I am currently studying propagation of labels in graphs using semi-supervised learning algorithm LGC (Local Global Consistency). The graph is generated from a dataset downloaded from the UCI, e.g., Iris, where each row is a vertex. I use two algorithms for generating the network, one of them is the KNN it receives as a parameter the number of neighbors and the value of sigma, the other algorithm used is the E-Cut it receives as parameters a real epsilon and the value of sigma . What I want to implement is the only formula contained in the file I sent you in section 4.2. That average distance will be used as a parameter for network generation methods, the value of sigma is what is used in the RBF kernel, and item formula is used to estimate its value. To perform the calculation of the distances I use a function that calculates the distance between two vertices of the graph (or two vectors dataset).
Kernel RBF = exp (-FunctionDistance (xi, xj) / 2 * (sigma) ^ 2)
Estimation of the value of sigma = 1/3 * N * Sum (FunctionDistance (xi, xik)) which is precisely the formula I need to implement function using the neighborhood (), since the need to know the distance to each vertex xi neighbors K closer.
Thanks