Bao-Di Liu

Learning dictionary on manifolds for image classification

At present, dictionary based models have been widely used in image classification. The image features are approximated as a linear combination of bases selected from the dictionary in a sparse space, resulting in compact patterns. The features applied to image classification usually reside on low dimensional manifolds embedded in a high dimensional ambient space; traditional sparse coding algorithm, however, does not consider this topological structure. It can be characterized naturally by linear coefficients that reconstruct each data point from its neighbors. One of the central issues here is how to determine the neighbors and learn the coefficients. In this paper, the geometrical structures are encoded in two situations. In simple cases when data points distribute on a single manifold, it is explicitly modeled by locally linear embedding algorithm combined with k-nearest neighbors. Nevertheless, in real-world scenarios, complex data points often lie on multiple manifolds. Sparse representation algorithm combined with k-nearest neighbors is instead utilized to construct the topological structures, because it is capable of approximating the data point by selecting its homogenous neighbors adaptively to guarantee the smoothness of each manifold. After obtaining the local fitting relationship, these two topological structures are then embedded into sparse coding algorithm as regularization terms to formulate the corresponding objective functions of dictionary learning on single manifold (DLSM) and dictionary learning on multiple manifolds (DLMM), respectively. Upon this, a coordinate descent scheme is proposed to solve the unified optimization problems. Experimental results on several benchmark data sets, such as Caltech-256, Caltech-101, Scene 15, and UIUC-Sports, show that our proposed algorithms equal or outperform other state-of-the-art image classification algorithms.

Self-Explanatory Sparse Representation for Image Classification

Traditional sparse representation algorithms usually operate in a single Euclidean space. This paper leverages a self-explanatory reformulation of sparse representation, i.e., linking the learned dictionary atoms with the original feature spaces explicitly, to extend simultaneous dictionary learning and sparse coding into reproducing kernel Hilbert spaces (RKHS). The resulting single-view self-explanatory sparse representation (SSSR) is applicable to an arbitrary kernel space and has the nice property that the derivatives with respect to parameters of the coding are independent of the chosen kernel. With SSSR, multiple-view self-explanatory sparse representation (MSSR) is proposed to capture and combine various salient regions and structures from different kernel spaces. This is equivalent to learning a nonlinear structured dictionary, whose complexity is reduced by learning a set of smaller dictionary blocks via SSSR. SSSR and MSSR are then incorporated into a spatial pyramid matching framework and developed for image classification. Extensive experimental results on four benchmark datasets, including UIUC-Sports, Scene 15, Caltech-101, and Caltech-256, demonstrate the effectiveness of our proposed algorithm.

Discriminant sparse coding for image classification

Recently, dictionary learned by sparse coding has been widely adopted in image classification and has achieved competitive performance. Sparse coding is capable of reducing the reconstruction error in transforming low-level descriptors into compact mid-level features. Nevertheless, dictionary learned by sparse coding does not have the ability to distinguish different classes. That is to say, it is not the optimum dictionary for the classification task. In this paper, based on the global image statistics, a novel discriminant dictionary learning method combining linear discriminant analysis with sparse coding is proposed to obtain a more discriminative dictionary while preserving its descriptive abilities and a block coordinate descent algorithm is proposed to solve the optimization problem. Experimental results show that our algorithm has capabilities to learn dictionary with more discriminative power and achieves superior performance.

Face recognition using class specific dictionary learning for sparse representation and collaborative representation

Recently, sparse representation based classification (SRC) and collaborative representation based classification (CRC) have been successfully used for visual recognition and have demonstrated impressive performance. Given a test sample, SRC or CRC formulates its linear representation with respect to the training samples and then computes the residual error for each class. SRC or CRC assumes that the training samples from each class contribute equally to the dictionary in the corresponding class, i.e., the dictionary consists of the training samples in that class. This, however, leads to high residual error and instability. To overcome this limitation, we propose a class specific dictionary learning algorithm. To be specific, by introducing the dual form of dictionary learning, an explicit relationship between the basis vectors and the original image features is represented, which also enhances the interpretability. SRC or CRC can be thus considered as a special case of the proposed algorithm. Blockwise coordinate descent algorithm and Lagrange multipliers are then adopted to optimize the corresponding objective function. Extensive experimental results on five benchmark face recognition datasets show that the proposed algorithm achieves superior performance compared with conventional classification algorithms. HighlightsA novel class specific dictionary learning (CSDL) approach is proposed, where the standard collaborative representation based classification (CRC) or sparse representation based classification (SRC) can be considered as its special cases.The dual form of dictionary learning is proposed to enhance the interpretability.Our proposed CSDL achieves superior face recognition performance on several benchmark datasets.

Action recognition in still images using a combination of human pose and context information

In this work, a novel method is proposed for recognizing human actions in still images, which incorporates both pose and context information. Poselet-based action classifiers are learned using Poselet Activation Vector as features, which contain pose information for each action. And context-based action classifiers for each action are learned on contextual information, which is obtained by sparse coding on foreground and background. The confidences of an image belonging to each action are obtained through summing up the probability outputs of the poselet-based and the context-based classifiers. The contribution of this work is three folded. Firstly, sparse coding is adopted to find compact patterns of the original features. Secondly, a block coordinate descent algorithm is proposed for sparse coding, which can be performed very fast in practice. Thirdly, both pose and context information are taken into consideration for action recognition. The experimental results show the proposed method achieves the state-of-the-art performance on several benchmarks.

Elastic net regularized dictionary learning for image classification

Dictionary learning plays a key role in image representation for classification. A multi-modal dictionary is usually learned from feature samples across different classes and shared in the feature encoding process. Ideally each atom in dictionary corresponds to a single class of images, while each class of images corresponds to a certain group of atoms. Image features are encoded as linear combinations of selected atoms in a given dictionary. We propose to use elastic net as regularizer to select atoms in feature coding and related dictionary learning process, which not only benefits from the sparsity similar as ℓ1 penalty but also encourages a grouping effect that helps improve image representation. Experimental results of image classification on benchmark datasets show that with dictionary learned in the proposed way outperforms state-of-the-art dictionary learning algorithms.

Blockwise coordinate descent schemes for sparse representation

The current sparse representation framework is to decouple it as two subproblems, i.e., alternate sparse coding and dictionary learning using different optimizers, treating elements in bases and codes separately. In this paper, we treat elements both in bases and codes ho-mogenously. The original optimization is directly decoupled as several blockwise alternate subproblems rather than above two. Hence, sparse coding and bases learning optimizations are coupled together. And the variables involved in the optimization problems are partitioned into several suitable blocks with convexity preserved, making it possible to perform an exact block coordinate descent. For each separable subproblem, based on the convexity and monotonic property of the parabolic function, a closed-form solution is obtained. Thus the algorithm is simple, efficient and effective. Experimental results show that our algorithm significantly accelerates the learning process.

Low-rank image tag completion with dual reconstruction structure preserved

User provided tags, albeit play an essential role in image annotation, may inhibit accurate annotation as well since they are potentially incomplete. To address this problem, a novel tag completion method is proposed in this paper. In order to exploit as much information, the proposed method is designed with the following features: (1) Low-rank and error sparsity: the initial tag matrix D is decomposed into the complete tag matrix A and a sparse error matrix E, where A is further factorized into a basis matrix U and a sparse coefficient matrix V, i.e., D=UV+E. With KM, information sharing between related tags and similar samples can be achieved via subspace construction. (2) Local reconstruction structure consistency: the local linear reconstruction structures obtained in the original feature and tag spaces are preserved in both the low-dimensional feature subspace and tag subspace. (3) Promote basis diversity: the pair-wise dot products between the columns of U are minimized, in order to obtain more representative basis vectors. Experiments conducted on Corel5K dataset and the newly issued Flickr30Concepts dataset demonstrate the effectiveness and efficiency of the proposed method.

Robust nonnegative matrix factorization via L 1 norm regularization by multiplicative updating rules

Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear representation in a low dimensional space by using the product of two nonnegative matrices. In many applications data are often partially corrupted with large additive noise. When the positions of noise are known, some existing variants of N-MF can be applied by treating these corrupted entries as missing values. However, the positions are often unknown in many real world applications, which prevents the usage of traditional NMF or other existing variants of NMF. This paper proposes a Robust Nonnegative Matrix Factorization (RobustNMF) algorithm that explicitly models the partial corruption as large additive noise without requiring the information of positions of noise. In particular, the proposed method jointly approximates the clean data matrix with the product of two nonnegative matrices and estimates the positions and values of outliers/noise. An efficient iterative optimization algorithm with a solid theoretical justification has been proposed to learn the desired matrix factorization. Experimental results demonstrate the advantages of the proposed algorithm.

Self-Explanatory Convex Sparse Representation for Image Classification

Sparse representation technique has been widely used in various areas of computer vision over the last decades. Unfortunately, in the current formulations, there are no explicit relationship between the learned dictionary and the original data. By tracing back and connecting sparse representation with the K-means algorithm, a novel variation scheme termed as self-explanatory convex sparse representation (SCSR) has been proposed in this paper. To be specific, the basis vectors of the dictionary are refined as convex combination of the data points. The atoms now would capture a notion of centroids similar to K-means, leading to enhanced interpretability. Sparse representation and K-means are thus unified under the same framework in this sense. Besides, an appealing property also emerges that the weight and code matrices both tend to be naturally sparse without additional constraints. Compared with the standard formulations, SCSR is easier to be extended into the kernel space. To solve the corresponding sparse coding sub problem and dictionary learning sub problem, block-wise coordinate descent and Lagrange multipliers are proposed accordingly. To validate the proposed algorithm, it is implemented in image classification, a successful applications of sparse representation. Experimental results on several benchmark data sets, such as UIUC-Sports, Scene 15, and Caltech-256 demonstrate the effectiveness of our proposed algorithm.