This paper introduces a new algorithm, namely the Equi-Correlation Network (ECON), to perform supervised classification, and regression. ECON is a kernelized LARS-like algorithm, by which we mean that ECON uses an $l_1$ regularization to produce sparse estimators, ECON efficiently rides the regularization path to obtain the estimator associated to any regularization constant values, and ECON represents the data by way of features induced by a feature function. The originality of ECON is that it automatically tunes the parameters of the features while riding the regularization path. So, ECON has the unique ability to produce optimally tuned features for each value of the constant of regularization. We illustrate the remarkable experimental performance of ECON on standard benchmark datasets; we also present a novel application of machine learning in the field of computer graphics, namely the approximation of photometric solids.