An autoencoder-based piecewise linear model for nonlinear classification using quasilinear support vector machines

In this paper, we propose to implement a piecewise linear model to solve nonlinear classification problems. In order to realize a switch between linear models, a data-dependent gating mechanism achieved by an autoencoder is designed to assign gate signals automatically. We ensure that a diversity of gate signals is available so that it is possible for our model to switch between a large number of linear classifiers. Besides, we also introduce a sparsity level to add a manual control on the flexibility of the proposed model by using a winner-take-all strategy. Therefore, our model can maintain a balance between underfitting and overfitting problems. Then, given a learned gating mechanism, the proposed model is shown to be equivalent to a kernel machine by deriving a quasilinear kernel function with the gating mechanism included. Therefore, a quasilinear support vector machine can be applied to solve the nonlinear classification problems. Experimental results demonstrate that our proposed piecewise linear model performs better than or is at least competitive with its state-of-the-art counterparts.