  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.
