Sparse Multi-Modal Hashing

Learning hash functions across heterogenous high-dimensional features is very desirable for many applications involving multi-modal data objects. In this paper, we propose an approach to obtain the sparse codesets for the data objects across different modalities via joint multi-modal dictionary learning, which we call sparse multi-modal hashing (abbreviated as <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">SM² H</tex></formula> ). In <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">SM² H</tex></formula> , both intra-modality similarity and inter-modality similarity are first modeled by a hypergraph, then multi-modal dictionaries are jointly learned by Hypergraph Laplacian sparse coding. Based on the learned dictionaries, the sparse codeset of each data object is acquired and conducted for multi-modal approximate nearest neighbor retrieval using a sensitive Jaccard metric. The experimental results show that <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">SM² H</tex></formula> outperforms other methods in terms of mAP and Percentage on two real-world data sets.