High-dimensional data sets are often analyzed and explored via the\nconstruction of a latent low-dimensional space which enables convenient\nvisualization and efficient predictive modeling or clustering. For complex data\nstructures, linear dimensionality reduction techniques like PCA may not be\nsufficiently flexible to enable low-dimensional representation. Non-linear\ndimension reduction techniques, like kernel PCA and autoencoders, suffer from\nloss of interpretability since each latent variable is dependent of all input\ndimensions. To address this limitation, we here present path lasso penalized\nautoencoders. This structured regularization enhances interpretability by\npenalizing each path through the encoder from an input to a latent variable,\nthus restricting how many input variables are represented in each latent\ndimension. Our algorithm uses a group lasso penalty and non-negative matrix\nfactorization to construct a sparse, non-linear latent representation. We\ncompare the path lasso regularized autoencoder to PCA, sparse PCA, autoencoders\nand sparse autoencoders on real and simulated data sets. We show that the\nalgorithm exhibits much lower reconstruction errors than sparse PCA and\nparameter-wise lasso regularized autoencoders for low-dimensional\nrepresentations. Moreover, path lasso representations provide a more accurate\nreconstruction match, i.e. preserved relative distance between objects in the\noriginal and reconstructed spaces.\n