Is L2Norm better than cosine similarity?

[syeds-git]

I used similar approach in my flutter app but did not get satisfactory results using L2Norm. I then switched to cosine and started to get reasonable results. For L2Norm I am getting results which are somehow more than 1 usually between 10 & 20 and can't be used to identify the face. However using cosine the results are much more clearer. What sort of number you expect to get out of L2Norm? should they be between 0 & 1?

[shubham0204]

We can understand the difference from here. L2 Norm or the Euclidean Norm is a function which takes in a vector and returns a non-negative real number. In our case, we are calculating the Euclidean norm of the vector user_embedding - subject_embedding. The magnitude of this vector actually gives us the euclidean distance between the vectors user_embedding and subject_embedding in hyperspace. Calculating the L2 norm of the user_embedding - subject_embedding is nothing but calculating the euclidean distance between these two vectors in hyperspace.
Now, cosine similarity returns the cosine of the angle between these vectors, The range of cosine function is [ -1 , 1 ], so the cosine similarity also holds this range. A score of 1 would mean that both the vectors are parallel ( as cos( 0 ) = 1 ) whereas a score of -1 would mean the vectors are anti-parallel ( as cos( 180 ) = -1 ).
Two vectors might be far away from our subject_embedding but may have the same angle with subject_embedding. Thus cosine similarity would provide the same score for both these vectors.
As of my research, L2 norm should perform better than cosine similarity but we can keep both of them in the project.