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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Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and in this paper, we propose efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the l1-norm. Our method is efficient and scales gracefully to millions of variables, which we illustrate in two types of applications: first, we consider fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we apply our optimization tools in the context of dictionary learning, where learned dictionary elements naturally self-organize in a prespecified arborescent structure, leading to better performance in reconstruction of natural image patches. When applied to text documents, our method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models. We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on discrete analysis and geometry developed by ourselves, in which a number of discrete differential operators of various orders are constructed, which can be thought of as discrete analogues of their counterparts in the continuous case. In many problems in computer vision, data in multiple classes lie in multiple low-dimensional subspaces of a high-dimensional ambient space. However, most of the existing classification methods do not explicitly take this structure into account. In this paper, we consider the problem of classification in the multi-sub space setting using sparse representation techniques. We exploit the fact that the dictionary of all the training data has a block structure where the training data in each class form few blocks of the dictionary. We cast the classification as a structured sparse recovery problem where our goal is to find a representation of a test example that uses the minimum number of blocks from the dictionary. We formulate this problem using two different classes of non-convex optimization programs. We propose convex relaxations for these two non-convex programs and study conditions under which the relaxations are equivalent to the original problems. In addition, we show that the proposed optimization programs can be modified properly to also deal with corrupted data. To evaluate the proposed algorithms, we consider the problem of automatic face recognition. We show that casting the face recognition problem as a structured sparse recovery problem can improve the results of the state-of-the-art face recognition algorithms, especially when we have relatively small number of training data for each class. In particular, we show that the new class of convex programs can improve the state-of-the-art face recognition results by 10 with only 25 of the training data. In addition, we show that the algorithms are robust to occlusion, corruption, and disguise.