Newton Method-based Subspace Support Vector Data Description
Fahad Sohrab Firas Laakom Moncef Gabbouj
In this paper, we present an adaptation of Newton's method for the
optimization of Subspace Support Vector Data Description (S-SVDD). The
objective of S-SVDD is to map the original data to a subspace optimized for
one-class classification, and the iterative optimization process of data
mapping and description in S-SVDD relies on gradient descent. However, gradient
descent only utilizes first-order information, which may lead to suboptimal
results. To address this limitation, we leverage Newton's method to enhance
data mapping and data description for an improved optimization of subspace
learning-based one-class classification. By incorporating this auxiliary
information, Newton's method offers a more efficient strategy for subspace
learning in one-class classification as compared to gradient-based
optimization. The paper discusses the limitations of gradient descent and the
advantages of using Newton's method in subspace learning for one-class
classification tasks. We provide both linear and nonlinear formulations of
Newton's method-based optimization for S-SVDD. In our experiments, we explored
both the minimization and maximization strategies of the objective. The results
demonstrate that the proposed optimization strategy outperforms the
gradient-based S-SVDD in most cases.