You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: neg_sampling_objective.m
    path of file: ./repos/scGEAToolbox/+run/external/mt_UMAP
    
    the code of the file until where you have to start completion: function result = neg_sampling_objective(head_embedding, tail_embedding, head, tail, weights, a, b, negative_sample_rate, same_embedding)
%NEG_SAMPLING_OBJECTIVE Given a low-dimensional embedding and weights of
% 1-simplices of a high-dimensional simplicial complex, compute the
% associated negative sampling objective. This is the quantity that the

    
function result = neg_sampling_objective(head_embedding, tail_embedding, head, tail, weights, a, b, negative_sample_rate, same_embedding)
%NEG_SAMPLING_OBJECTIVE Given a low-dimensional embedding and weights of
% 1-simplices of a high-dimensional simplicial complex, compute the
% associated negative sampling objective. This is the quantity that the
% original Python UMAP implementation is attempting to minimize by using
% the negative sampling technique during stochastic gradient descent (SGD).
% Note that this value is distinct from cross entropy as presented in the
% original UMAP paper.
% This calculation uses the modified smooth formula Phi for
% low-dimensional weight that is used in SGD.
% Because the computation time is O(n^2), we recommend