# A Novel Approach to Incremental Diffusion for Continuous Dataset Updates in Image Retrieval
## 7 Experiments
### Parameter Study  
In this section, we study the impact of parameters on retrieval performance. In addition to the existing hyperparameters in the previous diffusion, we discuss two key parameters in our proposed method: \(k\), the number of anchors, and \(s\), the maximum number of anchors used to approximate every gallery feature. Unless otherwise stated, we optimize other parameters such as \(L\) and \(K\) mentioned in Section 6 through validation.  
The impact of varying anchor numbers \(k\) on retrieval performance is analyzed in Figure 2 using the \(\mathcal{R}\)Oxford dataset with parameter \(s=10\). Experimental results demonstrate that smaller anchor sets lead to suboptimal performance due to insufficient reconstruction of gallery features and limited structural diversity, while increasing \(k\) progressively improves mean average precision (mAP) until a plateau is reached at \(k=2048\). Beyond this threshold, additional anchors yield negligible gains (less than 0.5%), indicating a saturation point where further increases no longer meaningfully enhance the approximation of the global data distribution or the gallery graph structure. This behavior aligns with theoretical expectations and findings in anchor-based methods [30], where optimal performance balances computational efficiency and representation fidelity. The results confirm that \(k=2048\) adequately captures the gallery data structure, which justifies its adoption in subsequent experiments for the datasets \(\mathcal{R}\)Oxford and \(\mathcal{R}\)Paris.  
Figure 3 shows a ceteris paribus analysis on the parameter \(s\). We observe that the retrieval performance tends to be better as \(s\) increases. Intuitively speaking, the more nearest anchors used, the more precisely can a gallery image feature be reconstructed. Another intriguing finding is that the performance is great even though \(s=1\), meaning that each gallery feature is replaced by its nearest anchor. Such an extreme case resembles the database-side feature augmentation (DBA) proposed by [31], where each gallery feature is replaced by the average of its nearest neighbors. As DBA has been reported to be beneficial to retrieval performance, our proposed method also shares this benefit. As a result, the combination of anchor-based diffusion and LAE surprisingly outperforms previous methods by a large margin. Note that the parameter \(s\) is closely related to the  
Figure 2: Retrieval performance (mAP) vs. the number of anchors, where the parameter \(s\) is fixed to 10.  
offline computational cost. For \(n\) images in the gallery, the overall cost of the LAE algorithm is \(\mathcal{O}(nks)\). Such a cost is affordable when \(k\gg s\), while it would become unacceptable when \(s\) is too large. Fortunately, the LAE algorithm is performed completely offline and therefore has no impact on the runtime efficiency. This trade-off should be kept in mind especially for large-scale datasets. In consideration of the pre-computational efficiency and the cost of handling new data, we choose to use a rather smaller \(s=50\) for later experiments.