The linearization approach used to compute the novelty probability may have limitations in capturing the complex non-linear relationships present in high-dimensional data. While it provides a simplified view of the manifold structure, it may struggle with capturing intricate patterns that deviate significantly from the linearized representation.
To improve this approach, one potential enhancement could be the incorporation of non-linear transformations or manifold learning techniques that can better capture the underlying structure of the data distribution. Methods like kernel methods, non-linear dimensionality reduction techniques, or neural networks with non-linear activations could be explored to enhance the representation of the manifold. Additionally, incorporating ensemble methods or hierarchical approaches that combine linear and non-linear representations may provide a more robust framework for computing novelty probabilities.