New here! I'm working in some crypto for a Ph.D. and I'm trying to figure out the best metrics to measure the different/error between a input vector of integers with the output that ideally is the same as the input. The key point is that the elements of the vector has no relation between them! For now I'm using norm2 and Hamming distance, but with no why...
Some ideas?
Given that the elements have no relation between them, it's important to consider metrics that are appropriate for comparing independent values, such as the ones you've mentioned (norm2 and Hamming distance).
Norm2 for Independent Vector Elements
The norm2, or the Euclidean norm, is a suitable choice for measuring the overall difference between vectors with independent elements. It calculates the magnitude of the vector, considering each element independently, and can provide a meaningful measure of the overall difference in magnitude between the input and output vectors.
Hamming Distance for Independent Vector Elements
The Hamming distance, although traditionally used for binary or categorical data, can also be applicable in the context of independent vector elements. It counts the number of positions at which the corresponding elements are different, regardless of any relationship between the elements. This can be useful for capturing the element-wise discrepancies between the input and output vectors without assuming any particular relationship between the elements.
Considerations for Other Metrics
In addition to norm2 and Hamming distance, other metrics such as the Manhattan distance (L1 norm) and the Minkowski distance could also be considered. These metrics take into account the absolute differences between the individual elements of the vectors, making them suitable for comparing independent values.
