# A Novel Approach to Incremental Diffusion for Continuous Dataset Updates in Image Retrieval
## 8 Conclusions  
This paper presents a novel anchor-based graph diffusion framework to address the critical challenge of incremental data updates in image retrieval systems. Our study establishes three primary contributions: (1) We propose the first incremental diffusion mechanism that decouples the offline pre-computation from online query processing through anchor graph approximation, enabling efficient handling of continuous dataset. (2) Through rigorous theoretical analysis, we demonstrate that local anchor embedding (LAE) with \(k\)-Means clustering provides a convex reconstruction preserving the manifold structure, achieving comparable performance while reducing pre-computation cost compared to conventional diffusion. (3) Extensive experiments on the benchmarks reveal that our method surpasses existing methods in both speed and performance under identical conditions. Having established these theoretical foundations, our experimental validation confirms the original hypothesis that combining anchor graphs (capturing global structure) with LAE (maintaining local geometry) provides an effective solution for incremental diffusion. The benchmark results demonstrate this approach successfully handles continuous data updates without sacrificing retrieval precision (Sections 7.3 and 7.4). The empirical results suggest two key implications for practical applications: First, the linear scalability (\(\mathcal{O}(nks)\)) of LAE reconstruction makes the framework particularly suitable for real-time image retrieval systems requiring continuous data updates. Second, our ablation studies on synthetic data scaling demonstrate stable performance even with up to 25% gallery growth, effectively overcoming the limitation of existing methods in handling newly added data. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Incremental Updates Support**} & \multirow{2}{*}{**Pre-Computation Complexity**} & \multicolumn{3}{c}{**ROxford**} & \multicolumn{3}{c}{**\(\mathcal{R}\)Paris**} \\ \cline{3-8}  & & & **Easy** & **Medium** & **Hard** & **Easy** & **Medium** & **Hard** \\ \hline k-NN [10] & - & - & 83.3 & 67.1 & 42.3 & 89.6 & 79.4 & 59.4 \\ k-NN + AGE [10] & - & - & - & 71.4 & 45.9 & - & 84.0 & 67.3 \\ Online Diffusion [4] & Yes (but high runtime cost) & \(\mathcal{O}(\approx\)\(k\tau)\) & 87.5 & 71.2 & 47.0 & 93.2 & 89.6 & 80.7 \\ Offline Diffusion [5] & No (full recomputation) & \(\mathcal{O}(n\kappa\tau)\) & 89.6 & 73.6 & 50.4 & 94.0 & 91.5 & 83.3 \\ \hline Proposed (100\% Gallery) & Yes (efficient LAE updates) & \(\mathcal{O}(kkr+nks)\) & **92.2** & **77.3** & **53.2** & **94.1** & 91.6 & **83.4** \\ \hline Proposed (95\% Gallery + 5\% Growth) & - & - & 87.7 & 72.9 & 49.2 & 93.9 & **92.1** & 83.3 \\ Proposed (90\% Gallery + 10\% Growth) & - & - & 85.3 & 71.3 & 48.3  
While achieving these advancements, we recognize two limitations: Our model is based on the assumption that the matrix \(\mathbf{Z}\) is approximately a unitary matrix, which holds only when the newly added data can be well approximated by the existing data with low error. Moreover, the LAE parameter \(s\) requires manual tuning for different feature spaces. The primary focus of our work is to address the limitation of diffusion algorithms in handling newly added data. Previous methods have been entirely incapable of managing new data updates. While our proposed method still has certain limitations, it represents a significant breakthrough, as it provides a foundational step toward overcoming this challenge. Future work will explore online anchor updating strategies and automatic parameter optimization using reinforcement learning. These extensions may further enhance the framework's applicability in production environments with streaming data inputs. From a broader perspective, our findings provide methodological guidance for building incremental image retrieval systems.