A sparse representation method based on kernel and virtual samples for face recognition

To improve the classification accuracy of face recognition, a sparse representation method based on kernel and virtual samples is proposed in this paper. The proposed method has the following basic idea: first, it extends the training samples by copying the left side of the original training samples to the right side to form virtual training samples. Then the virtual training samples and the original training samples make up a new training set and we use a kernel-induced distance to determine M nearest neighbors of the test sample from the new training set. Second, it expresses the test sample as a linear combination of the selected M nearest training samples and finally exploits the determined linear combination to perform classification of the test sample. A large number of face recognition experiments on different face databases illustrate that the error ratios obtained by our method are always lower more or less than face recognition methods including the method mentioned in Xu and Zhu [21], the method proposed in Xu and Zhu [39], sparse representation method based on virtual samples (SRMVS), collaborative representation based classification with regularized least square (CRC_RLS), two-phase test sample sparse representation (TPTSSR), and the feature space-based representation method.     

Face image recognition via collaborative representation on selected training samples

In this paper, we present a collaborative representation-based classification on selected training samples (CRC_STS) for face image recognition. The CRC_STS uses a two stage scheme: The first stage is to select some most significant training samples from the original training set by using a multiple round of refining process. The second stage is to use collaborative representation classifier to perform classification on the selected training samples. Our method can be regarded as a sparse representation approach but without imposing l₁-norm constraint on representation coefficients. The experimental results on three well known face databases show that our method works very well.     

A two-phase face recognition method in frequency domain

In this paper, we propose a two-phase face recognition method in frequency domain using discrete cosine transform (DCT) and discrete Fourier transform (DFT). The absolute values of DCT coefficients or DFT amplitude spectra are used to represent the face image, i.e. the transformed image. Then a two-phase face classification method is applied to the transformed images. This method is as follows: its first phase uses the Euclidean distance formula to calculate the distance between a test sample and each sample in the training sets, and then exploits the Euclidean distance of each training sample to determine K nearest neighbors for the test sample. Its second phase represents the test sample as a linear combination of the determined K nearest neighbors and uses the representation result to perform classification. In addition, we use various numbers of DCT coefficients and DFT amplitude spectra to test the effect on our algorithms. The experimental results show that our method outperforms the two-phase face recognition method based on space domain of face images.     

Novel classification rule of two-phase test sample sparse representation

In this paper, a novel classifier based on two-phase test sample sparse representation (TPTSSR) classifier and coarse k nearest neighbor (C-kNN) classifier, called novel classification rule of two-phase test sample sparse representation (NCR-TPTSSR) classifier, is proposed for image recognition. Being similar to TPTSSR classifier and C-kNN classifier, NCR-TPTSSR classifier also uses the two phases to classify the test sample. However, the classification rule of NCR-TPTSSR classifier is different to the decision rule of TPTSSR classifier and C-kNN classifier. A large number of experiments on FERET face database, AR face database, JAFFE face database and PolyU FKP database are used to evaluate the proposed algorithm. The experimental results demonstrate that the proposed method achieves better recognition rate than TPTSSR classifier, C-kNN classifier, nearest feature center (NFC) classifier, nearest feature line (NFL) classifier, nearest neighbor (NN) and so on.     

A novel virtual samples-based sparse representation method for face recognition

A limited training set usually limits the performance of face recognition in practice. Even sparse representation-based methods which outperform in face recognition cannot avoid such situation. In order to effectively improve recognition accuracy of sparse representation-based methods on a limited training set, a novel virtual samples-based sparse representation (VSSR) method for face recognition is proposed in this paper. In the proposed method, virtual training samples are constructed to enrich the size and diversity of a training set and a sparse representation-based method is used to classify test samples. Extensive experiments on different face databases confirm that VSSR is robust to illumination variations and works better than many representative representation-based face recognition methods.     

Sparse representation-based classification algorithm for optical Tibetan character recognition

A sparse representation-based two-phase classification algorithm is proposed for off-line handwritten Tibetan character recognition. The first phase realizes coarse classification with the K-NN classifier by finding the K nearest neighbours of a test sample in the dictionary constructed by K-SVD with samples of all classes, and the classes of these neighbours are regarded as the candidate classes of the test sample. The second phase performs fine classification with the sparse representation classifier by sparsely representing the test sample with all elements of the dictionary constructed by K-SVD with samples of all candidate classes, and the test sample is finally classified into the candidate class with the maximal contribution in sparse representation. Experiments on the Tibetan off-line handwritten character database show that an optimal recognition rate of 97.17% has been reached and it is 2.12% higher than that of K-NN.     

A face recognition algorithm based on collaborative representation

In this paper, we propose a face recognition algorithm by incorporating a neighbor matrix into the objective function of sparse coding. We first calculate the neighbor matrix between the test sample and each training sample by using the revised reconstruction error of each class. Specifically, the revised reconstruction error (RRE) of each class is the division of the l₂-norm of reconstruction error to the l₂-norm of reconstruction coefficients, which can be used to increase the discrimination information for classification. Then we use the neighbor matrix and all the training samples to linearly represent the test sample. Thus, our algorithm can preserve locality and similarity information of sparse coding. The experimental results show that our algorithm achieves better performance than four previous algorithms on three face databases.     

Tensor methods for the exceptional group E6

We present a tensor formalism to describe irreducible representations of the exceptional group E₆. Irreducible tensors are characterized by covariant and contravariant indices associated with the irreducible representation 27, and a third (orthogonal-type) index associated with the 78; contractions of these indices with a set of invariant tensors are required to vanish for irreducibility. The formalism is applied to the reduction of Kronecker products of E₆ irreducible representations. As a further illustration of the method, we construct explicitly the Higgs potential for scalar fields in the E₆ representations 27, 78, 351, 351′.     

Comparison of pattern recognition methods in classifying high-resolution BOLD signals obtained at high magnetic field in monkeys

Pattern recognition methods have shown that functional magnetic resonance imaging (fMRI) data can reveal significant information about brain activity. For example, in the debate of how object categories are represented in the brain, multivariate analysis has been used to provide evidence of a distributed encoding scheme [Science 293:5539 (2001) 2425–2430]. Many follow-up studies have employed different methods to analyze human fMRI data with varying degrees of success [Nature reviews 7:7 (2006) 523–534]. In this study, we compare four popular pattern recognition methods: correlation analysis, support-vector machines (SVM), linear discriminant analysis (LDA) and Gaussian naïve Bayes (GNB), using data collected at high field (7 Tesla) with higher resolution than usual fMRI studies. We investigate prediction performance on single trials and for averages across varying numbers of stimulus presentations. The performance of the various algorithms depends on the nature of the brain activity being categorized: for several tasks, many of the methods work well, whereas for others, no method performs above chance level. An important factor in overall classification performance is careful preprocessing of the data, including dimensionality reduction, voxel selection and outlier elimination.     

Improve the two-phase test samples representation method for palmprint recognition

Palmprint recognition, as a very important personal identification technology, is taking more and more attention. A recently proposed method – two-phase test samples representation method (TPTSR) has attracted much attention and performed very well in biometrics. The TPTSR not only is a competent representation-based classification method, but also is computationally much more efficient than the original sparse representation methods. However, though the TPTSR seems to be suitable for palmprint recognition, it has not been widely tested and it is not known how to properly set the parameter (the number of the nearest neighbors), which is definitely crucial for real-world applications. This paper will analyze the performance of the method in the palmprint identification for the first time and explore the proper value of the parameter of the method. In order to address the above issues, lots of experiments on the palmprint recognition are conducted. This paper also shows experimental comparisons between TPTSR and several other methods. This paper provides significant instructions apply TPTSR to palmprint recognition.     

Integrating the original face images and “symmetrical faces” to perform face recognition

Using the original and ‘symmetrical face’ training samples to perform representation based face recognition was first proposed in [1]. It simultaneously used the original and ‘symmetrical face’ training samples to perform a two-step classification and achieved an outstanding classification result. However, in [1] the “symmetrical face” is devised only for one method. In this paper, we do some improvements on the basis of [1] and combine this “symmetrical faces” transformation with several representation based methods. We exploit all original training samples, left “symmetrical face” training samples and right “symmetrical face” training samples for classification and use the score fusion for ultimate face recognition. The symmetry of the face is first used to generate new samples, which is different from original face image but can really reflect some possible appearance of the face. It effectively overcomes the problem of non-sufficient training samples. The experimental results show that the proposed scheme can be used to improve a number of traditional representation based methods including those that are not presented in the paper.     

Analysis of ν2 of H2Se

The infrared absorption spectrum of ν₂ of H₂Se in the region from 885 to 1347 cm^?1 was obtained with a resolution limit of 0.025 cm^?1 on the University of Denver 50-cm FTIR spectrometer system. We have assigned 1604 lines for the six isotopomers of H₂Se, including 25 lines for the H₂⁷⁴Se isotopomer, and have analyzed them using Watson's A-reduced Hamiltonian in the I^r rotational representation. Ground state constants for each of the five most abundant isotopomers were obtained from fits of microwave transitions combined with weighted averaged ground state combination differences formed from the infrared bands (010), (020), (100), and (001). Upper state constants for each of the five most abundant isotopomers were obtained from least-squares fits of the spectral lines of ν₂, keeping the ground state constants fixed to the values determined from our ground state fits. An alternate set of ground state constants together with isotopic mass adjustment constants for all six isotopomers was determined by simultaneously fitting all available microwave transitions and infrared ground state combination differences. Keeping this set of ground state constants fixed, a single set of upper state constants and isotopic mass adjustment constants for the ν₂ band was determined by a simultaneous fit of infrared spectral lines from all six isotopomers.     

基于WSSRC单样本人脸识别及样本扩充方法研究

由于传统的SRC方法的实时性不强、单样本条件下算法性能低等缺点,提出了融合全局和局部特征的加权超级稀疏表示人脸识别方法(WSSRC),同时采用一种三层级联的虚拟样本产生方法获取冗余样本,将生成的多种表情和多种姿态的新样本当成训练样本,运用WSSRC算法进行人脸识别分类。在单样本的情况下,实验证实在ORL人脸库上该方法比传统的SRC方法提高了15.53%的识别率,使用在FERET 人脸库上则提高7.67%。这样的方法与RSRC 、SSRC、DMMA、DCT-based DMMA、I-DMMA相比,一样具备较好的识别性能。     

Second order time evolution of the multigroup diffusion and P1 equations for radiation transport

An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P₁ forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.     

Accuracy of ferric/ferrous determinations in micas: A comparison of Mössbauer spectroscopy and the Pratt and Wilson wet-chemical methods

We compare ferric/ferrous determinations in mica granules and powders, as obtained by the Pratt and Wilson wet chemical (WC) methods and by Mössbauer spectroscopy (MS). The Pratt method is accurate whereas the Wilson method is not but both have the same precision (σ = 1.2 wt.% FeO). Assuming that the Pratt WC method gave accurate ferric/ferrous ratios leads to a calculated ferric/ferrous ratio of MS recoilless fractions at room temperature for a given biotite sample of f ₃₊/f ₂₊ = 1.009(5). Also, the Mica-Fe and Mica-Mg international standards are shown to be unsuitable, with significant size-fraction dependencies of their oxidation states. These results are discussed in the general context of evaluating accuracy and precision of WC methods by comparisons with MS and of the special problems related to accuracy and precision with MS itself.     

Modular Fisher Discriminant Sparse Representation for robust face recognition

This paper proposes a novel framework for robust face recognition based on sparse representation and discrimination ranking. This method consists of three stages. The first stage partitions each training sample into some overlapped modules and then computes each module's Fisher ratio, respectively. The second stage selects modules which have higher Fisher ratios to comprise a template to filter training and test images. The dictionary is constructed by the filtered training images. The third stage computes the sparse representation of filtered test sample on the dictionary to perform identification. The advantages of the proposed method are listed as follows: the first stage can preserve the local structure. The second stage removes the modules that have little contribution for classification. Then the method uses the retaining modules to classify the test sample by SRC which makes the method robust. Compared with the related methods, experimental results on benchmark face databases verify the advancement of the proposed method. The proposed method not only has a high accuracy but also can be clearly interpreted.     

Split Bregman iteration solution for sparse optimization in image restoration

It is always a challenging task to develop effective and accurate models for robust image restoration. In this paper, the family of sparse and redundant representation frameworks is considered as an alternative for the above problem. The principle of the family is expatiated on the development and research progress. Two well-known denoising methods are presented and analyzed on their properties. The K-SVD algorithm is an effective method for sparse representation. The iteratively approximate algorithms are always used for the solution of sparse coding operations. Here, a convexification of the l₀ norm to the l₁ norm is adopted in the implementation of K-SVD method. Then a split Bregman iteration solution is proposed for l₁ regularization problems in the performance of the sparse representation of the K-SVD algorithm. The split Bregman iterative method is well studied and fused into the famous K-SVD method. The PSNR (Peak Signal to Noise Ratio) and MSSIM (Mean Structural Similarity) are used to evaluate the performance of those methods. Experimental results on different types of images indicate that our proposed method not only achieve comparable results with the state of art methods, but also make the original method more efficient. Besides, it also provides a valuable and promising reference for image restoration techniques.     

Analysis of ν2 of H233S and H234S

We have extended our analysis of the (010) vibrational state of H₂S, this time using Watson's A-reduced Hamiltonian (through P⁸ terms) in the I′ rotational representation. We have determined separate sets of (010) upper state constants for each isotopomer (H₂³²S, H₂³³S, and H₂³⁴S) by fitting the ν₂ spectral lines, keeping the ground state constants fixed to the values determined by Flaud, Camy-Peyret, and Johns. Determinable coefficients for H₂³²S and a slightly revised set of ν₂ line assignments for H₂³³S and H₂³⁴S are also reported.     

Semi-supervised Discriminant Analysis and Sparse Representation-based self-training for Face Recognition

In this paper, we consider the problem of automatic face recognition with limited manually labeled training data. We propose a new semi-supervised self-training approach which is used to automatically augment the manually labeled training set with new unlabeled data. Semi-supervised Discriminant Analysis is used in each iteration of self-training for discriminative dimensionality reduction by making use of both labeled and unlabeled training data. Sparse representation is applied for classification. Experimental results on four independent databases show that our algorithm outperforms other face recognition methods under 3 different configurations, namely transductive, semi-supervised and single training image.     

Refractive index of Ga1−xAlxAs

A semi-empirical method for calculating the room temperature refractive index of Ga_1?xAl_xAs at energies below the direct band edge is presented. This quantity is important in the design of GaAs heterostructure lasers as well as other wave-guiding devices using these materials. The calculated values compare favorably with recent data. The method is shown to be useful for the Ga_1?xAs_xP system as well.