Gram-Schmidt Research Articles

Conterminous United States Landsat-8 top of atmosphere and surface reflectance tasseled cap transformation coefficients

The tasseled cap transformation (TCT) has been widely used to decompose satellite multi-spectral information into “brightness”, “greenness”, and “wetness” components. Published TCT coefficients for the Landsat sensor series have mainly been derived using top of atmosphere (TOA) reflectance and sparse data sets. Studies to derive TCT coefficients for Landsat surface reflectance (SR) are lacking. In this study, the TCT coefficients were derived independently for Landsat-8 Operational Land Imager (OLI) SR and TOA reflectance using the Gram-Schmidt orthogonalization (GSO) method. To ensure that the derived TCT coefficients are robust and broadly applicable, representative samples of soil, vegetation, and water were selected from summer and autumn Landsat-8 OLI Analysis Ready Data (ARD) sampled from 40.4 million 30 m pixel locations across the conterminous United States (CONUS). Given that the blue band is susceptible to atmospheric contamination due to its shorter wavelength, two groups of TCT coefficients were derived: one from 6 bands (Blue, Green, Red, NIR, SWIR1, SWIR2) and one from 5 bands without the blue band. As TCT results cannot be validated in a formal way, the TCT components for CONUS summer TOA and SR composites were generated and compared with National Land Cover Database (NLCD) land cover classes to provide a synoptic assessment and provide confidence in the results. In addition, three ARD tiles selected to encompass a mix of land cover types, predominantly, desert in Nevada, wetland and urban in Florida, and agriculture in North Dakota, were used to analyze the seasonal variation of the TCT components. The results demonstrate that the derived Landsat-8 TCT coefficients can effectively characterize brightness, greenness, and wetness components across the CONUS, and show good consistency for discrimination of land cover types and track seasonal surface variations. There was no significant difference between each TCT component derived using the 6-band and 5-band TCT coefficients considering a large sample of CONUS pixels. Therefore, the 5-band TCT coefficients provided in this study are recommended for use, as the blue band is atmospherically sensitive and difficult to atmospherically correct reliably.

Impact of Image-Processing Routines on Mapping Glacier Surface Facies from Svalbard and the Himalayas Using Pixel-Based Methods

Glacier surface facies are valuable indicators of changes experienced by a glacial system. The interplay of accumulation and ablation facies, followed by intermixing with dust and debris, as well as the local climate, all induce observable and mappable changes on the supraglacial terrain. In the absence or lag of continuous field monitoring, remote sensing observations become vital for maintaining a constant supply of measurable data. However, remote satellite observations suffer from atmospheric effects, resolution disparity, and use of a multitude of mapping methods. Efficient image-processing routines are, hence, necessary to prepare and test the derivable data for mapping applications. The existing literature provides an application-centric view for selection of image processing schemes. This can create confusion, as it is not clear which method of atmospheric correction would be ideal for retrieving facies spectral reflectance, nor are the effects of pansharpening examined on facies. Moreover, with a variety of supervised classifiers and target detection methods now available, it is prudent to test the impact of variations in processing schemes on the resultant thematic classifications. In this context, the current study set its experimental goals. Using very-high-resolution (VHR) WorldView-2 data, we aimed to test the effects of three common atmospheric correction methods, viz. Dark Object Subtraction (DOS), Quick Atmospheric Correction (QUAC), and Fast Line-of-Sight Atmospheric Analysis of Hypercubes (FLAASH); and two pansharpening methods, viz. Gram–Schmidt (GS) and Hyperspherical Color Sharpening (HCS), on thematic classification of facies using 12 supervised classifiers. The conventional classifiers included: Mahalanobis Distance (MHD), Maximum Likelihood (MXL), Minimum Distance to Mean (MD), Spectral Angle Mapper (SAM), and Winner Takes All (WTA). The advanced/target detection classifiers consisted of: Adaptive Coherence Estimator (ACE), Constrained Energy Minimization (CEM), Matched Filtering (MF), Mixture-Tuned Matched Filtering (MTMF), Mixture-Tuned Target-Constrained Interference-Minimized Filter (MTTCIMF), Orthogonal Space Projection (OSP), and Target-Constrained Interference-Minimized Filter (TCIMF). This experiment was performed on glaciers at two test sites, Ny-Ålesund, Svalbard, Norway; and Chandra–Bhaga basin, Himalaya, India. The overall performance suggested that the FLAASH correction delivered realistic reflectance spectra, while DOS delivered the least realistic. Spectra derived from HCS sharpened subsets seemed to match the average reflectance trends, whereas GS reduced the overall reflectance. WTA classification of the DOS subsets achieved the highest overall accuracy (0.81). MTTCIMF classification of the FLAASH subsets yielded the lowest overall accuracy of 0.01. However, FLAASH consistently provided better performance (less variable and generally accurate) than DOS and QUAC, making it the more reliable and hence recommended algorithm. While HCS-pansharpened classification achieved a lower error rate (0.71) in comparison to GS pansharpening (0.76), neither significantly improved accuracy nor efficiency. The Ny-Ålesund glacier facies were best classified using MXL (error rate = 0.49) and WTA classifiers (error rate = 0.53), whereas the Himalayan glacier facies were best classified using MD (error rate = 0.61) and WTA (error rate = 0.45). The final comparative analysis of classifiers based on the total error rate across all atmospheric corrections and pansharpening methods yielded the following reliability order: MXL > WTA > MHD > ACE > MD > CEM = MF > SAM > MTMF = TCIMF > OSP > MTTCIMF. The findings of the current study suggested that for VHR visible near-infrared (VNIR) mapping of facies, FLAASH was the best atmospheric correction, while MXL may deliver reliable thematic classification. Moreover, an extensive account of the varying exertions of each processing scheme is discussed, and could be transferable when compared against other VHR VNIR mapping methods.

Modeling approach for flexible shaft-disk-drum rotor systems with elastic connections and supports

A dynamic modeling method is proposed for shaft-disk-drum (SDM) rotor systems with elastic connections and supports, upon which coupling vibrations of disk, drum and shaft are investigated. Firstly, the energy functions of shaft, disk and drum are derived based on Euler-Bernoulli beam, Kirchhoff plate and Sanders’ shell theories, respectively, where the rotation induced gyroscopic and centrifugal effects are taken into account. Artificial springs are defined at the ends of shaft to simulate the elastic supporting conditions. Similarly, elastic springs are defined at the joint interfaces between rotor components, that is, the shaft, disk and drum, to represent the elastic connection conditions. Then, employing the orthogonal polynomials achieved by Gram-Schmidt process to expand displacement fields, the motion equations for flexible SDM rotor systems are derived by using Lagrange equation. By comparing the present results with those in literature and from finite element analysis, the proposed modeling approach is verified. Lastly, the effects of drum geometry and connection conditions on the dynamic of flexible SDM rotor systems are investigated. The modeling approach proposed here overcomes the deficiencies of existing approaches on continuum theory, and can be extended to multi-stage flexible SDM rotor systems with more complex configurations conveniently.

Towards a universal and privacy preserving EEG-based authentication system

EEG-based authentication has gained much interest in recent years. However, despite its growing appeal, there are still various challenges to their practical use, such as lack of universality, lack of privacy-preserving, and lack of ease of use. In this paper, we have tried to provide a model for EEG-based authentication by focusing on these three challenges. The proposed method, employing deep learning methods, can capture the fingerprint of the users’ EEG signals for authentication aim. It is capable of verifying any claimed identity just by having a genuine EEG fingerprint and taking a new EEG sample of the user who has claimed the identity, even those who were not observed during the training. The role of the fingerprint function is similar to the hash functions in password-based authentication and it helps preserve the user’s privacy by storing the fingerprint, rather than the raw EEG signals. Moreover, for targeting the lack of ease of use challenge, Gram-Schmidt orthogonalization process reduces the required number of channels to just three ones. The experiments show that the proposed method can reach around 98% accuracy in the authentication of completely new users with only three channels of Oz, T7, and Cz.

An Efficient Hardware Implementation of Detecting Targets from Remotely Sensed Hyperspectral Images

Real-time implementation of hyperspectral imagery is an emerging research area which has notable remote sensing applications. It is challenging to process a huge volume of hyperspectral data under real-time constraints. Field programmable gate arrays are considered as an efficient hardware suited for onboard processing system. ATGP is a proven target detection algorithm which can automatically detect the target without any predefined data. In the traditional method, this algorithm involves orthogonal subspace projector which makes the hardware design too complex and slow. To speed up the process, Gram-Schmidt orthogonalization operator is used. Gram-Schmidt orthogonalization technique uses inner product instead of matrix inverse which makes the hardware design easy to implement in FPGA board. A detailed comparative analysis is carried out using three different hyperspectral images to emphasize the performance of the design which is adopted in this technique. The processing speed of the proposed ATGP-GS algorithm is 3.484 s for ROSIS Pavia University dataset, 1.781 s for HYDICE Urban dataset and 1.609 s for AVIRIS Cuprite dataset. The proposed algorithm is implemented in Virtex 6 ML605 evaluation board to evaluate the real-time performance of the system.

Dual Hashing Index Cancellable Finger Vein Template Based on Gaussian Random Mapping

In the existing cancellable finger vein template protection schemes, the original biometric features cannot be well protected, which results in poor security. In addition, the performance of matching recognition performances after generating a cancellable template is poor. Therefore, a dual hashing index cancellable finger vein template protection based on Gaussian random mapping is proposed in this study. The scheme is divided into an enrollment stage and a verification stage. In the two stages, symmetric data encryption technology was used to generate encryption templates for matching. In the enrollment stage, first, the extracted finger vein features were duplicated to obtain an extended feature vector; then, this extended vector was uniformly and randomly permuted to obtain a permutation feature vector. The above two vectors were combined into a two-dimensional feature matrix. The extended and permuted feature vector made full use of the original biometric features and further enhanced the non-invertibility. Second, a random Gaussian projection vector with m×q dimensions was generated, and a random orthogonal projection matrix was generated by the Schmidt orthogonalization of the previously generated random vector. This approach accurately transferred the characteristics of the biometric features to another feature space and ensured that the biological template is revocable. Finally, the inner product of the two-dimensional feature vector and random orthogonal projection matrix was obtained and superimposed into a row. The dual index values of the largest and second largest values were repeated m times to obtain a hash code for matching. The secondary maximum value index was introduced to adjust the error generated by the random matrix, which improved the recognition rate of the algorithm. In the verification stage, another hash code for matching was generated based on symmetric data encryption technology, and then the two hash codes were cross matched to obtain the final matching result. The experimental results show that this scheme attains good recognition performance with the PolyU and SDUMLA-FV databases, that it meets the design standard for cancellable biometric identification, and that it is robust to security and privacy attacks.

Evaluation of Multi-Source High-Resolution Remote Sensing Image Fusion in Aquaculture Areas

Image fusion of satellite sensors can generate a high-resolution multi-spectral image from inputs of a high spatial resolution panchromatic image and a low spatial resolution multi-spectral image for feature extraction and target recognition, such as enclosure seines and floating rafts. However, there is currently no clear and definite method of image fusion for different aquaculture areas distribution extraction from high-resolution satellite images. This study uses three types of high-resolution remote sensing images, GF-1 (Gaofen-1), GF-2 (Gaofen-2), and WV-2 (WorldView-2), covering the raft and enclosure seines aquacultures in the Xiangshan Bay, China, to evaluate panchromatic and multispectral image fusion techniques to determine which is the best. This study applied PCA (principal component analysis), GS (Gram-Schmidt), and NNDiffuse (nearest neighbor diffusion) algorithms to panchromatic and multispectral images fusion of GF-1, GF-2, and WV-2. Two quantitative methods are used to evaluate the fusion effect. The first used seven statistical parameters, including gray mean value, standard deviation, information entropy, average gradient, correlation coefficient, deviation index, and spectral distortion. The second is the CQmax index. Comparing the evaluation results by these seven common statistical indicators with the results of the image fusion evaluation by index CQmax, the results prove that the CQmax index can be applied to the evaluation of image fusion effects in different aquaculture areas. For the floating raft cultured area, the conclusion is consentaneous; NNDiffuse was also optimal for GF-1 and GF-2 data, and PCA was optimal for WV-2 data. For the enclosure seines culture area, the conclusion of quantitative evaluations is not consistent and it shows that there is no definite good method that can be applied to all areas; therefore, careful evaluation and selection of the best applicable image fusion method are required according to the study area and sensor images.

A unified modeling approach for rotating flexible shaft-disk systems with general boundary and coupling conditions

In the current work, a unified modeling approach is developed for rotating flexible shaft-disk systems under general boundary conditions to investigate the general coupling vibrations of shaft and disk. Initially, the energy functions of disk and shaft are obtained based on Kirchhoff and Euler-Bernoulli beam theories, respectively, where centrifugal effects and gyroscopic effects induced by rotation are considered. Artificial springs are employed at shaft ends and between disk and shaft to represent general boundary and coupling conditions, respectively. Then, by taking the orthogonal polynomials generated via Gram-Schmidt process as admissible functions, Lagrange equation is applied to obtain motion equations for flexible shaft-disk systems. The method is validated through the comparison of the obtained results with those reported in open literature. Finally, the influences of geometric parameters, general coupling and boundary conditions on the natural frequencies and dynamic responses of flexible shaft-disk systems are studied. The proposed method is capable of overcoming the deficiencies of exiting modeling methods based on continuum theory and can be conveniently extended to complex rotor systems with multiple flexible disks and supports under general boundary and coupling conditions.

Computational Intelligence Method for Detection of White Blood Cells Using Hybrid of Convolutional Deep Learning and SIFT.

Infection diseases are among the top global issues with negative impacts on health, economy, and society as a whole. One of the most effective ways to detect these diseases is done by analysing the microscopic images of blood cells. Artificial intelligence (AI) techniques are now widely used to detect these blood cells and explore their structures. In recent years, deep learning architectures have been utilized as they are powerful tools for big data analysis. In this work, we are presenting a deep neural network for processing of microscopic images of blood cells. Processing these images is particularly important as white blood cells and their structures are being used to diagnose different diseases. In this research, we design and implement a reliable processing system for blood samples and classify five different types of white blood cells in microscopic images. We use the Gram-Schmidt algorithm for segmentation purposes. For the classification of different types of white blood cells, we combine Scale-Invariant Feature Transform (SIFT) feature detection technique with a deep convolutional neural network. To evaluate our work, we tested our method on LISC and WBCis databases. We achieved 95.84% and 97.33% accuracy of segmentation for these data sets, respectively. Our work illustrates that deep learning models can be promising in designing and developing a reliable system for microscopic image processing.

Accelerated identification algorithms for rational models based on the vector transformation

AbstractAn accelerated algorithm, termed as Gram–Schmidt orthogonalization gradient‐based iterative algorithm, is proposed for rational models in this article. The algorithm can obtain the optimal parameter estimates in one iteration for the reason that the information vectors obtained by using the vector transformation are independent of each other. Compared to the least squares algorithm and the traditional gradient‐based iterative algorithm, the proposed algorithm does not require the matrix inversion and eigenvalue calculation, thus it can be applied to nonlinear systems with complex structures or large‐scale systems. Since the information vector of the rational models contains the latest output that is correlated with the noise, a bias‐compensated Gram–Schmidt orthogonalization gradient‐based iterative algorithm is introduced, by which the unbiased parameter estimates can be obtained. Two simulated examples are applied to demonstrate the efficiency of the proposed algorithm.

ADVANCED GRAM-SCHMIDT METHOD FOR RADAR SIGNAL PROCESSING

Context. When protecting radar stations from active noise interference acting along the side lobes of the antenna directional pattern, spatial filtering of signals is used, which is realized by using antennas that are spaced apart in space. In this case, the difference in the directions of reception of the useful signal and the interference makes it possible to form the optimal value of the weighting coefficients of the adaptive spatial filters to suppress the interference. However, if the interfering source moves into the main beam region, then the spatial differences between the wanted signal and the interference are reduced. This leads to significant distortion of the main antenna radiation pattern. As a result, the accuracy of measuring the angular coordinates deteriorates, as well as the sensitivity of the radar receiver. The article proposes a structural-parametric method for adapting a spatial filter, which ensures effective operation of the radar when exposed to the active noise interference both from the direction of the side lobes and from the direction of the main beam.
 Goal. Improving the efficiency of the radar when the active noise interference source is shifted from the direction to the side lobes to the direction of the main beam.
 Method. The proposed method makes it possible, due to the structural adaptation of the multichannel spatial filter, to exclude the distortion of the main beam of the radiation pattern of the radar antenna and to ensure its operation under conditions of possible interference from the main beam. Structural adaptation of the spatial filter is realized by the current analysis of the weighting coefficients of the compensation blocks.
 Results. The structural diagram of the multichannel spatial filter by the Gram-Schmidt method with structural-parametric adaptation, as well as the structural diagram of the compensation block, has been improved. As a result of the simulation, the possibility of eliminating distortions of the radiation pattern of the main antenna of the radar in conditions of the possible impact of the active noise interference along the main beam of the radiation pattern of the radar has been confirmed.
 Conclusions. The scientific novelty of the work consists in the improvement of the signal-processing algorithm at spatial filtering both when exposed to the active noise interference from the direction of the side lobes, and when the interference source is shifted to the direction of the main beam of radar. The practical novelty of the work lies in the development of a structural diagram and a mathematical model of an improved spatial filter with structural-parametric adaptation.

A Novel Strategy for Improving the Counter Propagation Artificial Neural Networks in Classification Tasks

Counter-Propagation-Artificial-Neural-Networks (C P-ANNs) have been applied in several domains due to their learning and classification abilities. Regardless of their strength, the CP-ANNs still have some limitations in pattern recognition tasks when they encounter ambiguities during the learning process, which leads to the inaccurate classification of the Kohonen-Self-Organizing-Map (K-SOM). This problem has an impact on the performance of the CP-ANNs. Therefore, this paper proposes a novel strategy to improve the CP-ANNs by the Gram-Schmidt algorithm (GSHM) as a pre-processing step of the original data without changing their architecture. Three datasets examples from various domains, such as correlation, crop, and fertilizer, were employed for experimental validation. To obtain the results, we relied on two simulations. The first simulation uses CP-ANNs, and the datasets are inputted into the network without any prior pre-processing. The second simulation uses MCP-ANNs, and the datasets are pre-processed through the GSHM block. Experiment results show that the proposed MCP-ANNs recognize all patterns with a classification accuracy of 100% versus 62.5% for CP-ANNs in the Correlation Dataset. Furthermore, the proposed MCP-ANNs reduce the execution time and training parameter values in all datasets versus CP-ANNs. Thus, the proposed approach based on the GSHM algorithm significantly improves the performance of the CP-ANNs.

Variable Screening Optimization Algorithm for Mahalanobis-Taguchi System

This paper proposes a Mahalanobis-Taguchi system variable screening optimization method based on binary quantum behavior particle swarm.The main procedures and methods are as follows, Firstly, the Mahalanobis distance value is calculated by the Gram-Schmidt orthogonalization method.We build the multi-objective mixed planning model. The binary quantum behavior particle swarm optimization algorithm is used to solve the optimal combination. A new prediction system based on Mahalanobis-Taguchi metric is established, and the task of accurate discrimination is accomplished.

Sub-Region Localized Hashing for Fine-Grained Image Retrieval.

Fine-grained image hashing is challenging due to the difficulties of capturing discriminative local information to generate hash codes. On the one hand, existing methods usually extract local features with the dense attention mechanism by focusing on dense local regions, which cannot contain diverse local information for fine-grained hashing. On the other hand, hash codes of the same class suffer from large intra-class variation of fine-grained images. To address the above problems, this work proposes a novel sub-Region Localized Hashing (sRLH) to learn intra-class compact and inter-class separable hash codes that also contain diverse subtle local information for efficient fine-grained image retrieval. Specifically, to localize diverse local regions, a sub-region localization module is developed to learn discriminative local features by locating the peaks of non-overlap sub-regions in the feature map. Different from localizing dense local regions, these peaks can guide the sub-region localization module to capture multifarious local discriminative information by paying close attention to dispersive local regions. To mitigate intra-class variations, hash codes of the same class are enforced to approach one common binary center. Meanwhile, the gram-schmidt orthogonalization is performed on the binary centers to make the hash codes inter-class separable. Extensive experimental results on four widely used fine-grained image retrieval datasets demonstrate the superiority of sRLH to several state-of-the-art methods. The source code of sRLH will be released at https://github.com/ZhangYajie-NJUST/sRLH.git.

Data-Driven Sparse Polynomial Chaos Expansion for Models with Dependent Inputs

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in the literature. Recently, different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications. Typical approaches include building PCEs based on the Gram-Schmidt algorithm or transforming the dependent inputs into independent inputs. However, the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions, respectively. In this paper, we propose a data-driven approach to build sparse PCEs for models with dependent inputs. The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output. The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency. Four numerical examples are implemented to validate the proposed algorithm.

Image Fusion of Ku-Band-Based SCATSAT-1 and MODIS Data for Cloud-Free Change Detection Over Western Himalayas

Image-based fusion is a state-of-the-art process to extract vital information by combining the two or more images acquired from different satellite sensors. Recently launched (September 26, 2016) Indian Space Research Organization’s (ISRO) Ku-band (13.5 GHz)-based Scatterometer Satellite (SCATSAT-1) as an active microwave sensor can offer the day–night, all-weather monitoring services, which are not possible with the optical-based visible and infrared remote sensing satellites. Therefore, the fusion of optical and microwave data offers the cloud-free detection of Earth surface transitions and helps in emergency response to natural hazards, security, and defense. The objectives of the proposed framework are: 1) nearest neighbor-based fusion (NNF) of ISRO’s SCATSAT-1 and National Aeronautics and Space Administration’s (NASA) Moderate Resolution Imaging Spectroradiometer (MODIS) optical data; 2) generation of thematic maps using artificial neural network (ANN)-based classification of the fused data; 3) detection of spatiotemporal variations via postclassification comparison (PCC)-based change detection; 4) cross-referencing with well-defined fusion methods, i.e., Gram–Schmidt (GS), Brovey transformation (BT), and Ehlers; and 5) impact analysis of clouds on the input dataset and fusion methods. This study has been conducted over the Western Himalayas to estimate the snow cover changes under cloudy conditions with two datasets, i.e., winter and monsoon. The experimental outcomes confirm the efficacy of the proposed framework in the effective removal of clouds, generation of classified maps, and change maps. The present study includes an exhaustive list of applicative situations for cloud-free monitoring using freely and daily-based SCATSAT-1 and MODIS datasets.

Quantum Blockchain Based on Dimensional Lifting Generalized Gram-Schmidt Procedure

The advancement of quantum computers undermines the security of classical blockchain, necessitating either a post-quantum upgrade of the existing architecture or creation of an inherently quantum blockchain. Here we propose a practically realizable model of a fully quantum blockchain based on a generalized Gram-Schmidt procedure utilizing dimensional lifting. In this model, information of transactions stored in a multi-qubit state are subsequently encoded using the generalized Gram-Schmidt process. The chain is generated as a result of the reliance of orthogonalized state on the sequence of states preceding it. Various forking scenarios and their countermeasures are considered for the proposed model. It is shown to be secure even against quantum computing attacks using the no-cloning theorem and non-democratic nature of Generalized Gram-Schmidt orthogonalization. Finally, we outline a framework for a quantum token built on the same architecture as our blockchain.

Hybrid Precoding for Millimeter Wave MIMO: Trace Optimization Approach

The hybrid precoding problem in point-to-point millimeter wave (mmWave) multiple input multiple output (MIMO) for narrowband channel is established as a Frobenius norm minimization problem. It is translated into trace minimization problem, and two algorithms are proposed to solve it. In the first method based on alternating minimization, we alternately determine the analog precoder and digital precoder, keeping the other constant to minimize the trace. The analog precoding subproblem with the fixed digital precoder is converted into a semi-definite programming (SDP) problem and solved by block coordinate descent (BCD) algorithm with suitable modifications. In the second method, we segregate the analog precoding and digital precoding subproblems by considering orthogonality of analog precoder. The analog precoding is further rephrased as a trace maximization problem and solved by an iterative power method by enforcing orthogonality constraint on the analog precoder. The adapted form of modified Gramm-Schmidt orthogonalization procedure is employed to impose orthogonality on the analog precoder. The proposed methods are extended for wideband channel by considering orthogonal frequency division multiplexing (OFDM). The proposed methods not only exhibit a good performance but also come with lower computational complexity when compared to existing methods with comparable performances.

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>

Block Gram-Schmidt algorithms and their stability properties

Block Gram-Schmidt algorithms serve as essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability properties remains open. This work provides a comprehensive categorization of block Gram-Schmidt algorithms, particularly those used in Krylov subspace methods to build orthonormal bases one block vector at a time. Known stability results are assembled, and new results are summarized or conjectured for important communication-reducing variants. Additionally, new block versions of low-synchronization variants are derived, and their efficacy and stability are demonstrated for a wide range of challenging examples. Numerical examples are computed with a versatile Matlab package hosted at https://github.com/katlund/BlockStab, and scripts for reproducing all results in the paper are provided. Block Gram-Schmidt implementations in popular software packages are discussed, along with a number of open problems. An appendix containing all algorithms type-set in a uniform fashion is provided.