Research On Constrained Matrix Based Image Representation And Retrieval

With the development of smart phones and popularization of mobile social applications like WeChat, the amounts of images on mobile internet are growing exponentially. Except the amount of images, the image resolution is also improved along with the development of image acquisi-tion equipment. High definition gives users more intuitive, vivid and delicate experience, which means the feature dimension for image learning algorithms to be processed becomes much higher. While the high-dimensional feature not only brings storage and computing challenges, but it can cause "curse of dimensionality" which is fatal for traditional learning algorithms. In addition, the importance of image management techniques such as image retrieval (particularly cross-media im-age retrieval) is highlighted with the emergence of massive image data. This paper focuses on the image fundamental problem-image representation and the hot issue-cross-media image retrieval.Image representation is a kind of algorithm which encodes images into feature vectors. The feature vectors are inputs for other learning algorithms(such as image clustering, image recog-nition, image retrieval, etc.). Effective image representation method can reduce data storage, transmission and learning costs. At the same time, it can characterize the underlying geometry and discover the semantic information of the image data to enhance learning performance. As image data set can be represented as a low-rank matrix. We focus on non-negative matrix factor-ization(NMF) algorithm which is very popular in recent years. Considering that NMF is not stable for subsequent learning and is insufficient in preserving locality and capturing sparsity, we propose several constrained non-negative matrix factorization algorithms.Image retrieval, especially cross-media image retrieval (such as image retrieval with a text query) is important for massive image data management. The core issue of cross-media image retrieval problem is the similarity computing between different feature space. Most of cross-media image retrieval algorithm devotes to mapping data points from different feature space into a com-mon subspace. In this framework, the above single-mode image representation algorithm cannot be used. We cast cross-media image retrieval problem into low-rank matrix completion and propose a novel algorithm. This algorithm can take advantage of low-dimensional image representation learned from single-mode image representation algorithm and relation between different feature space to learning global and local data consistency.More specifically, the main contributions of the paper are as follows:1. As the sparseness given by NMF is somewhat of a side-effect rather than a goal, in most prac-tical cases NMF cannot obtain sparse encodings. Therefore, when further used in learning tasks (such as classification, clustering and so on), the learned representations can not achieve optimal performance. Given that, we improve Concept Factorization algorithm which is a variation of NMF and propose a novel Locality-Constrained Concept Factorization(LCF) algorithm. LCF imposes a local coordinate coding constrained regularization to CF. By re-quiring the concepts(basis vectors) to be as close to the original data points as possible, each data learned by LCF can be represented by a linear combination of only a few basis con-cepts which means sparse coding. Similar with NMF, LCF obtains the optimal solution with multiplicative update rules. We demonstrate the effectiveness of LCF in comparison to the state-of-the-art approaches through a set of evaluations based on real world applications.2. Most existing NMF extended algorithms just focus on the non-negative matrix factorization model and ignore the more important stage, further using. Considering the learned encodings from a statistical view by modeling the data points via ridge regression, we use A-optimal method from Optimum Experimental Designs to restrict the learned encodings. With this constraint, the stability of regression model will be enhanced and the expected prediction error will be decrease. Taking this constraint as a regularization and introducing Hessian regularization, we propose a novel method called A-Optimal Non-negative Projection with Hessian regularization(AHNP). Compared with Laplacian regularization, Hessian regular-ization has better generalization ability. Therefore, AHNP leads to parts-based and manifold structure based representation. And the learned representation would bring in better regres-sion model. We use multiplicative update based algorithm to solve the optimization problem of AHNP. We conduct a series of experiments on real world data set to demonstrate the effectiveness of AHNP.3. Considering that traditional image representation can be used in image classification/clustering, target detection, image retrieval, and many other areas, but is useless in cross-media im-age retrieval because of semantic gap. We propose a novel low-rank matrix completion based semi-supervised learning algorithm called Matrix Completion for Cross-view Pairwise Constraint Propagation(MCPCP). MCPCP keeps local consistency by constructing neighbor graph with representation learned from uniMedia and preserves global consistency by mini-mizing the rank of cross-media relation matrix. In order to efficiently solve the optimization problem, we use ADMM algorithm which is easy to parallelize. We conduct cross-media re-trieval experiments on real world images-text data set to reveal the effectiveness of MCPCP.