Nonlinear Space Research Articles

Within‐component and between‐component multi‐kernel discriminating correlation analysis for colour face recognition

The key problem of colour face recognition technique is how to take full advantage of the colour information and extract effective discriminating features. To solve this problem, the authors propose a novel non-linear feature extraction approach for colour face recognition, named dual multi-kernel discriminating correlation analysis, which separately maps different colour components of face images into different non-linear kernel spaces, and then implements multi-kernel learning and discriminant analysis with the correlation metric not only within each colour component but also between diverse components. Then, to choose the optimum kernel space for each colour component and select the most suitable colour space for their approach, they design a kernel selection strategy and a colour space selection strategy, respectively. Experimental results in the face recognition grand challenge version 2 and labelled faces in the wilds databases validate the effectiveness of the proposed approach and two strategies.

Dimension reduction based on a penalized kernel support vector machine model

Prediction and dimension reduction play increasingly significant roles in high-dimensional data analysis; however, they suffer from model inaccuracy, selection inconsistency and a prohibitively expensive computational cost as the model dimension increases exponentially. Although a support vector machine (SVM) is one of the most powerful forecasting approaches that are widely used by the research community, it does not provide an interpretable model that violates the principle of Occam’s razor. In classical regression problems, a penalized linear SVM model for the dimension reduction task has been investigated in the linear feature space under the assumption that the underlying true model is linear. In this paper, the penalized kernel SVM (PKSVM) model is proposed and investigated combining with a SVM information criterion (SVMIC) for the dimension reduction task in the nonlinear kernel space using radial basis function for prediction and model representation. Instead of pursuing sparsity in the original feature space of the SVM, dimension reduction is performed in the kernel feature space. Computationally, a fast and simple-to-implement algorithm is derived. Furthermore, both SVMIC and cross-validation are utilized to select the kernel and regularization parameters to guarantee the model consistency. Real data applications including microarray data analysis and global solar radiation forecasting are provided. The first application selected significant components in genetic study and the important data information is extracted for grid-connected photovoltaic installations in the second application. The proposed dimension reduction technique avoids the model redundancy which is of great importance for knowledge discovery.

An adaptive RGB colour enhancement formulation for logarithmic image processing-based algorithms

This paper presents an effective colour enhancement framework for statistical and logarithmic image processing (LIP)-based enhancement algorithms. The proposed approach utilizes the fusion of partial, multiple computed luminance channels with colour image channel statistics obtained from the input colour image for adaptive colour enhancement. The proposed scheme does not modify the image intensity channel, avoiding colour fading typically observed in colour images processed with conventional algorithms. The colour enhancement scheme compensates for the weaknesses of greyscale-based contrast enhancement and illumination normalization algorithms by focusing on preserving/restoring or enhancing colour. The proposed system avoids the conversion to complex, non-linear colour spaces such as HSI and HSV while producing similar results without manual adjustment of parameters. Additionally, an adaptive scheme for detection of images with unbalanced colour and uneven illumination is combined with the proposed system. Results show that the proposed scheme augments colour results of greyscale-based contrast enhancement algorithms and is relatively less complex compared to most algorithms in the literature.

Performance Assessment of a Coupled Particle Swarm Optimization and Network Flow Programming Model for Optimum Water Allocation

Water resources allocation problems are mainly categorized in two classes of simulation and optimization. In most cases, optimization problems due to the number of variables, constraints and nonlinear feasible search space are known as a challenging subject in the literature. In this research, by coupling particle swarm optimization (PSO) algorithm and a network flow programming (NFP) based river basin simulation model, a PSO-NFP hybrid structure is constructed for optimum water allocation planning. In the PSO-NFP model, the NFP core roles as the fast inner simulation engine for finding optimum values for a large number of water discharges in the network links (rivers and canals) and nodes (reservoirs and demands) while the heuristic PSO algorithm forms the outer optimization cover to search for the optimum values of reservoirs capacities and their storage priorities. In order to assess the performance of the PSO-NFP model, three hypothetical test problems are defined, and their equivalent nonlinear mathematical programs are developed in LINGO and the results are compared. Finally, the PSO-NFP model is applied in solving a real river basin water allocation problem. Results indicate that the applied method of coupling PSO and NFP has an efficient ability for handling river basin-scale water resources optimization problems.

Nonlinear field space cosmology

We consider the FRW cosmological model in which the matter content of universe (playing a role of inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced Nonlinear Field Space Theory (NFST), where physical phase space of a given field is assumed to be compactified at large energies. For our analysis we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector we find that nonlinearity of the field phase space is becoming relevant for large volumes of universe and then it can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where nontrivial nature of its phase space can be neglected, while there is a non-vanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.

Nonlinear subspace clustering for image clustering

We present in this paper a nonlinear subspace clustering (NSC) method for image clustering. Unlike most existing subspace clustering methods which only exploit the linear relationship of samples to learn the affine matrix, our NSC reveals the multi-cluster nonlinear structure of samples via a nonlinear neural network. While kernel-based clustering methods can also address the nonlinear issue of samples, this type of methods suffers from the scalability issue. Specifically, our NSC employs a feed-forward neural network to map samples into a nonlinear space and performs subspace clustering at the top layer of the network, so that the mapping functions and the clustering issues are iteratively learned. Otherwise, our NSC applys a similarity measure based on the grouping effect to capture the local structure of data. Experimental results illustrate that our NSC outperforms the state-of-the-arts.

Cost-sensitive transfer kernel canonical correlation analysis for heterogeneous defect prediction

Cross-project defect prediction (CPDP) refers to predicting defects in a target project using prediction models trained from historical data of other source projects. And CPDP in the scenario where source and target projects have different metric sets is called heterogeneous defect prediction (HDP). Recently, HDP has received much research interest. Existing HDP methods only consider the linear correlation relationship among the features (metrics) of the source and target projects, and such models are insufficient to evaluate nonlinear correlation relationship among the features. So these methods may suffer from the linearly inseparable problem in the linear feature space. Furthermore, existing HDP methods do not take the class imbalance problem into consideration. Unfortunately, the imbalanced nature of software defect datasets increases the learning difficulty for the predictors. In this paper, we propose a new cost-sensitive transfer kernel canonical correlation analysis (CTKCCA) approach for HDP. CTKCCA can not only make the data distributions of source and target projects much more similar in the nonlinear feature space, where the learned features have favorable separability, but also utilize the different misclassification costs for defective and defect-free classes to alleviate the class imbalance problem. We perform the Friedman test with Nemenyi’s post-hoc statistical test and the Cliff’s delta effect size test for the evaluation. Extensive experiments on 28 public projects from five data sources indicate that: (1) CTKCCA significantly performs better than the related CPDP methods; (2) CTKCCA performs better than the related state-of-the-art HDP methods.

Martingale problem under nonlinear expectations

We formulate and solve the martingale problem in a nonlinear expectation space. Unlike the classical work of Stroock and Varadhan (1969) where the linear operator in the associated PDE is naturally defined from the corresponding diffusion process, the main difficulty in the nonlinear setting is to identify an appropriate class of nonlinear operators for the associated fully nonlinear PDEs. Based on the analysis of the martingale problem, we introduce the notion of weak solution for stochastic differential equations under nonlinear expectations and obtain an existence theorem under the H\"older continuity condition of the coefficients. The approach to establish the existence of weak solutions generalizes the classical Girsanov transformation method in that it no longer requires the two (probability) measures to be absolutely continuous.

A perturbative approach to the redshift space correlation function: beyond the Standard Model

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model which is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with ⩽ 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpch ⩽ s ⩽ 180Mpc/h. Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.

Sequence2Vec: a novel embedding approach for modeling transcription factor binding affinity landscape.

MotivationAn accurate characterization of transcription factor (TF)-DNA affinity landscape is crucial to a quantitative understanding of the molecular mechanisms underpinning endogenous gene regulation. While recent advances in biotechnology have brought the opportunity for building binding affinity prediction methods, the accurate characterization of TF-DNA binding affinity landscape still remains a challenging problem.ResultsHere we propose a novel sequence embedding approach for modeling the transcription factor binding affinity landscape. Our method represents DNA binding sequences as a hidden Markov model which captures both position specific information and long-range dependency in the sequence. A cornerstone of our method is a novel message passing-like embedding algorithm, called Sequence2Vec, which maps these hidden Markov models into a common nonlinear feature space and uses these embedded features to build a predictive model. Our method is a novel combination of the strength of probabilistic graphical models, feature space embedding and deep learning. We conducted comprehensive experiments on over 90 large-scale TF-DNA datasets which were measured by different high-throughput experimental technologies. Sequence2Vec outperforms alternative machine learning methods as well as the state-of-the-art binding affinity prediction methods.Availability and implementationOur program is freely available at https://github.com/ramzan1990/sequence2vec.Supplementary information Supplementary data are available at Bioinformatics online.

Nonlinear inverse heat conduction: Digitally filtered space marching with phase-plane and cross-correlation analyses

ABSTRACTThis paper utilizes concepts extracted from phase-plane and cross-correlation analyses for estimating the optimal regularization parameter required by a nonlinear space marching inverse heat conduction method. The regularization parameter for this approach is based on the cut-off frequency used in a low-pass Gauss digital filter for preprocessing the in-depth temperature data. The simulation uses two in-depth thermocouples which are representative of a physical experiment. Numerical results indicate a high level of robustness as the best prediction is extracted from the prediction space over the spectrum of cut-off frequencies. The feasibility and effectiveness of phase-plane and cross-correlation analyses are discussed.

Multi-criteria algorithms for portfolio optimization under practical constraints

Abstract Selection of promising assets and allocating capital among them is a crucial part of the financial decision-making process. Modern portfolio theory formulated it as a quadratic optimization problem of maximizing expected returns and minimizing the risk of the portfolio. This problem was modified to incorporate investor's preferences resulting in discrete non-linear search space which cannot be handled by traditional quadratic programming approaches. Relevant literature shows the success of evolutionary algorithms in modelling some of these preferences Multi-criteria algorithms for portfolio optimization under practical constraintsin a constrained optimization problem. This study proposes a candidate generation procedure and a repair mechanism for practical portfolio optimization model in multi-objective evolutionary algorithm (MOEA) settings. Both these methods together can handle a larger class of constraints namely cardinality, pre-assignment, budget, quantity (floor and ceiling) and round-lot constraints. Proposed methods can easily be incorporated into existing evolutionary algorithms. To evaluate their effectiveness, four MOEAs namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2), Global Weighting Achievement Scalarizing Function Genetic Algorithm (GWASFGA) and Pareto Envelope-based Selection Algorithm-II (PESA-II) have been adapted and their capability of approximating unconstrained efficient frontier are discussed. For empirical testing, seven datasets involving maximum up to 1290 assets are used. All the adapted algorithms are compared and evaluated on the basis of five well-known performance metrics for MOEAs. The potential of our adapted algorithms is presented in comparison with existing MOEAs for the identical problems.

A comparative study on the performance of neural networks in visual guidance and feedback applications

ABSTRACTVision-based systems increase the flexibility of industrial automation applications by providing non-touching sensory information for processing and feedback. Artificial neural networks (ANNs) help such conformities through prediction in overcoming nonlinear computational spaces. They transform multiple possibilities of outcomes or regions of uncertainty posed by the system components towards solution spaces. Trained networks impart a certain level of intelligence to robotic systems. This paper discusses two applications of machine vision. The 3 degrees of freedom (DOF) robotic assembly provides an accurate cutting of soft materials with visual guidance using pixel elimination. The 6-DOF robot combines visual guidance from a supervisory camera and visual feedback from an attached camera. Using a switching approach in the control strategy, pick and place applications are carried out. With the inclusion of ANN to make the strategies intelligent, both the systems performed better with regard to computational time and convergence. The networks make use of the extracted image features from the scene for different applications. Simulation and experimental results validate the proposed schemes and show the effectiveness of ANN in machine vision applications.

2MTF – VI. Measuring the velocity power spectrum

We present measurements of the velocity power spectrum and constraints on the growth rate of structure $f\sigma_{8}$, at redshift zero, using the peculiar motions of 2,062 galaxies in the completed 2MASS Tully-Fisher survey (2MTF). To accomplish this we introduce a model for fitting the velocity power spectrum including the effects of non-linear Redshift Space Distortions (RSD), allowing us to recover unbiased fits down to scales $k=0.2\,h\,{\rm Mpc}^{-1}$ without the need to smooth or grid the data. Our fitting methods are validated using a set of simulated 2MTF surveys. Using these simulations we also identify that the Gaussian distributed estimator for peculiar velocities of \cite{Watkins2015} is suitable for measuring the velocity power spectrum, but sub-optimal for the 2MTF data compared to using magnitude fluctuations $\delta m$, and that, whilst our fits are robust to a change in fiducial cosmology, future peculiar velocity surveys with more constraining power may have to marginalise over this. We obtain \textit{scale-dependent} constraints on the growth rate of structure in two bins, finding $f\sigma_{8} = [0.55^{+0.16}_{-0.13},0.40^{+0.16}_{-0.17}]$ in the ranges $k = [0.007-0.055, 0.55-0.150]\,h\,{\rm Mpc}^{-1}$. We also find consistent results using four bins. Assuming scale-\textit{independence} we find a value $f\sigma_{8} = 0.51^{+0.09}_{-0.08}$, a $\sim16\%$ measurement of the growth rate. Performing a consistency check of General Relativity (GR) and combining our results with CMB data only we find $\gamma = 0.45^{+0.10}_{-0.11}$, a remarkable constraint considering the small number of galaxies. All of our results are completely independent of the effects of galaxy bias, and fully consistent with the predictions of GR (scale-independent $f\sigma_{8}$ and $\gamma\approx0.55$).

Imprint of non-linear effects on HI intensity mapping on large scales

Intensity mapping of the HI brightness temperature provides a unique way of tracing large-scale structures of the Universe up to the largest possible scales. This is achieved by using a low angular resolution radio telescopes to detect emission line from cosmic neutral Hydrogen in the post-reionization Universe. We use general relativistic perturbation theory techniques to derive for the first time the full expression for the HI brightness temperature up to third order in perturbation theory without making any plane-parallel approximation. We use this result and the renormalization prescription for biased tracers to study the impact of nonlinear effects on the power spectrum of HI brightness temperature both in real and redshift space. We show how mode coupling at nonlinear order due to nonlinear bias parameters and redshift space distortion terms modulate the power spectrum on large scales. The large scale modulation may be understood to be due to the effective bias parameter and effective shot noise.

Semantic Image Retrieval with Feature Space Rankings

Learning to hash is receiving increasing research attention due to its effectiveness in addressing the large-scale similarity search problem. Most of the existing hashing algorithms are focused on learning hash functions in the form of numeric quantization of some projected feature space. In this work, we propose a novel hash learning method that encodes features’ relative ordering instead of quantizing their numeric values in a set of low-dimensional ranking subspaces. We formulate the ranking-based hash learning problem as the optimization of a continuous probabilistic error function using softmax approximation and present an efficient learning algorithm to solve the problem. As a generalization of Winner-Take-All (WTA) hashing, the proposed algorithm naturally enjoys the numeric stability benefits of rank correlation measures while being optimized to achieve high precision with very compact code. Additionally, the proposed method can also be easily extended to nonlinear kernel spaces to discover ranking structures that can not be revealed in linear subspaces. We demonstrate through extensive experiments that the proposed method can achive competitive performances as compared to a number of state-of-the-art hashing methods.

Hyperspectral sensing data analysis based on quasiconformal mapping-based multiple kernels learning machine.

Hyperspectral remote sensing has a strong ability of object information expression, so it provides better support for object classification. Many methods are proposed for the hyperspectral data classification. The spectrum classification is a classical nonlinear problem, and a kernel-based machine is feasible to classify the spectrum data. In the nonlinear kernel-based space, the spectrum data are more discriminative. The kernel functions determine the data distribution in the feature space. In this paper, we propose the quasiconformal multiple kernels-based machine learning for the hyperspectral data classification. In the framework, the structure of hyperspectral data is adaptively adjusted for classification. The multiple kernels extract the multiple features of hyperspectral data for classification. Multiple features-based machine learning exhibits a great potential on the classification of hyperspectral data. Two public datasets, India Pines dataset and Pavia University dataset, are used to test the proposed algorithm. Experimental results demonstrate that the proposed quasiconformal multiple kernels-based hyperspectral data classification method can show competitive performance.

Effect of nano-fillers distribution on the nonlinear conductivity and space charge behavior in SiC/PDMS composites

Flexible polymer based materials with excellent breakdown strength and weak space charge behavior have been widely used in the field of cable insulation and cable termination. The silicon carbide (SiC) is beneficial to homogenize the electric field distributions, suppress the space charge injection and enhance the dissipation in the polymer composite. In this work, the polydimethylsiloxane (PDMS) based composites filled with β-SiC nanoparticles were prepared by solution mixing and mechanical blending, respectively. Compared with the pure PDMS, the SiC/PDMS composites possess not only the increased nonlinear conductivity coefficient but also the largely enhanced capability of dissipation of space charge. Especially under high electric field environment, the impact caused by uneven distribution of the SiC fillers was significant. The results of the space charges measurement under high electric field revealed that the SiC nanoparticles could largely enhance the dissipation and accelerate the movement of space charge, which was due to less trap sites leading to the better dispersion of SiC nanoparticles.

Nonlinear space charge dynamics and modulational instability in the interaction of intense laser pulses with electron-positron plasmas

Nonlinear space charge dynamics and modulational instability in the interaction between ultrashort, intense laser pulses and electron-positron pair plasmas are investigated taking into account the relativistic ponderomotive force and the relativistic mass of electrons and positrons. By coupling Maxwell's equations and hydrodynamic model, the electron and positron density distributions and the dispersion relation for the modulational instability are obtained. Moreover, two coupled nonlinear equations for the scalar and vector potentials are derived and numerically solved. The results show that the growth rate of instability increases with the decrease in the electron and positron temperatures. Moreover, it is shown that when the temperatures of electrons and positrons are not equal to each other, the profiles of scalar potential are similar to bright-like or dark-like solitons.

A facial expression recognition system using robust face features from depth videos and deep learning

This work proposes a depth camera-based robust facial expression recognition (FER) system that can be adopted for better human machine interaction. Although video-based facial expression analysis has been focused on by many researchers, there are still various problems to be solved in this regard such as noise due to illumination variations over time. Depth video data in the helps to make an FER system person-independent as pixel values in depth images are distributed based on distances from a depth camera. Besides, depth images should resolve some privacy issues as real identity of a user can be hidden. The accuracy of an FER system is much dependent on the extraction of robust features. Here, we propose a novel method to extract salient features from depth faces that are further combined with deep learning for efficient training and recognition. Eight directional strengths are obtained for each pixel in a depth image where signs of some top strengths are arranged to represent unique as well as robust face features, which can be denoted as Modified Local Directional Patterns (MLDP). The MLDP features are further processed by Generalized Discriminant Analysis (GDA) for better face feature extraction. GDA is an efficient tool that helps distinguishing MLDP features of different facial expressions by clustering the features from the same expression as close as possible and separating the features from different expressions as much as possible in a non-linear space. Then, MLDP-GDA features are applied with Deep Belief Network (DBN) for training different facial expressions. Finally, the trained DBN is used to recognize facial expressions in a depth video for testing. The proposed approach was compared with other traditional approaches in a standalone system where the proposed one showed its superiority by achieving mean recognition rate of 96.25% where the other approaches could make 91.67% at the best. The deep learning-based training and recognition of the facial expression features can also be undertaken with cloud computing to support many users and make the system faster than a standalone system.