Abstract
Cross-view hashing has shown great potential for large-scale retrieval due to its superiority in terms of computation and storage. In real-world applications, data emerges in a streaming manner, e.g., new images and tags are uploaded to social media by users every day. Existing cross-view hashing methods have to retrain model on new multi-view data, which is time-consuming and not applicable in the real-world applications. To fill this gap, this paper proposes a new online cross-view hashing method, dubbed online unsupervised cross-view discrete hashing (OUCDH) that considers similarity preservation and quantization loss. OUCDH generates hash code as latent embedding shared by multiple views via matrix factorization. OUCDH can well preserve similarity among newly arriving data and old data with the help of anchor graph. An iterative efficient algorithm is developed for online optimization. OUCDH further updates hash code of old data to match that of newly arriving data in each iteration. Extensive experiments on three benchmarks demonstrate that the proposed OUCDH yields superior performance than existing state-of-the-art online cross-view hashing methods.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant No. 62176126, 61906091, the Natural Science Foundation of Jiangsu Province, China (Youth Fund Project) under Grant No. BK20190440, the Fundamental Research Funds for the Central Universities under Grant No. 30921011210.
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Appendix A: The proof of Theorem 3.1
Appendix A: The proof of Theorem 3.1
Fix Rt and update Bt. The minimizing problem (20) is equivalent to:
Due to \(\text {tr}(\mathrm {B}_{t}{\mathrm {V}_{t}}{~}^{\mathrm {T}}\mathrm {R}_{t}{~}^{\mathrm {T}})={\sum }_{i}{\sum }_{j}{\mathrm {B}_{ij}{\hat {\mathrm {V}}}_{ij}}\), where Bij and \({\hat {\mathrm {V}}}_{ij}\) denote the elements of Bt and \(\hat {\mathrm {V}}=\mathrm {R}_{t}\mathrm {V}_{t}\), respectively. We can solve the maximum problem letting Bij = 1 whenever \({\hat {\mathrm {V}}}_{ij}\geq 0\) and − 1 otherwise. That is to say, Bt = sgn(RtVt) in the beginning.
Fix Bt and update Rt.
For fixing Bt, the optimization problem is relevant to a classic Orthogonal Procrustes problem. We compute the SVD of the c × c matrix \(\mathrm {V}_{t}{\mathrm {B}_{t}}^{\mathrm {T}}\) as \({S{\Omega }{\hat {\text {S}}}^{\text {T}}}\) and let \(\mathrm {R}_{t}={\hat {\text {S}}\text {S}^{\text {T}}}\).
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Li, X., Wu, W., Yuan, YH. et al. Online unsupervised cross-view discrete hashing for large-scale retrieval. Appl Intell 52, 14905–14917 (2022). https://doi.org/10.1007/s10489-021-03014-w
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DOI: https://doi.org/10.1007/s10489-021-03014-w