Orthogonal Algorithm Research Articles

Orthogonal incremental non-negative matrix factorization algorithm and its application in image classification

To improve the sparseness of the base matrix in incremental non-negative matrix factorization, we in this paper present a new method, orthogonal incremental non-negative matrix factorization algorithm (OINMF), which combines the orthogonality constraint with incremental learning. OINMF adopts batch update in the process of incremental learning, and its iterative formulae are obtained using the gradient on the Stiefel manifold. The experiments on image classification show that the proposed method achieves much better sparseness and orthogonality, while retaining time efficiency of incremental learning.

Variable selection for high-dimensional regression models with time series and heteroscedastic errors

Although existing literature on high-dimensional regression models is rich, the vast majority of studies have focused on independent and homogeneous error terms. In this article, we consider the problem of selecting high-dimensional regression models with heteroscedastic and time series errors, which have broad applications in economics, quantitative finance, environmental science, and many other fields. The error term in our model is the product of two components: one time series component, allowing for a short-memory, long-memory, or conditional heteroscedasticity effect, and a high-dimensional dispersion function accounting for exogenous heteroscedasticity. By making use of the orthogonal greedy algorithm and the high-dimensional information criterion, we propose a new model selection procedure that consistently chooses the relevant variables in both the regression and the dispersion functions. The finite sample performance of the proposed procedure is also illustrated via simulations and real data analysis.

Temperature extraction method for infrared image of high voltage power equipment

An infrared temperature prediction method for power equipment is proposed based on the radial basis function (RBF) network optimized by quantum genetic algorithm (QGA) and orthogonal least squares algorithm (OLSA). The modified compound algorithm was used to optimize parameters of the RBF network. A temperature prediction model was established through the fitting of pixels and temperatures of the infrared image of an equipment. After image matching, the infrared temperature at a position can be directly obtained from the visible image. Meanwhile, we can also directly read temperature values of different positions from the infrared image and identify the corresponding positions in the visible image. Experimental results indicate that the algorithm proposed has a better prediction performance than the RBF network optimized by OLSA alone and by adaptive genetic algorithm (AGA) and OLSA. It improves the generalization capacity of RBF network, resulting a more stable input and a higher prediction accuracy. The algorithm proposed facilitates temperature analysis and condition-based maintenance for substations.

Data mining and image analysis using genetic programming

Genetic programming (GP) is an artificial intelligence technique that benefits from evolutionary computations allowing computers to solve problems automatically. In this paper, we present an optimized genetic-programming-based classifier that directly solves the multi-class classification problems in data mining and image analysis. A new fitness function is proposed for multiclass classification and brain tumor detection, which is validated by 10-fold cross validation. Instead of defining static thresholds as boundaries to differentiate between multiple labels, our work presents a method of classification where a GP system learns the relationships among experiential data and models them mathematically during the evolutionary process. We propose an optimized GP classifier based on a combination of pruning subtrees and a new fitness function. An orthogonal least squares algorithm is also applied in the training phase to create a robust GP classifier. Our approach has been assessed on six multiclass datasets and on a magnetic resonance imaging (MRI) brain image for tumor detection. The results of data classification for Iris, Wine, Glass, Pima, BUPA Liver and Balance Scale datasets are compared with existing algorithms. The high accuracy of brain tumor classification provided by our GP classifier confirms the strong ability of the developed technique for complicated classification problems. We compared our approach in terms of speed with previous GP algorithms as well. The analyzed results illustrate that the developed classifier produces a productive and rapid method for classification tasks that outperforms the previous methods for more challenging multiclass classification problems.

An efficient and stable Lagrangian matrix approach to Abel integral and integro-differential equations

This article studies Abel integral equations (AIEs) and singular integro-differential equations (SIDEs) and aims to develop two numerical schemes for them. It also emphasises on the comparative analysis of both AIEs & SIDEs which is based on mainly two process namely Gauss-Legendre roots as collocation node points and random node points over the domain [0,1]. For generating interpolating basis functions (IBF), we used Lagrangian interpolating polynomial and for orthonormal Lagrangian basis functions (OLBF), we used Gram-Schmidt orthogonalization algorithm, respectively. Firstly, we introduced the function approximation by using generated IBF and OLBF, then established the error bounds of these approximations. The constructed approximations by both the schemes convert the AIEs and SIDEs into the system of algebraic equations. We have also established error bounds, stability and convergence analysis of the proposed schemes by considering several mild mathematical conditions. Moreover, the stability of schemes is also established numerically. Finally, the test functions with the support of graphs clearly show the reliability and computational efficiency of the proposed methods.

A Gradient-Based Method for Robust SensorSelection in Hypothesis Testing.

This paper considers the binary Gaussian distribution robust hypothesis testing under a Bayesian optimal criterion in the wireless sensor network (WSN). The distribution covariance matrix under each hypothesis is known, while the distribution mean vector under each hypothesis drifts in an ellipsoidal uncertainty set. Because of the limited bandwidth and energy, we aim at seeking a subset of p out of m sensors such that the best detection performance is achieved. In this setup, the minimax robust sensor selection problem is proposed to deal with the uncertainties of distribution means. Following a popular method, minimizing the maximum overall error probability with respect to the selection matrix can be approximated by maximizing the minimum Chernoff distance between the distributions of the selected measurements under null hypothesis and alternative hypothesis to be detected. Then, we utilize Danskin’s theorem to compute the gradient of the objective function of the converted maximization problem, and apply the orthogonal constraint-preserving gradient algorithm (OCPGA) to solve the relaxed maximization problem without 0/1 constraints. It is shown that the OCPGA can obtain a stationary point of the relaxed problem. Meanwhile, we provide the computational complexity of the OCPGA, which is much lower than that of the existing greedy algorithm. Finally, numerical simulations illustrate that, after the same projection and refinement phases, the OCPGA-based method can obtain better solutions than the greedy algorithm-based method but with up to shorter runtimes. Particularly, for small-scale problems, the OCPGA -based method is able to attain the globally optimal solution.

Pose estimation of hidden object behind a thin scattering layer based on speckle correlation

The presence of an inhomogeneous scattering medium has brought great challenges to optical imaging and detection in many fields. In this work, we propose a speckle-autocorrelation based orthogonal projection algorithm to detect the flipped target hidden behind a scattering layer in X-Z plane and Y-Z plane. By calculating the speckle autocorrelation, we can quickly identify the posture of hidden target. We also develop an optimization method for the tracking of rotating object in X-Y plane. Those methods effectively expand the tracking dimensions of hidden target, allowing us to detect the flipping and rotational posture of the object behind scattering media. The reported strategy may find applications in many fields such as biomedical imaging, and ego-motion sensing.

Subspace Learning and Feature Selection via Orthogonal Mapping

A plethora of dimensionality reduction (DR) techniques, stemming from statistics, machine learning, or graph theory, has been developed. Their ultimate objective is to eliminate data redundancy without a significant information loss. A general formulation, known as graph embedding, offers a unified framework for describing several well-known DR algorithms. In this paper, the inclusion of several DR algorithms within this unified framework is demonstrated. The enforcement of orthogonality to the projection matrix within this framework is proven to be of vital importance, since Orthogonal Neighborhood Preserving Projections, Orthogonal Locality Preserving Projections, Orthogonal Isometric Projection, Orthogonal Linear Discriminant Analysis, and Orthogonal Local Tangent Space Alignment algorithms outperform their non-orthogonal counterparts, e.g., Neighborhood Preserving Embedding, Locality Preserving Projections, Isometric Mapping, Linear Discriminant Analysis, and Local Tangent Space Alignment. One may simultaneously also impose the $\ell _{2,1}$ norm regularization on the projection matrix, seeking for row-sparsity. This leads to the known Joint Feature Selection and Subspace Learning (JFSSL) framework. All DR algorithms are employed within JFSSL. It is proven that the use of orthogonal mapping algorithms within JFSSL against their non-orthogonal counterparts does not improve the recognition rate of NN classifier.

Fast Adaptive Gradient RBF Networks For Online Learning of Nonstationary Time Series

For a learning model to be effective in online modeling of nonstationary data, it must not only be equipped with high adaptability to track the changing data dynamics but also maintain low complexity to meet online computational restrictions. Based on these two important principles, in this paper, we propose a fast adaptive gradient radial basis function (GRBF) network for nonlinear and nonstationary time series prediction. Specifically, an initial compact GRBF model is constructed on the training data using the orthogonal least squares algorithm, which is capable of modeling variations of local mean and trend in the signal well. During the online operation, when the current model does not perform well, the worst performing GRBF node is replaced by a new node, whose structure is optimized to fit the current data. Owing to the local one-step predictor property of GRBF node, this adaptive node replacement can be done very efficiently. Experiments involving two chaotic time series and two real-world signals are used to demonstrate the superior online prediction performance of the proposed fast adaptive GRBF algorithm over a range of benchmark schemes, in terms of prediction accuracy and real-time computational complexity.

Orthogonal PLS (O‐PLS) and related algorithms

Orthogonal PLS (O‐PLS) and related algorithms

Fast Temporal Video Segmentation Based on Krawtchouk-Tchebichef Moments

With the increasing growth of multimedia data, the current real-world video sharing websites are being huge in repository size, more specifically video databases. This growth necessitates to look for superior techniques in processing video because video contains a lot of useful information. Temporal video segmentation (TVS) is considered essential stage in content-based video indexing and retrieval system. TVS aims to detect boundaries between successive video shots. TVS algorithm design is still challenging because most of the recent methods are unable to achieve fast and robust detection. In this regard, this paper proposes a TVS algorithm with high precision and recall values, and low computation cost for detecting different types of video transitions. The proposed algorithm is based on orthogonal moments which are considered as features to detect transitions. To increase the speed of the TVS algorithm as well as the accuracy, fast block processing and embedded orthogonal polynomial algorithms are utilized to extract features. This utilization will lead to extract multiple local features with low computational cost. Support vector machine (SVM) classifier is used to detect transitions. Specifically, the hard transitions are detected by the trained SVM model. The proposed algorithm has been evaluated on four datasets. In addition, the performance of the proposed algorithm is compared to several state-of-the-art TVS algorithms. Experimental results demonstrated that the proposed algorithm performance improvements in terms of recall, precision, and F1-score are within the ranges (1.31 - 2.58), (1.53 - 4.28), and (1.41 - 3.03), respectively. Moreover, the proposed method shows low computation cost which is 2% of real-time.

High Precision Self-Mixing Interferometer Based on Reflective Phase Modulation Method

In this paper, a novel self-mixing interferometer based on reflective phase modulation (RPM) method has been developed to perform micro-displacement reconstruction with nanometer accuracy. Broaden harmonic components spectrum of the self-mixing signal is produced by employing a high-frequency vibrating reflective mirror as the phase modulation device. Phase demodulation is implemented applying the orthogonal demodulation algorithm subject to the signal spectrum, in which orthogonal signal can be extracted from the harmonic components of the expanded Bessel function. The principle and signal processing approach are introduced in detail, and the simulation results indicate that the reconstruction error can be reduced as the number of reflections increases. A series of experiments at different vibration amplitudes show that the reconstructed errors are all less than 10 nm with modulation frequency of 1 kHz. And the minimum error of 3 nm has been achieved at the measured amplitude of 229 nm, which demonstrates the technical-superiority and high-performance of the method.

Virtual Angular-Domain Channel Estimation for FDD Based Massive MIMO Systems with Partial Orthogonal Pilot Design

This article proposes a virtual angular-domain channel estimation scheme for massive multiple-input multiple-output systems operating in frequency division duplex (FDD) mode. Different from the conventional scheme where orthogonal pilots are transmitted on different antennas, we propose to transfer the channel estimation problem to the virtual angular domain and utilize the channel sparsity to reduce the training and feedback overhead. An orthogonal matching pursuit with Gram-Schmidt orthogonalization algorithm is proposed to construct the unitary transformation between the spatial domain and the virtual angular domain, which achieves higher sparsity than the existing approaches. Furthermore, we propose to estimate the downlink (DL) dominant angular set, which captures most of the channel power with only a few elements, by utilizing the directional reciprocity of FDD systems, where a calibration algorithm is introduced to handle the different wavelengths of uplink and DL transmissions. Based on the estimated dominant sets, we introduce a partial orthogonal criterion for virtual angular-domain pilot design and further propose two pilot assignment algorithms which minimize pilot overhead and pilot-reuse interference, respectively. Theoretical analyses on pilot overhead and the mean square error (MSE) performance are also presented. Simulation results demonstrate that our proposed virtual angular-domain channel estimation scheme provides excellent MSE performance with much reduced pilot overhead and, consequently, enjoys much larger per-user achievable rate in comparison to the conventional schemes.

Feature Selection-Based Hierarchical Deep Network for Image Classification

In this paper, a novel hierarchical deep network is proposed to combine the deep convolutional neural network and the feature selection-based tree classifier efficiently for image classification. First, the concept ontology is built for organizing large-scale image classes hierarchically in a coarse-to-fine fashion. Second, a novel selective orthogonal algorithm is proposed to make sure deep features extracted for each level classifiers more in line with the requirements of different classification tasks. Also, the role of useful feature components in multi-level deep features are improved. The experimental results on three datasets show that adding a feature selection module in a hierarchical deep network can perform better performance in large-scale image classification.

Coding Analog of Superadditivity Using Entanglement-Assisted Quantum Tensor Product Codes Over $\mathbb {F}_{p^k}$

We provide a procedure to construct entanglement-assisted Calderbank–Shor–Steane (CSS) codes over qudits from the parity check matrices of two classical codes over $\mathbb {F}_q$ , where $q=p^k$ , $p$ is prime, and $k$ is a positive integer. The construction procedure involves the proposed Euclidean Gram–Schmidt orthogonalization algorithm, followed by a procedure to extend the quantum operators to obtain stabilizers of the code. Using this construction, we provide a construction of entanglement-assisted tensor product codes from classical tensor product codes over $\mathbb {F}_q$ . We further show that a nonzero rate entanglement-assisted tensor product code can be obtained from a classical tensor product code whose component codes yield zero rate entanglement-assisted CSS codes. We view this result as the coding analog of superadditivity.

Multicriteria task of distribution of flows of a transport communication network

The paper proposes a new approach to solving the problem of distribution of information flows on the communication network based on the method of constraints. A multi-pole multi-product graph is used as a mathematical model of the communication network structure. The problem of distribution of information flows is solved in three stages. At the first stage, the structural analysis of the network is carried out using the mathematical apparatus of Boolean algebra. As a result, we get a lot of ways to distribute information flows. At the second stage, the structural reliability of the found set of information flow distribution paths is calculated using the orthogonalization algorithm. At the final stage, using the method of constraints, a compromise version of the distribution of information flows of corresponding pairs of nodes is found.

Resolution Threshold Analysis of the Microwave Radar Coincidence Imaging

The resolution of the microwave radar coincidence imaging (MRCI) can break the diffraction limit, which has been validated by experiments. However, there is still no theoretical analysis. In this article, the resolution of the MRCI is theoretically analyzed using the orthogonal subspace projection algorithm based on the space spanned by the discrete reference radiation mode. First, a target location estimate (TLE) method using the data from the nonfocusing radar array of the MRCI system is proposed to estimate the target position assisted by the equivalent detection method. The estimation precision of the TLE method is approximately equal to the 3-dB beamwidth of the coherent transmitting radar array with the same aperture; hence, the imaging plane can be obtained. Then, the equivalent internal noise (generated by the error of the target distance estimation, i.e., the location of the imaging plane) is theoretically analyzed. Finally, the imaging resolution threshold of the MRCI system is theoretically analyzed. The relationship between the resolution threshold and the factors (such as the deployment of the transmitting radar array, the distance between the target and the radar array, and the signal-to-noise ratio of the imaging system) is summarized. The proposed estimation method and the analyses of the MRCI system are validated through a set of simulations and experiments.

Fractional Fourier Transform-Based Radio Frequency Interference Suppression for High-Frequency Surface Wave Radar

High-frequency surface wave radar (HF SWR) plays an important role in marine stereoscopic monitoring system. Nevertheless, the congestion of external radio frequency interference (RFI) in HF band degrades its performance seriously. In this article, two novel fractional Fourier transform (FRFT)-based RFI suppression approaches are proposed. One is based on the orthogonal projection of sequences from fractional Fourier domain, and the other is based on singular value decomposition (SVD) of Hankel matrix of sequences from fractional inverse-Fourier domain. Simulation and experimental data collected by HF SWR from Wuhan University were used to test the effectiveness as well as the application condition of the proposed RFI suppression algorithms. The FRFT-based orthogonal projection algorithm is practicable for suppressing stationary RFI with unvaried carrier frequency, while the FRFT-based SVD algorithm is applicable equally for mitigating nonstationary RFI with time-varying carrier frequency or occasional duration time. The processing results may provide useful guidelines for interference suppression of HF SWR, and inspiring the further application of the FRFT-based methods for signal processing.

Localization of sparse and coherent sources by orthogonal least squares

This paper proposes an efficient method for the joint localization of sources and estimation of the covariance of their signals. In practice, such an estimation is useful to study correlated sources existing, for instance, in the presence of spatially distributed sources or reflections, but is confronted with the challenge of computational complexity due to a large number of required estimates. The proposed method is called covariance matrix fitting by orthogonal least squares. It is based on a greedy dictionary based approach exploiting the orthogonal least squares algorithm in order to reduce the computational complexity of the estimation. Compared to existing methods for sources correlation matrix estimation, its lower computational complexity allows one to deal with high dimensional problems (i.e., fine discretization of the source space) and to explore large regions of possible sources positions. As shown by numerical results, it is more accurate than existing methods and does not require the tuning of any regularization parameter. Experiments in an anechoic chamber involving correlated sources or reflectors show the ability of the method to locate and identify physical and mirror sources as well.

An optimized model based on convolutional neural networks and orthogonal learning particle swarm optimization algorithm for plant diseases diagnosis

Abstract The plant disease classification based on using digital images is very challenging. In the last decade, machine learning techniques and plant images classification tools such as deep learning can be used for recognizing, detecting and diagnosing plant diseases. Currently, deep learning technology has been used for plant disease detection and classification. In this paper, an ensemble model of two pre-trained convolutional neural networks (CNNs) namely VGG16 and VGG19 have been developed for the task plant disease diagnosis by classifying the leaves images of healthy and unhealthy. In this context, CNNs are used due to its capability of overcoming the technical problems which are associated with the classification problem of plant diseases. However, CNNs suffer from a great variety of hyperparameters with specific architectures which is considered as a challenge to identify manually the optimal hyperparameters. Therefore, orthogonal learning particle swarm optimization (OLPSO) algorithm is utilized in this paper to optimize a number of these hyperparameters by finding optimal values for these hyperparameters rather than using traditional methods such as the manual trial and error method. In this paper, to prevent CNNs from falling into the local minimum and to train efficiently, an exponentially decaying learning rate (EDLR) schema is used. In this paper, the problem of the imbalanced used dataset has been solved by using random minority oversampling and random majority undersampling methods, and some restrictions in terms of both the number and diversity of samples have been overcome. The obtained results of this work show that the accuracy of the proposed model is very competitive. The experimental results are compared with the performance of other pre-trained CNN models namely InceptionV3 and Xception, whose hyperparameters were selected using a non-evolutionary method. The comparison results demonstrated that the proposed diagnostic approach has achieved higher performance than the other models.