# A Novel Approach to Incremental Diffusion for Continuous Dataset Updates in Image Retrieval
## 1 Introduction  
Supervised representation learning and unsupervised ranking algorithms are foundational in modern image retrieval [1]. Neural networks typically learn image representations from a fully annotated source dataset, and the trained model is expected to produce ideally distributed image features on both the source dataset and unseen target datasets. In this ideal distribution, the features of visually similar images should be closer in distance, while dissimilar images should be farther apart. However, achieving such an ideal distribution is challenging due to the domain gap between source and target datasets, underscoring the role of ranking algorithms that enhance retrieval performance by exploiting local data structure. Addressing these challenges necessitates rational modeling approaches that harmonize computational efficiency with adaptability to dynamic datasets, ensuring robust retrieval performance even as data evolve. Diffusion is one of the leading techniques in unsupervised ranking algorithms [2, 3]. Although there are now many variants, the core idea of diffusion remains the same as when it was proposed. That is, in simplicity, diffusing the weight on the query through a graph where each node (image) is connected to its local neighbors. By considering the local structure of the data distribution, diffusion usually yields better performance than distance-based retrieval. The traditional diffusion process is to construct a graph from the data and then perform a random walk on the graph, such as [PERSON]'s diffusion [4]. We call this online diffusion because all steps are performed at runtime. To address the computational inefficiency of online diffusion, ref. [5] proposed an offline version in which most of the steps are pre-computed, making the online computational cost negligible. The downside tothis approach is that it lacks the ability to handle growing data. Offline diffusion requires recomputing all the pre-computed results whenever new data are added to the gallery, which makes its biggest advantage in terms of efficiency fade away. Although the size of the benchmark dataset is sometimes fixed, we inevitably encounter data updates in practical applications. For instance, in real-time image retrieval systems requiring continuous adaptation to new visual content (e.g., e-commerce platforms adding product images daily) or edge computing applications with constrained computational resources and dynamically growing galleries (e.g., mobile devices incrementally storing user-generated photos). Specifically, our method addresses critical needs in scenarios such as multimodal biometric recognition (e.g., integrating new fingerprint or iris data without full retraining) [6], mobile fingerprint authentication (e.g., incrementally updating templates from diverse sensor inputs) [7], and large-scale facial recognition systems (e.g., handling newly registered users in real time) [8]. In these applications, gallery datasets often expand continuously, yet existing diffusion methods fail to efficiently incorporate new data without costly recomputation. Our anchor-based incremental diffusion tackles this by decoupling offline anchor graph construction from online updates, enabling seamless integration of new samples through local anchor embedding. This ensures both computational efficiency and robust retrieval performance, making the framework particularly suitable for deployment in production environments with streaming data inputs. Inspired by [9], which builds an asymmetric graph between the anchor points and the gallery features, we introduce the use of anchors in the diffusion as well. In this paper, unlike previous diffusion methods, we propose to perform diffusion on an anchor graph rather than on a sample graph constructed from overall image features. Here, anchors refer to the cluster centers obtained by K-Means. Meanwhile, each image feature is presented as a weighted sum of anchor points through local anchor embedding.