Matrix Decomposition Method Research Articles

A dictionary learning algorithm for compression and reconstruction of streaming data in preset order

<p style='text-indent:20px;'>There has been an emerging interest in developing and applying dictionary learning (DL) to process massive datasets in the last decade. Many of these efforts, however, focus on employing DL to compress and extract a set of important features from data, while considering restoring the original data from this set a secondary goal. On the other hand, although several methods are able to process streaming data by updating the dictionary incrementally as new snapshots pass by, most of those algorithms are designed for the setting where the snapshots are randomly drawn from a probability distribution. In this paper, we present a new DL approach to compress and denoise massive dataset in real time, in which the data are streamed through in a preset order (instances are videos and temporal experimental data), so at any time, we can only observe a biased sample set of the whole data. Our approach incrementally builds up the dictionary in a relatively simple manner: if the new snapshot is adequately explained by the current dictionary, we perform a sparse coding to find its sparse representation; otherwise, we add the new snapshot to the dictionary, with a Gram-Schmidt process to maintain the orthogonality. To compress and denoise noisy datasets, we apply the denoising to the snapshot directly before sparse coding, which deviates from traditional dictionary learning approach that achieves denoising via sparse coding. Compared to full-batch matrix decomposition methods, where the whole data is kept in memory, and other mini-batch approaches, where unbiased sampling is often assumed, our approach has minimal requirement in data sampling and storage: i) each snapshot is only seen once then discarded, and ii) the snapshots are drawn in a preset order, so can be highly biased. Through experiments on climate simulations and scanning transmission electron microscopy (STEM) data, we demonstrate that the proposed approach performs competitively to those methods in data reconstruction and denoising.</p>

Multiple Kernel Representation Learning on Networks

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this problem are matrix factorization and random walk-based models. In this paper, we aim to bring together the best of both worlds, towards learning node representations. In particular, we propose a weighted matrix factorization model that encodes random walk-based information about nodes of the network. The benefit of this novel formulation is that it enables us to utilize kernel functions without realizing the exact proximity matrix so that it enhances the expressiveness of existing matrix decomposition methods with kernels and alleviates their computational complexities. We extend the approach with a multiple kernel learning formulation that provides the flexibility of learning the kernel as the linear combination of a dictionary of kernels in data-driven fashion. We perform an empirical evaluation on real-world networks, showing that the proposed model outperforms baseline node embedding algorithms in downstream machine learning tasks.

Hyperspectral Anomaly Detection via S 1/2 and Total Variation Low Rank Matrix Decomposition

Anomaly detection (AD) on hyperspectral images has been widely researched in recent decades due to its high practicability and wide range of application scenarios. Such AD methods derived from low-rank matrix decomposition (LRMD) have appeared rapidly and been applied effectively. However, most of them focused on the use of spectral information and neglected the abundant spatial characteristics. In this letter, a spectral-spatial total variation (TV) (SSTV) regularized low-rank matrix decomposition method with a Schatten 1/2 quasi-norm (<inline-formula> <tex-math notation="LaTeX">$S_{1/2}$ </tex-math></inline-formula>) and denoising is proposed. First, to exploit the hyperspectral imagery (HSI) characteristics from the spectral perspective, we propose the low-rank matrix decomposition method with <inline-formula> <tex-math notation="LaTeX">$S_{1/2}$ </tex-math></inline-formula> norm and image denoising modules. Second, we incorporate the SSTV regularization by employing a 2-D TV (TV) spatially and 1-D TV along the spectral dimension to realize the maximized utilization of spatial characteristics of HSI. Finally, the alternating direction multiplier method (ADMM) is brought in the calculating process to attain the consequent detection results. The superiority of the proposed method has been demonstrated by the excellent performance on three real datasets.

Twofold of algebraic decomposition method used for a watermarking scheme with $LWT$ over medical images

Mathematics has always been of great importance in various sciences, especially computer science. The mechanism used to embed various types of information in a host medical images to safeguard the privacy of the patient including the patient's name, doctor's digital signature is called watermarking. There are a lot of improved watermark algorithms, however, this information is susceptible to attack when the data are transferred over universal internet channels. This paper proposed a robust watermark algorithm that uses a Lifting Wavelet Transform $(LWT)$ and two times of the Hessenberg Matrix Decomposition Method $(HMDM)$ to embed a watermark in a chosen channel of the host image after performing the transform. The experimental results demonstrate that the improvement appears (higher robustness against $JPEG$ compression attack) and good imperceptibility against some attacks, to evaluate the fineness of the original with watermarked images and the extracted watermark respectively.

Performance of batch service queue model with second optional service, repairable breakdown and standby server

In this paper, we investigate the performance of batch service queue model with second optional service, repairable breakdown and warm standby server. Both primary operating and warm standby servers provide First Essential Service (FES) and Second Optional Service (SOS) to customers, wherein FES is all arriving customers and only some of them may further request the SOS. The service times, failure times and repair times of both primary operating and warm standby server are assumed to follow exponential distributions. We use Runge-Kutta method to obtain the transient state probabilities and matrix-decomposition method to obtain the steady-state probabilities of the model. Also, a cost model is presented to determine the optimal service rates so that the expected cost is minimised. Finally, the effect of the model parameters on the system behaviour is demonstrated through numerical results and discussions.

Effects of spatial autocorrelation structure for friction angle on the runout distance in heterogeneous sand collapse

This paper proposes a stochastic method for analyzing the runout distance of sand collapse considering the spatial variability of shear strength, in which random field theory and generalized interpolation material point method are integrated into a Monte-Carlo simulation basis. The random field is generated by Cholesky matrix decomposition method and implemented into the material point level, hence heterogeneity and large deformations are simultaneously considered in the modeling process. A sand collapse case is simulated with both homogeneous and heterogeneous condition assumptions by the proposed method. The effect of five theoretical autocorrelation functions (ACFs) on the runout distance of the collapse is highlighted since the ACFs are commonly adopted to characterize the spatial variability of soil properties due to sparse site observation data. It is shown that the deterministic analysis may underestimate the runout distance, while the heterogeneous model provides realistic results. Moreover, five ACFs and different coefficients of variation of friction angle (COVφ) are compared to investigate their influences on the runout distance modeling. The results show that the uncertainty of runout distance increases with the increase in COVφ. Meanwhile, the variances of the runout distance also become larger with COVφ increasing. Based on the proportion of the runout distance which exceeds the deterministic value, the results indicate that the deterministic analysis notably underestimates the risk induced by large runout distances in real heterogeneous granular flows (e.g., landslide, debris-avalanches).

Skin carcinogenesis in mice using UVB radiation

Ultraviolet B (UVB) radiation is directly related to sunburn and other visible changes on the skin surface, including discoloration and skin carcinoma. This study investigates the influence of UVB rays (wavelength from 290-320nm) on the formation of cancerous tissues and also shows the differences between abnormal and normal tissue. The mice were stimulated with DMBA chemical protocol and exposure to UVB radiation for skin carcinogenesis. Normal and cancerous skin tissue were stained with Hematoxylin and Eosin, then were measured to obtain optical properties by applying Mueller-Matrix Decomposition, which is considered as an effective skin structure analysis method. Long term exposure to UVB radiation caused skin inflammation and the appearance of crystal bumps. Histopathology results clearly indicate the increasing number of papilloma cells, and prolonged damage by UVB radiation. Skin structural analysis was specified with the optical parameters by Mueller Matrix Decomposition method. The extension of skin carcinoma significantly lessened the values of Linear Birefringence (LB) and Circular Birefringence (CB), as well as the variation of Linear Dichroism (LD) and Circular Dichroism (CD) parameters help validate the differences between normal and squamous cell skin sample.

Surface subsidence monitoring with an improved distributed scatterer interferometric SAR time series method in a filling mining area

Statistically homogeneous pixel (SHP) selection and DS phase optimization are two critical steps in the distributed scatterer interferometric SAR (DS-InSAR) time series method. In this paper, a new algorithm named dynamic hypothesis test of confidence interval (D-HTCI) is proposed, which reduces the wrong selection rate of SHP and increases the number of SHP selections. Using adaptive spatial nonlocal filtering method for DS phase optimization, the phase standard deviation (PSD) and the sum of phase differences (SPD) show that compared with the traditional covariance matrix decomposition method, the optimization quality is improved by 2.1 and 1.8 times, respectively. Combining 24 scenes Sentinel-1A data from September 17, 2017 to July 14, 2018, the method is applied to monitor surface subsidence of the Daizhuang filling mining area (Jining, Shandong, China). The results show that the proposed method has mm-level accuracy for monitoring of surface subsidence in a filling mining area.

Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization.

Non-negative matrix factorization is a relatively new method of matrix decomposition which factors an m×n data matrix X into an m×k matrix W and a k×n matrix H, so that X≈W×H. Importantly, all values in X, W, and H are constrained to be non-negative. NMF can be used for dimensionality reduction, since the k columns of W can be considered components into which X has been decomposed. The question arises: how does one choose k? In this paper, we first assess methods for estimating k in the context of NMF in synthetic data. Second, we examine the effect of normalization on this estimate’s accuracy in empirical data. In synthetic data with orthogonal underlying components, methods based on PCA and Brunet’s Cophenetic Correlation Coefficient achieved the highest accuracy. When evaluated on a well-known real dataset, normalization had an unpredictable effect on the estimate. For any given normalization method, the methods for estimating k gave widely varying results. We conclude that when estimating k, it is best not to apply normalization. If underlying components are known to be orthogonal, then Velicer’s MAP or Minka’s Laplace-PCA method might be best. However, when orthogonality of the underlying components is unknown, none of the methods seemed preferable.

Classification of human skin cancer using Stokes-Mueller decomposition method and artificial intelligence models

A hybrid framework consisting of the Stokes- decomposition method and various artificial intelligence (AI) models is proposed for classifying human melanoma and nonmelanoma skin cancer samples. In the proposed approach, the Stokes-Mueller matrix decomposition method is first used to extract the effective optical parameters of normal, squamous cell carcinoma, basal cell carcinoma, and melanoma skin cancer samples. The parameters are pre-processing using feature scaling and dimensional reduction techniques, and are then used to train nine different AI models, namely ExtraTree, Random Forest, Decision Tree, XGBoost, Support Vector Machine, k-Nearest Neighbors (k-NN), Radius Neighbors, Multilayer Perceptron (MLP), and Ridge. Finally, the trained models are used to classify a small number of normal and cancerous skin tissue samples. It is shown that all of the models have a classification accuracy (F1 score) of more than 90% given an appropriate pre-processing of the input parameters. Furthermore, the ExtraTree, k-NN, and MLP models achieve an accuracy of 100%. Overall, the results confirm that the proposed framework provides a promising approach for the efficient and accurate classification of human skin cancer tissue samples.

Stabilization for uncertain stochastic T\u2013S fuzzy system driven by L\xe9vy noise

Different from the other work, the almost sure asymptotic stability of an uncertain stochastic T–S fuzzy system driven by Lévy noise has been investigated. However, the Lévy noise caused the càdlàg paths in the system, and the uncertainty was the linear fractional form, which made difference to the general norm-bounded type. Using the special stochastic techniques and new matrix decomposition method, we deal with the càdlàg paths and uncertainty of the system. As the main results, the sufficient conditions of almost sure asymptotic stability for stochastic T–S fuzzy system driven by Lévy noise have been presented. On this basis, the closed-loop system is robustly almost surely asymptotically stable with fuzzy state-feedback controller. Furthermore, our stabilization criteria are based on linear matrix inequalities (LMIs), whence the feedback controller could be designed more easily in practice.

An evolutionary event detection model using the Matrix Decomposition Oriented Dirichlet Process

With the huge expansion of user generated content on social networks, event detection has emerged as a major challenge and source of knowledge discovery. This knowledge is employed in different applications such as recommender systems, crisis management systems, and decision support systems. Dynamicity, overlapping, and evolutionary behavior are the most important issues in event detection. This paper proposes a novel evolutionary model for event detection to capture the dynamism and evolving behavior of events. The proposed method uses a matrix decomposition technique and a Dirichlet Process to detect events and handle their dynamicity. This model consists of two components, namely preliminary event detection and event evolvement tracking. The former component extracts preliminary events from the available data using the matrix decomposition method. Then, subsequent data is employed into a Non-Parametric Bayesian Network, namely Dirichlet Process Mixture Model to evolve the preliminary events. During the evolvement process, data may migrate between extracted events or new events may be discovered. The experimental results and comparisons with several recently developed approaches show the superiority of the proposed approach, and its ability to capture the evolutionary behavior of events over time.

Polaromics: deriving polarization parameters from a Mueller matrix for quantitative characterization of biomedical specimen

A Mueller matrix is a comprehensive representation of the polarization transformation properties of a sample, encoding very rich information on the microstructure of the scattering objects. However, it is often inconvenient to use individual Mueller matrix elements to characterize the microstructure due to a lack of explicit connections between the matrix elements and the physics properties of the scattering samples. In this review, we summarize the methods to derive groups of polarization parameters, which have clear physical meanings and associations with certain structural properties of turbid media, including various Mueller matrix decomposition (MMD) methods and the Mueller matrix transformation (MMT) technique. Previously, experimentalists have chosen the most suitable method for the specific measurement scheme. In this review, we introduce an emerging novel research paradigm called ‘polaromics’. In this paradigm, both MMD and MMT parameters are considered as polarimetry basis parameters (PBP), which are used to construct polarimetry feature parameters (PFPs) for the quantitative characterization of complex biomedical samples. Machine learning techniques are involved to find PFPs that are sensitive to specific micro- or macrostructural features. The goal of this review is to provide an overview of the emerging ‘polaromics’ paradigm, which may pave the way for biomedical and clinical applications of polarimetry.

Flexible Covariance Matrix Decomposition Method for Data Augmentation and Its Application to Brainwave Signals

The acquisition of a large-volume brainwave database is challenging because of the stressful experiments that are required; however, data synthesis techniques can be used to address this limitation. Covariance matrix decomposition (CMD), a widely used data synthesis approach, generates artificial data using the correlation between features and random noise. However, previous CMD methods constrain the stochastic characteristics of artificial datasets because the random noise used follows a standard distribution. Therefore, this study has improved the performance of CMD by releasing such constraints. Specifically, a generalized normal distribution (GND) was used as it can alter the kurtosis and skewness of the random noise, affecting the distribution of the artificial data. For the validation of GND performance, a motor imagery brainwave classification was conducted on the artificial dataset generated by GND. The GND-based data synthesis increased the classification accuracy obtained with the original data by approximately 8%.

Evaluation of slope reliability considering the rotation of the correlation structure of soil properties

At present, research on the spatial variability of soil parameters mostly considers isotropy and transverse anisotropy correlation structures; by comparison, little research on other general correlation structures is available. To address this issue, the present study generates a general rotated anisotropy correlation structure random field considering stratum rotation by using random field theory and the matrix decomposition method. FLAC3D and strength reduction theory are used to analyze the influence of the rotation angle of the correlation structure and the angle between the principal axes of the correlation structure on slope reliability. Thereafter, the influences of the coefficient of variation (COV) and shear strength cross-correlation on slope reliability are revealed. Results show that slope stability first increases and then decreases with increasing rotation angle of the correlation spindle. Slope stability is related to the rotation angle of the correlation spindles. In the two-parameter random field of shear strength, slopes in which the dip direction of the strata is against the dip direction of the slope demonstrate higher reliability than slopes in which the dip direction of the strata is along the dip direction of the slope. This effect is more obvious when the COV is small. Compared with the slope reliability analysis results obtained when considering the cross-correlation of shear strength parameters, the results obtained when cross-correlation is ignored demonstrate underestimation of the probability of failure.

Identifying Entangled Physics Relationships Through Sparse Matrix Decomposition to Inform Plasma Fusion Design

A sustainable burn platform through inertial confinement fusion (ICF) has been an ongoing challenge for over 50 years. Mitigating engineering limitations and improving the current design involves an understanding of the complex coupling of physical processes. While sophisticated simulation codes are used to model ICF implosions, these tools contain necessary numerical approximation but miss physical processes that limit predictive capability. Identification of relationships between controllable design inputs to ICF experiments and measurable outcomes (e.g., neutron yield, neutron velocity, areal density) from performed experiments can help guide the future design of experiments and development of simulation codes, to potentially improve the accuracy of the computational models used to simulate ICF experiments. We use sparse matrix decomposition methods to identify clusters of a few related design variables. Sparse principal component analysis (SPCA) identifies groupings that are related to the physical origin of the variables (laser, hohlraum, and capsule). A variable importance analysis finds that in addition to variables highly correlated with neutron yield, such as picket power and laser energy, variables that represent a dramatic change of the ICF design, such as number of pulse steps, are also very important. The obtained sparse components are then used to train a random forest (RF) regression surrogate for predicting total yield. The RF performance on the training and testing data compares with the performance of the RF trained using all the design variables considered. This work is intended to inform design changes in future ICF experiments by augmenting the expert intuition and simulation results.

Preemptive scheduling on unrelated machines with fractional precedence constraints

Many programming models, e.g., MapReduce, introduce precedence constraints between the jobs. This paper formalizes a notion of precedence constraints, called fractional precedence constraints, where the progress of follower jobs only has to lag behind (fractionally) their leads. For a general set of fractional precedence constraints between the jobs, this paper provides a new class of preemptive scheduling algorithms on unrelated machines that have arbitrary processing speeds. In particular, for a given makespan, we establish both sufficient and necessary conditions on the existence of a feasible job schedule, and then propose an efficient scheduling algorithm based on a novel matrix decomposition method, if the sufficient conditions are satisfied. The algorithm is shown to be a Polynomial-Time Approximation Scheme (PTAS), i.e., its solution is able to achieve any feasible makespan with an approximation bound of 1+ϵ, for an arbitrary ϵ>0.

User Behavior Identification and Personalized Recommendation Based on Web Data Mining

A good understanding of user behavior and consumption preferences can provide support for website operators to improve their service quality. However, the existing personalized recommendation systems generally have problems such as low Web data mining efficiency, low degree of automated recommendation, and low durability. Targeting at these unsolved issues, this paper mainly carries out the following works: Firstly, the authors established a user behavior identification and personalized recommendation model based on Web data mining, it gave the user behavior analysis process based on Web data mining, improved the traditional k-means algorithm, and gave the detailed execution steps of the improved algorithm; moreover, it also elaborated on the K nearest neighbor model based on user scoring information, the score matrix decomposition method, and the personalized recommendation method for network users. At last, experimental results verified the effectiveness of the constructed model.

Characterization of Mueller matrix elements for classifying human skin cancer utilizing random forest algorithm.

.Significance: The Mueller matrix decomposition method is widely used for the analysis of biological samples. However, its presumed sequential appearance of the basic optical effects (e.g., dichroism, retardance, and depolarization) limits its accuracy and application.Aim: An approach is proposed for detecting and classifying human melanoma and non-melanoma skin cancer lesions based on the characteristics of the Mueller matrix elements and a random forest (RF) algorithm.Approach: In the proposal technique, 669 data points corresponding to the 16 elements of the Mueller matrices obtained from 32 tissue samples with squamous cell carcinoma (SCC), basal cell carcinoma (BCC), melanoma, and normal features are input into an RF classifier as predictors.Results: The results show that the proposed model yields an average precision of 93%. Furthermore, the classification results show that for biological tissues, the circular polarization properties (i.e., elements , , , and of the Mueller matrix) dominate the linear polarization properties (i.e., elements , , , and of the Mueller matrix) in determining the classification outcome of the trained classifier.Conclusions: Overall, our study provides a simple, accurate, and cost-effective solution for developing a technique for classification and diagnosis of human skin cancer.

Study on an anti-reverberation method based on PCI-SVM

Aiming at the problem that targets are difficult to detect in the marine reverberation environment, this paper studies traditional PCI methods, AR pre-whitening methods, and low-rank matrix decomposition methods, but because traditional PCI methods are difficult to rank, AR pre-whitening methods are difficult to determine the order, and low-rank Matrix factorization method is slow in calculation speed. Based on this research, this paper proposes an anti-reverberation method based on PCI-SVM. This method combines Principal Component Inversion (PCI) and Support Vector Machine (SVM), first obtains the eigenvalues by the principal component inversion algorithm, and then uses the support vector machine to classify and rank the eigenvalues, thereby receiving active sonar the received echo signal is decomposed into subspace to realize the separation of reverberation subspace. This paper uses this method to process simulation data, lake trial data, and sea trial data separately and compares the data processing results with the direct matched filtering method. The comparison results show that the reverberation data processed by the PCI-SVM method has signal detection capabilities Increase by 3.8 dB, 12 dB, and 1.9 dB respectively. At the same time, the PCI-SVM method is compared with the traditional AR anti-reverberation method and PCI anti-reverberation method. The comparison results show that the PCI-SVM method adopted in this paper has better robustness and anti-reverberation ability.