the stopping condition v -> vinf is the mixing time stopping condition described in our paper on the right side of page 6 near the bottom. It runs the Poisson learning iterations until the random walks have sufficiently mixed.

Yeah you are right about "a small difference can be significant". For example in one trial in MNIST with 10 labeled points:

y_w=[0.12175954 0.08535535 0.09380349 0.09859625 0.09878728 0.08385491 0.11197693 0.08958659 0.11030213 0.10597753]
mean=[0.17887512 0.05756588 0.0893375 0.09388537 0.08571841 0.05030871 0.11645314 0.07309792 0.13852043 0.1162375]

but

u - y_w       acc=10.23% 
u - mean      acc=78.78%

And for the stopping condition, I missed that part earlier. Thanks for pointing out.

	def mean_shifted_laplace_learning(W,I,g,norm='none'):

	#Laplace learning
	u = laplace_learning(W,I,g,norm=norm)

	#Mean shift
	c = np.mean(u,axis=1)
	u = u - c[:,np.newaxis]

	return u