Deep Support Vector Machines for Regression Problems

In this paper we describe a novel extension of the support vector machine, called the deep support vector machine (DSVM). The original SVM has a single layer with kernel functions and is therefore a shallow model. The DSVM can use an arbitrary number of layers, in which lower-level layers contain support vector machines that learn to extract relevant features from the input patterns or from the extracted features of one layer below. The highest level SVM performs the actual prediction using the highest-level extracted features as inputs. The system is trained by a simple gradient ascent learning rule on a min-max formulation of the optimization problem. A two-layer DSVM is compared to the regular SVM on ten regression datasets and the results show that the DSVM outperforms the SVM.