Kernelized Supervised Laplacian Eigenmap for Visualization and Classification of Multi-Label Data

•We solves the “out-of-sample problem”, inability of handling new data, that previous (supervised) Laplacian eigenmaps have, by a set of linear sums of kernels, and we propose a Kernelized Supervised Laplacian Eigenmap for Multi-Label (KSLE-ML).•We show that nonsingularity of Gram matrix is a sufficient condition for this simulation to be exactly the same as Laplacian eigenmaps.•We reveal that parameter selection is more important than kernel selection in KSLE-ML experimentally, so that RBF kernel solely can be used for the general purpose.•We show a method of separability-guided feature extraction that is based on a high separability of classes in 2D visualization.•We confirm empirically the effectiveness of separability-guided feature extraction by showing that the separability is kept well even for mapping of newly arrived samples without class labels in KSLE-ML. We also demonstrate that the effectiveness increases as the number of samples and the mapping dimension increases.