Natural language processing requires solving several tasks of increasing complexity, which involve learning to associate structures like graphs and sequences to a given text. For instance, dependency parsing involves learning of a tree that describes the dependency-based syntactic structure of a given sentence. A widely used method to improve domain knowledge representation in this task is to consider combinations of features, called templates, which are used to encode useful information with nonlinear pattern. The total number of all possible feature combinations for a given template grows exponentialy in the number of features and can result in computational intractability. Also, from an statistical point of view, it can lead to overfitting. In this scenario, it is required a technique that avoids overfitting and that reduces the feature set. A very common approach to solve this task is based on scoring a parse tree, using a linear function of a defined set of features. It is well known that sparse linear models simultaneously address the feature selection problem and the estimation of a linear model, by combining a small subset of available features. In this case, sparseness helps control overfitting and performs the selection of the most informative features, which reduces the feature set. Due to its exibility, robustness and simplicity, the perceptron algorithm is one of the most popular linear discriminant methods used to learn such complex representations. This algorithm can be modified to produce sparse models and to handle nonlinear features. We propose the incremental learning of the combination of a sparse linear model with an induction procedure of non-linear variables in a structured prediction scenario. The sparse linear model is obtained through a modifications of the perceptron algorithm. The induction method is the Entropy-Guided Feature Generation. The empirical evaluation is performed using the Portuguese Dependency Parsing data set from the CoNLL 2006 Shared Task. The resulting parser attains 92.98 per cent of accuracy, which is a competitive performance when compared against the state-of-art systems. On its regularized version, it accomplishes an accuracy of 92.83 per cent, shows a striking reduction of 96.17 per cent in the number of binary features and reduces the learning time in almost 90 per cent, when compared to its non regularized version.