To better select the correct training sample and obtain the robust representation of the query sample, this paper proposes a discriminant-based sparse optimization learning model. This learning model integrates discriminant and sparsity together. Based on this model, we then propose a classifier called locality-based discriminant sparse representation (LDSR). Because discriminant can help to increase the difference of samples in different classes and to decrease the difference of samples within the same class, LDSR can obtain better sparse coefficients and constitute a better sparse representation for classification. In order to take advantages of kernel techniques, discriminant and sparsity, we further propose a nonlinear classifier called kernel locality-based discriminant sparse representation (KLDSR). Experiments on several well-known databases prove that the performance of LDSR and KLDSR is better than that of several state-of-the-art methods including deep learning based methods.
proposed sparse representation classification (SRC) in 2009. It represents the testing sample using the linear combination of training samples of all classes. SRC solves @math -minimization optimization problem as To reduce the computation cost and obtain the better representation, proposed the collaborative representation based classification (CRC). In CRC, the authors argued that the collaborative representation should be better than the linear combination of training samples. CRC solves the @math -minimization optimization problem as They are two typical sparse-based methods. A lot improved version of SRC CRC have been proposed for various visual recognition tasks. They include the probabilistic-based sparse methods @cite_34 , discriminant-based dictionary learning @cite_17 @cite_27 , kernel-based sparse methods @cite_42 @cite_2 , Gabor-based sparse methods @cite_38 and many others @cite_18 @cite_26 .
@cite_38 @cite_18 @cite_26 @cite_42 @cite_27 @cite_2 @cite_34 @cite_17
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In this paper, we propose a two-phase test sample representation method for face recognition. The first phase of the proposed method seeks to represent the test sample as a linear combination of all the training samples and exploits the representation ability of each training sample to determine M “nearest neighbors” for the test sample. The second phase represents the test sample as a linear combination of the determined M nearest neighbors and uses the representation result to perform classification. We propose this method with the following assumption: the test sample and its some neighbors are probably from the same class. Thus, we use the first phase to detect the training samples that are far from the test sample and assume that these samples have no effects on the ultimate classification decision. This is helpful to accurately classify the test sample. We will also show the probability explanation of the proposed method. A number of face recognition experiments show that our method performs very well. Face recognition (FR) with a single training sample per person (STSPP) is a very challenging problem due to the lack of information to predict the variations in the query sample. Sparse representation based classification has shown interesting results in robust FR, however, its performance will deteriorate much for FR with STSPP. To address this issue, in this paper we learn a sparse variation dictionary from a generic training set to improve the query sample representation by STSPP. Instead of learning from the generic training set independently w.r.t. the gallery set, the proposed sparse variation dictionary learning (SVDL) method is adaptive to the gallery set by jointly learning a projection to connect the generic training set with the gallery set. The learnt sparse variation dictionary can be easily integrated into the framework of sparse representation based classification so that various variations in face images, including illumination, expression, occlusion, pose, etc., can be better handled. Experiments on the large-scale CMU Multi-PIE, FRGC and LFW databases demonstrate the promising performance of SVDL on FR with STSPP. Sparse representation-based classifier (SRC), a combined result of machine learning and compressed sensing, shows its good classification performance on face image data. However, SRC could not well classify the data with the same direction distribution. The same direction distribution means that the sample vectors belonging to different classes distribute on the same vector direction. This paper presents a new classifier, kernel sparse representation-based classifier (KSRC), based on SRC and the kernel trick which is a usual technique in machine learning. KSRC is a nonlinear extension of SRC and can remedy the drawback of SRC. To make the data in an input space separable, we implicitly map these data into a high-dimensional kernel feature space by using some nonlinear mapping associated with a kernel function. Since this kernel feature space has a very high (or possibly infinite) dimensionality, or is unknown, we have to avoid working in this space explicitly. Fortunately, we can indeed reduce the dimensionality of the kernel feature space by exploiting kernel-based dimensionality reduction methods. In the reduced subspace, we need to find sparse combination coefficients for a test sample and assign a class label to it. Similar to SRC, KSRC is also cast into an l1-minimization problem or a quadratically constrained l1 -minimization problem. Extensive experimental results on UCI and face data sets show KSRC improves the performance of SRC. Sparse representation based classification has led to interesting image recognition results, while the dictionary used for sparse coding plays a key role in it. This paper presents a novel dictionary learning (DL) method to improve the pattern classification performance. Based on the Fisher discrimination criterion, a structured dictionary, whose dictionary atoms have correspondence to the class labels, is learned so that the reconstruction error after sparse coding can be used for pattern classification. Meanwhile, the Fisher discrimination criterion is imposed on the coding coefficients so that they have small within-class scatter but big between-class scatter. A new classification scheme associated with the proposed Fisher discrimination DL (FDDL) method is then presented by using both the discriminative information in the reconstruction error and sparse coding coefficients. The proposed FDDL is extensively evaluated on benchmark image databases in comparison with existing sparse representation and DL based classification methods. Motivated by the idea that the correlation structure of the entire training set can disclose the relationship between the test sample and the training samples, we propose the combined sparse representation (CSR) classifier for disease recognition. The CSR classifier minimizes the correlation structure of the entire training set multiplied by its transposition and the sparse coefficient together for classification. Including the kernel concept, we propose the kernel combined sparse representation classifier utilizing the high-dimensional nonlinear information instead of the linear information in the CSR classifier. Furthermore, considering the information of the training samples and the class center, we then propose the center-based kernel combined sparse representation (CKCSR) classifier. CKCSR uses the center-based kernel matrix to increase the center-based information that is helpful for classification. The proposed classifiers have been evaluated by extensive experiments on several well-known databases including the EXACT09 database, Emphysema-CT database, mini-MIAS database, Wisconsin breast cancer database, and HD-PECTF database. The experimental results demonstrate that the proposed classifiers achieve better recognition rates than the sparse representation-based classification, collaborative representation based classification, and several state-of-the-art methods.