A sparse representation-based classifier (SRC) is developed and shows great potential for real-world face recognition. This paper presents a dimensionality reduction method that fits SRC well. SRC ...adopts a class reconstruction residual-based decision rule, we use it as a criterion to steer the design of a feature extraction method. The method is thus called the SRC steered discriminative projection (SRC-DP). SRC-DP maximizes the ratio of between-class reconstruction residual to within-class reconstruction residual in the projected space and thus enables SRC to achieve better performance. SRC-DP provides low-dimensional representation of human faces to make the SRC-based face recognition system more efficient. Experiments are done on the AR, the extended Yale B, and PIE face image databases, and results demonstrate the proposed method is more effective than other feature extraction methods based on the SRC.
Symmetry is one of the central mysteries of quantum mechanics and plays an essential role in multipartite entanglement. In this paper, we consider the separability problem of quantum states in the ...symmetric space. We establish the relation between the separability of multiqubit symmetric states and the decomposability of Hermitian positive semidefinite matrices. This relation allows us to exchange concepts and ideas between quantum entanglement and Vandermonde decomposition. As an application, we build a suite of tools to investigate the decomposability and show the power of this relation both in theoretical and numerical aspects. For theoretical results, we establish the witness for the decomposability similar to the entanglement witness and characterize the decomposability of some subclasses of matrices. Furthermore, we provide the necessary conditions for the decomposability. Besides, we suggest a numerical algorithm to check whether a given matrix is decomposable. The numerical examples are tested to show the effectiveness.
In this paper, we study canonical correlation analysis (CCA), which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables. The ...main contributions of the paper are: 1) to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple CCA problem, 2) to obtain the explicit characterization for all solutions of the multiple CCA problem even when the corresponding covariance matrices are singular, 3) to develop a new sparse CCA algorithm, and 4) to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the CCA problem. We test several simulated and real-world datasets in gene classification and cross-language document retrieval to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed method is competitive with the state-of-the-art sparse CCA algorithms.
It has always been a challenging task to develop a fast and an efficient incremental linear discriminant analysis (ILDA) algorithm. For this purpose, we conduct a new study for linear discriminant ...analysis (LDA) in this paper and develop a new ILDA algorithm. We propose a new batch LDA algorithm called LDA/QR. LDA/QR is a simple and fast LDA algorithm, which is obtained by computing the economic QR factorization of the data matrix followed by solving a lower triangular linear system. The relationship between LDA/QR and uncorrelated LDA (ULDA) is also revealed. Based on LDA/QR, we develop a new incremental LDA algorithm called ILDA/QR. The main features of our ILDA/QR include that: 1) it can easily handle the update from one new sample or a chunk of new samples; 2) it has efficient computational complexity and space complexity; and 3) it is very fast and always achieves competitive classification accuracy compared with ULDA algorithm and existing ILDA algorithms. Numerical experiments based on some real-world data sets demonstrate that our ILDA/QR is very efficient and competitive with the state-of-the-art ILDA algorithms in terms of classification accuracy, computational complexity, and space complexity.
Aluminum nitride (AlN) ceramic is widely used in lots of fields, but its high-efficiency preparation still needs to be developed. In this paper, AlN nanoparticles are prepared from urea and aluminum ...chloride hydrate by a facile urea glass route in NH3 atmosphere. The products are characterized by X-ray powder diffraction, laser particle size analyzer, scanning electron microscope and transmission electron microscope. The results show that the urea content present less effects on the crystal phase of the AlN ceramic powder. Hexagonal aluminum nitride (h-AlN) nanoparticles with high purity can be obtained when the heat treatment temperature is above 900 °C. The crystallite size of AlN nanoparticles is enlarged with increasing temperature. The optimized molar ratio of urea to aluminum salt is 6 and the sintering temperature is 1000 °C. The average crystallite size of this product is 17.0 nm and the average particle size (D50) is 159.5 nm. The element distributions of N and Al in the AlN nanoparticles are highly coincident, which means that N and Al atoms in ceramic nanoparticles are well combined.
•High purity AlN nanoparticles were prepared by a facile urea glass route in NH3 atmosphere.•Pure h-AlN nanoparticles were obtained by increasing the temperature above 900 °C.•The microstructure of AlN nanoparticles were studied by HRTEM.
In this paper we present a new implementation for the null space based linear discriminant analysis. The main features of our implementation include: (i) the optimal transformation matrix is obtained ...easily by only orthogonal transformations without computing any eigendecomposition and singular value decomposition (SVD), consequently, our new implementation is eigendecomposition-free and SVD-free; (ii) its main computational complexity is from a economic QR factorization of the data matrix and a economic QR factorization of a
n×
n matrix with column pivoting, here
n is the sample size, thus our new implementation is a fast one. The effectiveness of our new implementation is demonstrated by some real-world data sets.
Linear discriminant analysis (LDA) as a well-known supervised dimensionality reduction method has been widely applied in many fields. However, the lack of sparsity in the LDA solution makes ...interpretation of the results challenging. In this paper, we propose a new model for sparse uncorrelated LDA (ULDA). Our model is based on the characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum ℓ 1 -norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as an ℓ 1 -minimization problem with orthogonality constraint. To solve this problem, we devise two algorithms: 1) by applying the linearized alternating direction method of multipliers and 2) by applying the accelerated linearized Bregman method. Simulation studies and high-dimensional real data examples demonstrate that our algorithms not only compute extremely sparse solutions but also perform well in classification.
•The tritium breeding rate (TBR) of Li2PbxTi1-xO3 (0 < x < 0.9) was evaluated by MCNP4C.•The TBR of Li2PbxTi1-xO3 rises with increasing Pb content and neutron source energy.•Li2PbxTi1-xO3 in the ...inboard blanket could simplify the solid blanket structure.•In as-synthesized powders, Li2PbO3 combines with Li2TiO3 tightly at the nano-scale.
In deuterium–tritium (D-T) fusion reactors, the design of tritium breeding materials plays very critical role in tritium self-sufficiency. Compared to materials like Li2O, Li2TiO3 has a weaker tritium breeding capability, because of the lower density of Li. For this reason, there is a need to further explore new lithium-containing ceramics. In this paper we have designed a new tritium-breeding Li2PbxTi1-xO3. Tritium production calculations are performed on a 2 m thickness spherical shells of Li2PbxTi1-xO3 with four types of 6Li abundance (7.5 %, 20 %, 50 %, 90 %) and six species of neutron source energy（0.025 eV, 1 MeV, 2.5 MeV, 2.7 MeV, 7.4 MeV and 14.1 MeV）located at the center. It is shown that such a modification may result in the tritium breeding ratio increase to 1.4 in the sphere. Based on simulations, the Li2Pb0.5Ti0.5O3 was synthesized via the sol–gel route, and the microscopic morphology of Li2Pb0.5Ti0.5O3 were briefly investigated. Upon analysis, it's found that lead is uniformly present in the ceramic material in the form of Li2PbO3. In comparison with Li2TiO3 ceramics, Li2PbxTi1-xO3 exhibits stronger tritium breeding capability.
In system design the exact model matching problem with stability consists of compensating a given system, using a realizable control law of a specified structure, in order to ensure the stability of ...the compensated system and achieve a target closed-loop transfer function. In this paper we develop a novel numerical method to verify the solvability of the problem for left invertible systems and further construct a desired solution. Our method has a complexity which is cubic in the state dimension of the system and the desired model and can be implemented in a numerically reliable way.
In this technical note, we develop a numerically reliable method to design an interactor for a general descriptor system relative to a stability region C g and an offending zero set Ω. Our main ...result is based on a condensed form. This condensed form is independent of the offending zeros Ω, and is computed using only orthogonal transformations and hence is numerically backward stable.
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