Robust cross-modal correlation space learning via manifold topology density normalization

To address the issue that canonical correlation analysis is sensitive to outliers and has difficulty capturing nonlinear patterns in different density regions under the condition of high-dimensional and small sample sizes, this paper proposes the robust cross-modal correlation space learning via manifold topological density normalization. This method constructs an ordered metric for relative neighborhoods in the Euclidean space, effectively identifying outliers with asymmetric neighbor relationships in low-density regions. Based on the relative neighborhood order, combined with the Euclidean space, the shared nearest neighbor topological structure, and the local density distribution, multi-modal robust similarity matrix is constructed. It adapts to different density regions, reduces the influence of noise and outliers, better reveals the intrinsic geometry of the manifold, satisfies the regularization characteristics of the manifold, and converges to the real manifold structure. By adopting the divide-and-conquer strategy, the objective function of manifold topological density normalization correlation space learning is derived. The objective function is theoretically optimized and solved to obtain the space projection matrix. In the subspace, the neighbor relationship of the original space is still maintained. The experiments on the Paderborn dataset demonstrate the robustness and effectiveness of this method.