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

It is important to properly tune the kernel scale/bandwidth σb, which determines its scale of connectivity. Several studies have proposed schemes for tuning σb, see for example [10, 3, 12, 5]. Here, we focus on two schemes, a global bandwidth and a local bandwidth. The local bandwidth proposed in [12], involves setting a local-scale σi for each data point xi,i= 1,...,n. The scale is chosen using the L1 distance from the k-th nearest neighbor of the point xi.