A new graph representation for cable–membrane structures

In this paper, a new graph representation is proposed which is applicable to cable–membrane structures modelled using both one- and two-dimensional elements. The proposed graph representation is an engineering design approach and not based on a mathematically derived representation. The proposed graphs are partitioned using state-of-the-art tools, including METIS [METIS, a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices (1997); J Parallel Distribut Comput (1997)], and JOSTLE [Advances in computational mechanics with parallel and distributed processing (1997); Parallel dynamic graph-partitioning for unstructured meshes (1997); Int J High Perform Comput Appl 13 (1999) 334; Appl Math Model 25 (2000) 123]. The graph representation performs better than standard graph representations for those cases when the rules of geometric locality and uniform element distribution around nodes are violated. The relation of the proposed graph representation to the most advanced hyper-graph representation [IEEE Trans Parallel Distribut Syst 10 (1999) 673; Parallel Comput 26 (2000) 673] is also discussed.     

Full-parameter constrained parsimonious subspace identification with steady-state information for DC–DC converters

A full-parameter constrained parsimonious subspace identification method that incorporates the steady-state a priori information of the system is proposed to model the DC–DC converters. A parsimonious model with fewer parameters is used to represent the system, and then an optimal weighted methods is used to estimate the system parameters matrices by taking into account both dynamical data and steady-state data. Compared with traditional data-driven methods for DC–DC converters, the subspace-based method can simultaneously estimate model structure and parameter with appropriate computational complexity. Moreover, compared with the traditional full-parameter constrained subspace approach, the proposed algorithm can accurately estimate the system parameters with a smaller variance. The experimental results on a DC–DC synchronous buck converter verify the effectiveness and superiority of the proposed method.     

Assessment of time–frequency representation techniques for thoracic sounds analysis

A step forward in the knowledge about the underlying physiological phenomena of thoracic sounds requires a reliable estimate of their time–frequency behavior that overcomes the disadvantages of the conventional spectrogram. A more detailed time–frequency representation could lead to a better feature extraction for diseases classification and stratification purposes, among others. In this respect, the aim of this study was to look for an omnibus technique to obtain the time–frequency representation (TFR) of thoracic sounds by comparing generic goodness-of-fit criteria in different simulated thoracic sounds scenarios. The performance of ten TFRs for heart, normal tracheal and adventitious lung sounds was assessed using time–frequency patterns obtained by mathematical functions of the thoracic sounds. To find the best TFR performance measures, such as the 2D local (ρ_mean) and global (ρ) central correlation, the normalized root-mean-square error (NRMSE), the cross-correlation coefficient (ρ_IF) and the time–frequency resolution (res_TF) were used. Simulation results pointed out that the Hilbert–Huang spectrum (HHS) had a superior performance as compared with other techniques and then, it can be considered as a reliable TFR for thoracic sounds. Furthermore, the goodness of HHS was assessed using noisy simulated signals. Additionally, HHS was applied to first and second heart sounds taken from a young healthy male subject, to tracheal sound from a middle-age healthy male subject, and to abnormal lung sounds acquired from a male patient with diffuse interstitial pneumonia. It is expected that the results of this research could be used to obtain a better signature of thoracic sounds for pattern recognition purpose, among other tasks.     

Spatial–spectral locality constrained elastic net hypergraph for hyperspectral image clustering

Hypergraph is an effective method used to represent the contextual correlation within hyperspectral imagery for clustering. Nevertheless, how to discover the closely correlated samples to form hyperedges is the key issue for constructing an informative hypergraph. In this article, a new spatial–spectral locality constrained elastic net hypergraph learning model is proposed for hyperspectral image clustering (i.e. unsupervised classification). In order to utilize the spatial–spectral correlation among the pixels in hyperspectral images, first, we construct a locality-constrained dictionary by selecting K relevant pixels within a spatial neighbourhood, which activates the most correlated atoms and suppresses the uncorrelated ones. Second, each pixel is represented as a linear combination of the atoms in the dictionary under the elastic net regularization. Third, based on the obtained representations, the pixels and their most related pixels are linked as hyperedges, which can effectively capture high–order relationships among the pixels. Finally, a hypergraph Laplacian matrix is built for unsupervised learning. Experiments have been conducted on two widely used hyperspectral images, and the results show that the proposed method can achieve a superior clustering performance when compared to state-of-the-art methods.     

Predator–prey optimization based clustering algorithm for wireless sensor networks

Neural Computing and Applications - Grouping the sensor nodes into clusters is an effective way to organize wireless sensor networks and to prolong the networks’ lifetime. This paper presents...     

General split gaussian Cross–Entropy clustering

Robust mixture models approaches, which use non-normal distributions have recently been upgraded to accommodate asymmetric data. In this article we propose a new method based on the General Split Gaussian distribution (GSG) and Cross–Entropy Clustering (CEC). The GSG is a flexible density with reasonably small number of parameters which are easy to estimate. We combine the model with a clustering method which allows to treat groups separately and estimate parameters individually in each cluster. Consequently, we introduce an effective clustering algorithm which deals with non-normal data.     

A linearized input–output representation of flexible multibody systems for control synthesis

In this paper, a linearized input–output representation of flexible multibody systems is proposed in which an arbitrary combination of positions, velocities, accelerations, and forces can be taken as input variables and as output variables. The formulation is based on a nonlinear finite element approach in which a multibody system is modeled as an assembly of rigid body elements interconnected by joint elements such as flexible hinges and beams. The proposed formulation is general in nature and can be applied for prototype modeling and control system analysis of mechatronic systems. Application of the theory is illustrated through a detailed model development of an active vibration isolation system for a metrology frame of a lithography machine.     

SWGMM: a semi-wrapped Gaussian mixture model for clustering of circular–linear data

Finite mixture models are widely used to perform model-based clustering of multivariate data sets. Most of the existing mixture models work with linear data; whereas, real-life applications may involve multivariate data having both circular and linear characteristics. No existing mixture models can accommodate such correlated circular–linear data. In this paper, we consider designing a mixture model for multivariate data having one circular variable. In order to construct a circular–linear joint distribution with proper inclusion of correlation terms, we use the semi-wrapped Gaussian distribution. Further, we construct a mixture model (termed SWGMM) of such joint distributions. This mixture model is capable of approximating the distribution of multi-modal circular–linear data. An unsupervised learning of the mixture parameters is proposed based on expectation maximization method. Clustering is performed using maximum a posteriori criterion. To evaluate the performance of SWGMM, we choose the task of color image segmentation in LCH space. We present comprehensive results and compare SWGMM with existing methods. Our study reveals that the proposed mixture model outperforms the other methods in most cases.     

Asymmetric clustering using the alpha–beta divergence

We propose the use of an asymmetric dissimilarity measure in centroid-based clustering. The dissimilarity employed is the Alpha–Beta divergence (AB-divergence), which can be asymmetrized using its parameters. We compute the degree of asymmetry of the AB-divergence on the basis of the within-cluster variances. In this way, the proposed approach is able to flexibly model even clusters with significantly different variances. Consequently, this method overcomes one of the major drawbacks of the standard symmetric centroid-based clustering.     

A Neumann series of Bessel functions representation for solutions of Sturm–Liouville equations

A Neumann series of Bessel functions (NSBF) representation for solutions of Sturm–Liouville equations and for their derivatives is obtained. The representation possesses an attractive feature for applications: for all real values of the spectral parameter \(\omega \) the estimate of the difference between the exact solution and the approximate one (the truncated NSBF) depends on N (the truncation parameter) and the coefficients of the equation and does not depend on \(\omega \). A similar result is valid when \(\omega \in {\mathbb {C}}\) belongs to a strip \(\left| \hbox {Im }\omega \right| <C\). This feature makes the NSBF representation especially useful for applications requiring computation of solutions for large intervals of \(\omega \). Error and decay rate estimates are obtained. An algorithm for solving initial value, boundary value or spectral problems for the Sturm–Liouville equation is developed and illustrated on a test problem.     

A hybrid genetic algorithm–fuzzy c-means approach for incomplete data clustering based on nearest-neighbor intervals

Incomplete data are often encountered in data sets used in clustering problems, and inappropriate treatment of incomplete data can significantly degrade the clustering performance. In view of the uncertainty of missing attributes, we put forward an interval representation of missing attributes based on nearest-neighbor information, named nearest-neighbor interval, and a hybrid approach utilizing genetic algorithm and fuzzy c-means is presented for incomplete data clustering. The overall algorithm is within the genetic algorithm framework, which searches for appropriate imputations of missing attributes in corresponding nearest-neighbor intervals to recover the incomplete data set, and hybridizes fuzzy c-means to perform clustering analysis and provide fitness metric for genetic optimization simultaneously. Several experimental results on a set of real-life data sets are presented to demonstrate the better clustering performance of our hybrid approach over the compared methods.     

A novel minorization–maximization framework for simultaneous feature selection and clustering of high-dimensional count data

Pattern Analysis and Applications - Count data are commonly exploited in machine learning and computer vision applications; however, they often suffer from the well-known curse of dimensionality,...     

The subspace Gaussian mixture model—A structured model for speech recognition

We describe a new approach to speech recognition, in which all Hidden Markov Model (HMM) states share the same Gaussian Mixture Model (GMM) structure with the same number of Gaussians in each state. The model is defined by vectors associated with each state with a dimension of, say, 50, together with a global mapping from this vector space to the space of parameters of the GMM. This model appears to give better results than a conventional model, and the extra structure offers many new opportunities for modeling innovations while maintaining compatibility with most standard techniques.     

An unsupervised approach for co-channel speech separation using Hilbert–Huang transform and Fuzzy C-Means clustering

In this paper we discuss an unsupervised approach for co-channel speech separation where two speakers are speaking simultaneously over same channel. We propose a two stage separation process where the initial stage is based on empirical mode decomposition (EMD) and Hilbert transform generally known as Hilbert–Huang transform. EMD decomposes the mixed signal into oscillatory functions known as intrinsic mode functions. Hilbert transform is applied to find the instantaneous amplitudes and Fuzzy C-Means clustering is applied to group the speakers at initial stage. In second stage of separation speaker groups are transformed into time–frequency domain using short time Fourier transform (STFT). Time–frequency ratio’s are computed by dividing the STFT matrix of mixed speech signal and STFT matrix of stage1 recovered speech signals. Histogram of the ratios obtained can be used to estimate the ideal binary mask for each speaker. These masks are applied to the speech mixture and the underlying speakers are estimated. Masks are estimated from the speech mixture and helps in imputing the missing values after stage1 grouping of speakers. Results obtained show significant improvement in objective measures over other existing single-channel speech separation methods.     

FreeFEM++ code for reaction-diffusion equation–based topology optimization: for high-resolution boundary representation using adaptive mesh refinement

Structural and Multidisciplinary Optimization - In this article, we present a simple FreeFEM++ code to represent high-resolution boundaries of the optimal shape using reaction-diffusion...     

Dempster–Shafer clustering using Potts spin mean field theory

 In this article we investigate a problem within Dempster–Shafer theory where 2 ^q −1 pieces of evidence are clustered into q clusters by minimizing a metaconflict function, or equivalently, by minimizing the sum of weight of conflict over all clusters. Previously one of us developed a method based on a Hopfield and Tank model. However, for very large problems we need a method with lower computational complexity. We demonstrate that the weight of conflict of evidence can, as an approximation, be linearized and mapped to an antiferromagnetic Potts spin model. This facilitates efficient numerical solution, even for large problem sizes. Optimal or nearly optimal solutions are found for Dempster–Shafer clustering benchmark tests with a time complexity of approximately O(N ²log² N). Furthermore, an isomorphism between the antiferromagnetic Potts spin model and a graph optimization problem is shown. The graph model has dynamic variables living on the links, which have a priori probabilities that are directly related to the pairwise conflict between pieces of evidence. Hence, the relations between three different models are shown.     

Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems

We prove a dichotomy theorem for the rank of propositional contradictions, uniformly generated from first-order sentences, in both the Lovász-Schrijver (LS) and Sherali-Adams (SA) refutation systems. More precisely, we first show that the propositional translations of first-order formulae that are universally false, that is, fail in all finite and infinite models, have LS proofs whose rank is constant, independent of the size of the (finite) universe. In contrast to that, we prove that the propositional formulae that fail in all finite models, but hold in some infinite structure, require proofs whose SA rank grows polynomially with the size of the universe. Until now, this kind of so-called complexity gap theorem has been known for tree-like Resolution and, in somehow restricted forms, for the Resolution and Nullstellensatz systems. As far as we are aware, this is the first time the Sherali-Adams lift-and-project method has been considered as a propositional refutation system (since the conference version of this paper, SA has been considered as a refutation system in several further papers). An interesting feature of the SA system is that it simulates LS, the Lovász-Schrijver refutation system without semi-definite cuts, in a rank-preserving fashion.