I am developing my own Architecture Search algorithm using Pythons numpy. Currently I am trying to determine how to develop a cost function that can see the distance between X and Y, or two matrices. I'd like to reduce the difference between the two, to a meaningful scalar value.
Ideally between 0 and 1, so that if both sets of elements within the matrices are the same numerically and positionally, a 0 is returned.
In the example below, I have the output of my algorithm X. Both X and Y are the same shape. I tried to sum the difference between the two matrices; however I'm not sure that using summation will work in all conditions. I also tried returning the mean. I don't think that either approach will work though. Aside from looping through both matrices and comparing elements directly, is there a way to capture the degree of difference in a scalar?
Y = np.arange(25).reshape(5, 5)
for i in range(1000):
X = algorithm(Y)
# I try to reduce the difference between the two matrices to a scalar value
cost = np.sum(X-Y)
There are many ways to calculate a scalar "difference" between two matrices. Here are just two examples.
The mean square error:
((m1 - m2) ** 2).mean() ** 0.5
The max absolute error:
np.abs(m1 - m2).max()
The choice of the metric depends on your problem.
I know this is kind of late...but is that first example considered the L2 norm?
Yes, it is the L2 norm.