A Complete Deep Support Vector Data Description for One Class Learning

Abstract

In recent years, Deep Support Vector Data Description (Deep SVDD) has emerged as a leading method in the field of anomaly detection. However, inaccuracies in parameter solving have been identified as a limitation of this approach, which negatively affects its accuracy and efficiency. To address this issue, we propose a new method, called Complete Deep Support Vector Data Description (CD-SVDD). Our CD-SVDD is constructed with a traditional deep neural network and utilizes a modified SVDD as its last layer. Its parameters are solved by an alternate iteration algorithm that ensures both high precision and fast convergence of solutions. By keeping the network weights fixed, we solve the center and radius of the modified SVDD based on its convex dual optimization problem. With the exact center and radius, we then update the parameters of the neural network by backpropagation. Compared to the existing deep SVDD, all parameters of our method are precisely solved. So, our method is defined to be “complete”. This approach enables us to maintain the $\nu $ -property found in shallow SVDD, which is beneficial for parameter selection and model interpretability. To evaluate the performance of CD-SVDD, we conducted extensive numerical experiments with five existing methods on two image datasets, CIFAR-10 and CIFAR-100, as well as five recorded benchmark datasets. Our results demonstrate that CD-SVDD achieves superior accuracy and efficiency in the detection of anomalies.

Keywords

• Anomaly detection
• deep learning
• support vector data description
• strong duality