This paper presents a new framework for visual bag-of-words (BOW) refinement and reduction to overcome the drawbacks associated with the visual BOW model which has been widely used for image classification. Although very influential in the literature, the traditional visual BOW model has two distinct drawbacks. Firstly, for efficiency purposes, the visual vocabulary is commonly constructed by directly clustering the low-level visual feature vectors extracted from local keypoints, without considering the high-level semantics of images. That is, the visual BOW model still suffers from the semantic gap, and thus may lead to significant performance degradation in more challenging tasks (e.g. social image classification). Secondly, typically thousands of visual words are generated to obtain better performance on a relatively large image dataset. Due to such large vocabulary size, the subsequent image classification may take sheer amount of time. To overcome the first drawback, we develop a graph-based method for visual BOW refinement by exploiting the tags (easy to access although noisy) of social images. More notably, for efficient image classification, we further reduce the refined visual BOW model to a much smaller size through semantic spectral clustering. Extensive experimental results show the promising performance of the proposed framework for visual BOW refinement and reduction.
In this paper, we formulate visual BOW refinement as a multi-class graph-based SSL problem. Considering that graph construction is the key step of graph-based SSL, we develop a new @math -graph construction method using structured sparse representation, other than the traditional @math -graph construction method only using sparse representation. As compared with sparse representation, our structured sparse representation has a distinct advantage, i.e., the extra structured sparsity can be induced into @math -graph construction and thus the noise in the data can be suppressed to the most extent. In fact, the structured sparsity penalty used in this paper is defined as @math -norm Laplacian regularization, which is formulated directly over all the eigenvectors of the normalized Laplacian matrix. Hence, our new @math -norm Laplacian regularization is different from the @math -Laplacian regularization @cite_34 as an ordinary @math -generalization (with @math ) of the traditional Laplacian regularization (see further comparison in Section ). In this paper, we focus on exploiting the manifold structure of the data for @math -graph construction with structured sparse representation, regardless of other types of structured sparsity @cite_45 @cite_14 used in the literature.
@cite_14 @cite_34 @cite_45
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The key task in graph-oriented learning is con-structing an informative graph to model the geometrical and discriminant structure of a data manifold. Since traditional graph construction methods are sensitive to noise and less datum-adaptive to changes in density, a new graph construction method so-calledl1-Graph has been proposed [1] recently. A graph construction method needs to have two important properties: sparsity and locality. However, the l1-Graph is strong in sparsity property, but weak in locality. In order to overcome such limitation, we propose a new method of constructing an informative graph using automatic group sparse regularization based on the work ofl1-Graph, which is called as group sparse graph (GroupSp-Graph). The newly developed GroupSp-Graph has the same noise-insensitive property asl1-Graph, and also can successively preserve the group and local information in the graph. In other words, the proposed group sparse graph has both properties of sparsity and locality simultaneously. Furthermore, we integrate the proposed graph with several graph-oriented learning algorithms: spectral em-bedding, spectral clustering, subspace learning and manifold regularized non-negative matrix factorization. The empirical studies on benchmark data sets show that the proposed algo-rithms achieve considerable improvement over classic graph constructing methods and the l1-Graph method in various learning task. In this letter, we propose a novel low-rank-represen-tation (LRR) based manifold-regularization approach for zero-shot learning (ZSL). Most existing regularization-based ZSL approaches perform the alignment between visual feature space and semantic space based on the affinity matrix constructed from the test instances. The affinity matrix plays a significant role in exploiting the manifold structures of visual feature space, hence we propose to use the LRR to guide the affinity-matrix construction by exploring the subspace structures of data. Considering the locality and similarity information among data, we incorporate a Laplacian regularization term to the LRR framework to ensure that the learned affinity matrix can capture the local geometric structures in data. We also explicitly impose the nonnegative sparse constraint on the affinity matrix to facilitate the learning of local manifold structures. Moreover, we use an effective manifold-regularization methodology to learn discriminative semantic representations of test instances, leading to significant improvements in classification performance over the unseen classes. Extensive experiments on three benchmark datasets demonstrate that the proposed approach outperforms the state of the arts. Manifold regularized sparse coding shows promising performance for various applications. The key issue that must be considered in the application is how to adaptively select the suitable graph hyper-parameters in manifold learning for the sparse coding task. Usually, cross validation is applied, but it does not necessarily scale up and easily leads to overfitting. In this article, multiple graph sparse coding (MGrSc) and multiple Hypergraph sparse coding (MHGrSc) for image representation are proposed. Inspired by the Ensemble Manifold Regularizer, we formulate multiple graph and multiple Hypergraph regularizers to guarantee the smoothness of sparse codes along the geodesics of a data manifold, which is characterized by fusing the multiple previously given graph Laplacians or Hypergraph Laplacians. Then, the proposed regularziers, respectively, are incorporated into the traditional sparse coding framework, which results in two unified objective functions of sparse coding. Alternating optimization is used to optimize the objective functions, and two, novel manifold regularized sparse coding algorithms are presented. The proposed two sparse coding methods learn both the composite manifold and the sparse coding jointly, and it is fully automatic for learning the graph hyper-parameters in the manifold learning. Image clustering tests on real world datasets demonstrated that the proposed sparse coding methods are superior to the state-of-the-art methods. We give an approximation algorithm for non-uniform sparsest cut with the following guarantee: For any @math , given cost and demand graphs with edge weights @math respectively, we can find a set @math with @math at most @math times the optimal non-uniform sparsest cut value, in time @math provided @math . Here @math is the @math 'th smallest generalized eigenvalue of the Laplacian matrices of cost and demand graphs; @math (resp. @math ) is the weight of edges crossing the @math cut in cost (resp. demand) graph and @math is the sparsity of the optimal cut. In words, we show that the non-uniform sparsest cut problem is easy when the generalized spectrum grows moderately fast. To the best of our knowledge, there were no results based on higher order spectra for non-uniform sparsest cut prior to this work. Even for uniform sparsest cut, the quantitative aspects of our result are somewhat stronger than previous methods. Similar results hold for other expansion measures like edge expansion, normalized cut, and conductance, with the @math 'th smallest eigenvalue of the normalized Laplacian playing the role of @math in the latter two cases. Our proof is based on an l1-embedding of vectors from a semi-definite program from the Lasserre hierarchy. The embedded vectors are then rounded to a cut using standard threshold rounding. We hope that the ideas connecting @math -embeddings to Lasserre SDPs will find other applications. Another aspect of the analysis is the adaptation of the column selection paradigm from our earlier work on rounding Lasserre SDPs [GS11] to pick a set of edges rather than vertices. This feature is important in order to extend the algorithms to non-uniform sparsest cut.