Differentiable Unsupervised Feature Selection based on a Gated Laplacian - Supplementary Materials

It is important to properly tune the kernel scale/bandwidthσb, which determines its scale of connectivity. The scale is chosen using the L1 distance from thek-th nearest neighbor of the pointxi. Explicitly, the calculation for each point is σi =C ||xi xk||2,i=1,...,N, (1) where xk is the k-th nearest(Euclidean)neighbor of the point xi, and C is a predefinedconstant in the range [1,5]. A global scale ˆσb, is defined as the max overσi. The regularization parameterλ controls the amount of sparsity obtained by DUFS.