Due to the rapid development of mobile Internet techniques, cloud computation and popularity of online social networking and location-based services, massive amount of multimedia data with geographical information is generated and uploaded to the Internet. In this paper, we propose a novel type of cross-modal multimedia retrieval called geo-multimedia cross-modal retrieval which aims to search out a set of geo-multimedia objects based on geographical distance proximity and semantic similarity between different modalities. Previous studies for cross-modal retrieval and spatial keyword search cannot address this problem effectively because they do not consider multimedia data with geo-tags and do not focus on this type of query. In order to address this problem efficiently, we present the definition of $k$NN geo-multimedia cross-modal query at the first time and introduce relevant conceptions such as cross-modal semantic representation space. To bridge the semantic gap between different modalities, we propose a method named cross-modal semantic matching which contains two important component, i.e., CorrProj and LogsTran, which aims to construct a common semantic representation space for cross-modal semantic similarity measurement. Besides, we designed a framework based on deep learning techniques to implement common semantic representation space construction. In addition, a novel hybrid indexing structure named GMR-Tree combining geo-multimedia data and R-Tree is presented and a efficient $k$NN search algorithm called $k$GMCMS is designed. Comprehensive experimental evaluation on real and synthetic dataset clearly demonstrates that our solution outperforms the-state-of-the-art methods.
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