Toward Self-Adaptive Adjacency Graph Similarity Deep Domain Transfer

Deep networks require large, well-labeled data for effective training, but acquiring such data can be prohibitively costly or impractical. Domain adaptation (DA) addresses this challenge by transferring knowledge from a labeled source domain to an unlabeled target domain. While most existing DA methods focus on minimizing global distribution discrepancies across domains, they often neglect data local geometric structure, which is critical for transferable feature representation. In this work, we propose a novel self-adaptive adjacency graph (SAAG) algorithm that leverages point-to-feature space projection (P2SP) through recursive learning to compute adaptive neighborhood weights. By selecting neighbors that minimize the point-to-feature space (P2S) distance via a traversal-based approach, our method effectively captures local geometric relationships. Building on it, we introduce geometry-aware mean discrepancy (GAMD), a new graph similarity metric that models cross-domain distribution divergence while embedding intrinsic data geometry. GAMD offers three key benefits for DA: 1) it captures inherent local geometric structures of data; 2) embeds them in a reproducing kernel Hilbert space (RKHS) to explore shared cross-domain representations; and 3) enables domain-invariant feature learning through a geometry-aware metric. Experimental results on four cross-domain benchmarks demonstrate that our approach outperforms some existing methods, validating its effectiveness in leveraging local geometry for improved unsupervised DA.