By transforming data into binary representation, i.e., Hashing, we can perform high-speed search with low storage cost, and thus, Hashing has collected increasing research interest in the recent years. Recently, how to generate Hashcode for multimodal data (e.g., images with textual tags, documents with photos, and so on) for large-scale cross-modality search (e.g., searching semantically related images in database for a document query) is an important research issue because of the fast growth of multimodal data in the Web. To address this issue, a novel framework for multimodal Hashing is proposed, termed as Collective Matrix Factorization Hashing (CMFH). The key idea of CMFH is to learn unified Hashcodes for different modalities of one multimodal instance in the shared latent semantic space in which different modalities can be effectively connected. Therefore, accurate cross-modality search is supported. Based on the general framework, we extend it in the unsupervised scenario where it tries to preserve the Euclidean structure, and in the supervised scenario where it fully exploits the label information of data. The corresponding theoretical analysis and the optimization algorithms are given. We conducted comprehensive experiments on three benchmark data sets for cross-modality search. The experimental results demonstrate that CMFH can significantly outperform several state-of-the-art cross-modality Hashing methods, which validates the effectiveness of the proposed CMFH.

Due to its psychological and physiological interpretation of naturally occurring data, Nonnegative Matrix Factorization (NMF) has attracted considerable attention for learning effective representation for images. And its graph-regularized extensions have shown promising results by exploiting the low dimensional manifold structure of data. Actually, their performance can be further improved because they still suffer from several important problems, i.e., sensitivity to noise in data, trivial solution problem, and ignoring the discriminative information. In this paper, we propose a novel method, referred to as Robust Nonnegative Matrix Factorization with Discriminability (RNMFD), for image representation, which can effectively and simultaneously cope with problems mentioned above by imposing a sparse noise matrix for data reconstruction and approximate orthogonal constraints. We carried out extensive experiments on five benchmark image datasets and the results demonstrate the superiority of our RNMFD in comparison with several state-of-the-art methods.

Concept Factorization (CF), as a variant of Nonnegative Matrix Factorization (NMF), has been widely used for learning compact representation for images because of its psychological and physiological interpretation of naturally occurring data. And graph regularization has been incorporated into the objective function of CF to exploit the intrinsic low-dimensional manifold structure, leading to better performance. But some shortcomings are shared by existing CF methods. 1) The squared loss used to measure the data reconstruction quality is sensitive to noise in image data. 2) The graph regularization may lead to trivial solution and scale transfer problems for CF such that the learned representation is meaningless. 3) Existing methods mostly ignore the discriminative information in image data. In this paper, we propose a novel method, called Robust and Discriminative Concept Factorization (RDCF) for image representation. Specifically, RDCF explicitly considers the influence of noise by imposing a sparse error matrix, and exploits the discriminative information by approximate orthogonal constraints which can also lead to nontrivial solution. We propose an iterative multiplicative updating rule for the optimization of RDCF and prove the convergence. Experiments on 5 benchmark image datasets show that RDCF can significantly out-perform several state-of-the-art related methods, which validates the effectiveness of RDCF.

Nearest neighbor search methods based on hashing have attracted considerable attention for effective and efficient large-scale similarity search in computer vision and information retrieval community. In this paper, we study the problems of learning hash functions in the context of multimodal data for cross-view similarity search. We put forward a novel hashing method, which is referred to Collective Matrix Factorization Hashing (CMFH). CMFH learns unified hash codes by collective matrix factorization with latent factor model from different modalities of one instance, which can not only supports cross-view search but also increases the search accuracy by merging multiple view information sources. We also prove that CMFH, a similarity-preserving hashing learning method, has upper and lower boundaries. Extensive experiments verify that CMFH significantly outperforms several state-of-the-art methods on three different datasets.

Spectral-based hashing (SpH) is the most used method for cross-view hash function learning (CVHFL). However, the following three problems are shared by many existing SpH methods. Firstly, preserving intra- and inter-similarity simultaneously increases models' complexity significantly. Secondly, linear model applied in many SpH methods is hard to handle multimodal data in cross-view scenarios. Thirdly, to learn irrelevant multiple bits, SpH imposes orthogonality constraints which decreases the mapping quality substantially with the increase of bit number. To address these challenges, we propose a novel SpH method for CVHFL in this paper, referred to as Kernel-based Supervised Hashing for Cross-view Similarity Search (KSH-CV). We prove that the intra-adjacency matrix is redundant given inter-adjacency matrix. Then we define our objective function in a supervised and k-ernelized way which just needs to preserve inter-similarity. Furthermore a novel Adaboost algorithm, which minimizes exponential mapping loss function for cross-view similarity search, is derived to solve the objective function efficiently while avoiding orthogonality constraints. Extensive experiments verifies that KSH-CV can significantly outperform several state-of-the-art methods on three cross-view datasets.

Similarity search methods based on hashing for effective and efficient cross-modal retrieval on large-scale multimedia databases with massive text and images have attracted considerable attention. The core problem of cross-modal hashing is how to effectively construct correlation between multi-modal representations which are heterogeneous intrinsically in the process of hash function learning. Analogous to Canonical Correlation Analysis (CCA), most existing cross-modal hash methods embed the heterogeneous data into a joint abstraction space by linear projections. However, these methods fail to bridge the semantic gap more effectively, and capture high-level latent semantic information which has been proved that it can lead to better performance for image retrieval. To address these challenges, in this paper, we propose a novel Latent Semantic Sparse Hashing (LSSH) to perform cross-modal similarity search by employing Sparse Coding and Matrix Factorization. In particular, LSSH uses Sparse Coding to capture the salient structures of images, and Matrix Factorization to learn the latent concepts from text. Then the learned latent semantic features are mapped to a joint abstraction space. Moreover, an iterative strategy is applied to derive optimal solutions efficiently, and it helps LSSH to explore the correlation between multi-modal representations efficiently and automatically. Finally, the unified hashcodes are generated through the high level abstraction space by quantization. Extensive experiments on three different datasets highlight the advantage of our method under cross-modal scenarios and show that LSSH significantly outperforms several state-of-the-art methods.