7,332 research outputs found
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Zero attracting recursive least squares algorithms
No full textThe l1-norm sparsity constraint is a widely used
technique for constructing sparse models. In this contribution, two zero-attracting recursive least squares algorithms, referred to as ZA-RLS-I and ZA-RLS-II, are derived by employing the l1-norm of parameter vector constraint to facilitate the model sparsity. In order to achieve a closed-form solution, the l1-norm of the parameter vector is approximated by an adaptively weighted l2-norm, in which the weighting factors are set as the inversion of the associated l1-norm of parameter estimates that are readily available in the adaptive learning environment. ZA-RLS-II is computationally more efficient than ZA-RLS-I by exploiting the known results from linear algebra as well as the sparsity of the
system. The proposed algorithms are proven to converge, and adaptive sparse channel estimation is used to demonstrate the effectiveness of the proposed approach
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Semi-blind joint channel estimation and data detection on sphere manifold for MIMO with high-order QAM signaling
No full textA low-complexity semi-blind scheme is proposed for joint channel estimation and data detection on sphere manifold for multiple-input multiple-output (MIMO) systems with high-order quadrature amplitude modulation signaling. Specifically, the optimal channel estimator is expressed in the least squares form in terms of the received signals and unknown transmitted data, and by splitting the channel and transmitted data into their real parts and imaginary parts, the data detection becomes a problem defined on a scaled sphere manifold in the real domain. Our semi-blind algorithm consists of three stages: (i)~a few training symbols are employed to provide a rough initial MIMO channel estimate which in turn yields the initial zero-forcing (ZF) estimate of data samples; (ii)~the Riemannian conjugate gradient algorithm is used to estimate the data samples in real domain, and the detected data samples are used to estimate the final MIMO channel matrix; and (iii)~the final ZF data detection is carried out based on the final MIMO channel estimate. In particular, we present the first order Riemannian geometry of the sphere manifold which is utilized in the Riemannian conjugate gradient algorithm for solving (ii). Simulation results are employed to demonstrate the effectiveness of the proposed approach
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Complex-valued B-spline neural networks for modeling and inverting Hammerstein systems
No full textMany communication signal processing applications involve modeling and inverting complex-valued (CV) Hammerstein systems. We develop a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. In particular, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first-order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalization of Hammerstein channels
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A l -norm penalized orthogonal forward regression
No full textA l1-norm penalised orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leave-one-out mean square error (LOOMSE), by defining a new l1-norm penalised cost function in the constructed orthogonal space and associating each orthogonal basis with an individually tunable regularisation parameter. Due to orthogonality, the LOOMSE can be analytically computed without actually splitting the data-set, and moreover a closed form of the optimal regularisation parameter is derived by greedily minimising the LOOMSE incrementally. We also propose a simple formula for adaptively detecting and removing regressors to an inactive set so that the computational cost of the algorithm is significantly reduced. Examples are included to demonstrate the effectiveness of this new l1-POFR approach
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Particle swarm optimisation assisted classification using elastic net prefiltering
No full textA novel two-stage construction algorithm for linear-in-the-parameters classifiers is proposed, aiming at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage to construct a sparse linear-in-the-parameters classifier. For the first stage learning of generating the prefiltered signal, a two-level algorithm is introduced to maximise the model's generalisation capability, in which an elastic net model identification algorithm using singular value decomposition is employed at the lower level while the two regularisation parameters are selected by maximising the Bayesian evidence using a particle swarm optimization algorithm. Analysis is provided to demonstrate how "Occam's razor" is embodied in this approach. The second stage of sparse classifier construction is based on an orthogonal forward regression with the D-optimality algorithm. Extensive experimental results demonstrate that the proposed approach is effective and yields competitive results for noisy data set
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Nonlinear identification using orthogonal forward regression with nested optimal regularization
No full textAn efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm
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Sparse density estimation on the multinomial manifold
No full textA new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimator
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Sparse model construction using coordinate descent optimization
No full textWe propose a new sparse model construction method aimed at maximizing a model’s generalisation capability for a large class of linear-in-the-parameters models. The coordinate descent optimization algorithm is employed with a modified l1-penalized least squares cost function in order to estimate a single parameter and its regularization parameter simultaneously based on the leave one out mean square error (LOOMSE). Our original contribution is to derive a closed form of optimal LOOMSE regularization parameter for a single term model, for which we show that the LOOMSE can be analytically computed without actually splitting the data set leading to a very simple parameter estimation method. We then integrate the new results within the coordinate descent optimization algorithm to update model parameters one at the time for linear-in-the-parameters models. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approache
A study of the modern Chinese novel, Gao Yubao and its author Gao Yubao
No full textGao Yubao, a soldier in the Chinese People's Liberation Army, was nearly illiterate when he began to write his autobiographical novel, Gao Yubao, in 1949. The PLA's literary branch helped him finish the novel and after its publication Gao and his struggle to become literate by writing a novel served as an inspiration for others striving for education. Gao Yubao was republished several times up until as late as the 1970's and each time it was republished it was revised. This paper traces the history of the novel Gao Yubao and its author with special attention being given to comparing the changes made in the various editions of the novel. The conflicts between amateurism and professionalism and between fact and romanticization and those conflicts inherent in the constant revisings demanded of an already revised work are shown to be unresolvable because of the nature of contemporary Chinese literature.Arts, Faculty ofAsian Studies, Department ofGraduat
Accommodating Nomocharis in Lilium (Liliaceae)
No full textControversy regarding the status of the genus Nomocharis Franchet (1889: 113) has been undergoing since its recognition by Franchet (1889). Recent molecular studies (Nishikawa et al. 1999, Hayashi & Kawano 2000, Nishikawa et al. 2001, Ronsted et al. 2005, Peruzzi et al. 2009) have resolved Nomocharis as being nested within Lilium Linaeus (1753: 302). Results of our own previous studies (Gao et al. 2012, Gao et al. 2013a, Gao et al. 2013b), with expanded sampling of species of Nomocharis have been congruent with those of previous studies by others. Thus recognition of Nomocharis would render Lilium paraphyletic. We prefer to recognize a monophyletic Lilium here, although paraphyletic groups are sometimes advocated in literature (e.g., Brummitt, 2014; Ehrendorfer & Barfuss, 2014; George, 2014; Horandl, 2014; Stuessy & Horandl, 2014; Stuessy et al., 2014). Most recently, we proposed that the morphological divergence between Nomocharis and Lilium was the result of habitat specialization (Gao et al. 2015). The extensive introgression caused by hybridization within Lilium and Nomocharis (Gao et al. 2013a, 2015) supports a single-genus concept
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