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Feature learning in the presence of a mixed type of variables, numerical andcategorical types, is an important issue for related modeling problems. Forsimple neighborhood queries under mixed data space, standard practice is toconsider numerical and categorical variables separately and combining thembased on some suitable distance functions. Alternatives, such as Kernellearning or Principal Component do not explicitly consider the inter-dependencestructure among the mixed type of variables. In this work, we propose a novelstrategy to explicitly model the probabilistic dependence structure among themixed type of variables by an undirected graph. Spectral decomposition of thegraph Laplacian provides the desired feature transformation. The Eigen spectrumof the transformed feature space shows increased separability and moreprominent clusterability among the observations. The main novelty of our paperlies in capturing interactions of the mixed feature type in an unsupervisedframework using a graphical model. We numerically validate the implications ofthe feature learning strategy

Graph Spectral Feature Learning for Mixed Data of Categorical and Numerical Type