Image-text retrieval is a fundamental cross-modal task whose main idea is to learn image-text matching. Generally, according to whether there exist interactions during the retrieval process, existing image-text retrieval methods can be classified into independent representation matching methods and cross-interaction matching methods. The independent representation matching methods generate the embeddings of images and sentences independently and thus are convenient for retrieval with hand-crafted matching measures (e.g., cosine or Euclidean distance). As to the cross-interaction matching methods, they achieve improvement by introducing the interaction-based networks for inter-relation reasoning, yet suffer the low retrieval efficiency. This article aims to develop a method that takes the advantages of cross-modal inter-relation reasoning of cross-interaction methods while being as efficient as the independent methods. To this end, we propose a graph-based
Cross-modal Graph Matching Network (CGMN)
, which explores both intra- and inter-relations without introducing network interaction. In CGMN, graphs are used for both visual and textual representation to achieve intra-relation reasoning across regions and words, respectively. Furthermore, we propose a novel graph node matching loss to learn fine-grained cross-modal correspondence and to achieve inter-relation reasoning. Experiments on benchmark datasets MS-COCO, Flickr8K, and Flickr30K show that CGMN outperforms state-of-the-art methods in image retrieval. Moreover, CGMM is much more efficient than state-of-the-art methods using interactive matching. The code is available at
https://github.com/cyh-sj/CGMN
.
In this paper, we introduce a new graph operation called subdivision vertex-edge join (denoted by G 1 S ▹ ( G 2 V ∪ G 3 E ) for short), and then the adjacency spectrum, the Laplacian spectrum and the signless Laplacian spectrum of G 1 S ▹ ( G 2 V ∪ G 3 E ) are respectively determined in terms of the corresponding spectra for a regular graph G 1 and two arbitrary graphs G 2 and G 3 . All the above can be viewed as the generalizations of the main results in [X. Liu, Z. Zhang, Bull. Malays. Math. Sci. Soc., 2017:1–17]. Furthermore, we also determine the normalized Laplacian spectrum of G 1 S ▹ ( G 2 V ∪ G 3 E ) whenever G i are regular graphs for each index i = 1 , 2 , 3 . As applications, we construct infinitely many pairs of A-cospectral mates, L-cospectral mates, Q-cospectral mates and L -cospectral mates. Finally, we give the number of spanning trees, the (degree-)Kirchhoff index and the Kemeny’s constant of G 1 S ▹ ( G 2 V ∪ G 3 E ) , respectively.
A graph is called Laplacian integral if all its Laplacian eigenvalues are integers. In this paper, we give an edge subdividing theorem for Laplacian eigenvalues of a graph (Theorem 2.1) and characterize a class of k-cyclic graphs whose algebraic connectivity is less than one. Using these results, we determine all the Laplacian integral tricyclic graphs. Furthermore, we show that all the Laplacian integral tricyclic graphs are determined by their Laplacian spectra.
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