Convolutional Support Vector Machines For Image Classification

Abstract

The Convolutional Neural Network (CNN) is a machine learning model which excels in tasks that exhibit spatially local correlation of features, for example, image classification. However, as a model, it is susceptible to the issues caused by local minima, largely due to the fully-connected neural network which is typically used in the final layers for classification. This work investi- gates the effect of replacing the fully-connected neural network with a Support Vector Machine (SVM). It names the resulting model the Convolutional Support Vector Machine (CSVM) and proposes two methods for training. The first method uses a linear SVM and it is described in the primal. The second method can be used to learn a SVM with a non-linear kernel by casting the optimisation as a Multiple Kernel Learning problem. Both methods learn the convolutional filter weights in conjunction with the SVM parameters. The linear CSVM (L-CSVM) and kernelised CSVM (K-CSVM) in this work each use a single convolutional filter, however, approaches are described which may be used to extend the K-CSVM with multiple filters per layer and with multiple convolutional layers. The L-CSVM and K-CSVM show promising results on the MNIST and CIFAR-10 benchmark datasets.