Singular Value Decomposition Research Articles

An indoor positioning method based on bluetooth array/PDR fusion using the SVD-EKF

With the development of mobile internet and artificial intelligence, the core of current surveying and mapping science and technology is no longer confined solely to outdoor applications. High-precision indoor positioning technology is now one of the core technologies in the era of artificial intelligence. An angle measurement and positioning system based on wireless signal array antennas can achieve high accuracy in indoor unblocked conditions. However, indoor environment is unpredictable, and the user's behavior is also random. Inevitably, some signal reflection and other factors will affect the positioning accuracy. Considering all the aforementioned, this study analyzes the principles and characteristics of a Bluetooth signal based array antenna angle measurement and positioning system. In addition, aiming at the multi-phase problem caused by antenna switching, the frequency estimation method based on FFT (Fast Fourier Transform) is studied in this paper, achieving high-precision angle measurement and positioning. Aiming at the problem that the system positioning error increase in the complex and variable indoor environment, a fusion positioning method of Bluetooth array/PDR (Pedestrian Dead Reckoning) based on the SVD-EKF (Singular Value Decomposition–Extended Kalman Filter) is proposed. This study introduces a few improvements to the EKF (Extended Kalman Filter). First, the predicted state covariance matrix is decomposed by singular value decomposition, which improves the robustness of the EKF. Second, a Bluetooth array self-evaluation factor is introduced and combined with the Huber function to construct an adaptive factor, thus further enhancing filtering accuracy and environmental adaptability. Through static and dynamic data collected in indoor environment, the feasibility of the algorithm is verified. The results of static and dynamic experimental results show that the array angle measurement and positioning system can achieve high accuracy, the near point positioning maximum error is 0.3m and the far point positioning accuracy is 0.6m. The dynamic test results in the room show that after SVD-EKF algorithm optimization, the positioning error is reduced by 0.05m, which is equivalent to the EKF algorithm. However, in corridor areas, the improvement of accuracy of SVD-EKF algorithm is better than EKF, achieving an improvement of 0.373 m and a smoother positioning result compared to the traditional EKF algorithm. This study provides a new practical technology with a high precision and easy deployment for indoor positioning.

Singular-Value-Based Cluster Number Detection Method

The cluster number can directly affect the clustering effect and its application in real-world scenarios. Its determination is one of the key issues in cluster analysis. According to singular value decomposition (SVD), the characteristic directions of larger singular values likely represent the primary data patterns, trends, or structures corresponding to the main information. In clustering analysis, the main information and structure are likely related to the cluster structure itself. The number of larger singular values may correspond to the number of clusters, and their main information may correspond to different clusters. Based on this, a singular-value-based cluster number detection method is proposed. First, the transferred K-nearest neighbors (TKNN) density formula is proposed to address the limitation of the DPC algorithm in failing to identify centroids in sparse clusters of unbalanced datasets. Second, core data are selected by the DPC algorithm with a modified density formula to better capture the data distribution. Third, based on the selected core data, a sparse similarity matrix is constructed to further highlight the relationships between data and enhance the distribution of data features. Finally, SVD is performed on the sparse similarity matrix to obtain singular values, the cumulative contribution rate is introduced to determine the number of relatively large singular values (i.e., the cluster number). Experimental results show that our method is superior in determining the cluster number for datasets with complex shapes.

Uncovering Deterministic Behavior of Black Hole IGR J17091–3624: A Twin of GRS 1915+105

Abstract Understanding the nonlinear properties in accreting systems, particularly for black holes, from observation is illuminating as they are expected to be general relativistic magnetohydrodynamic flows that are nonlinear. Two commonly used features associated with nonlinear systems are chaos, which is deterministic, and randomness, which is stochastic. The differentiation between chaotic and stochastic systems is often considered to quantify the nonlinear properties of an astrophysical system. Particular emphasis is given to the fact that data are often noise contaminated and finite. We examine the dual nature of the black hole X-ray binary IGR J17091–3624, whose behavior has been closely studied in parallel to GRS 1915+105. Certain similarities in the temporal classes of these two objects have been explored in the literature. However, this has not been the case with their nonlinear dynamics: GRS 1915+105 shows signs of both determinism and stochasticity, while IGR J17091–3624 was found to be predominantly stochastic. Here, we confront the inherent challenge of noise contamination faced by previous studies, particularly Poisson noise, which adversely impacts the reliability of nonlinear results. We employ several denoising techniques to mitigate noise effects, and employ methods like principal component analysis, singular value decomposition, and correlation integrals to isolate the deterministic signatures. We find signs of determinism in IGR J17091–3624, thus supporting the hypothesis of it being similar to GRS 1915+105, even as a dynamical system. Our findings not only shed light on the complex nature of IGR J17091–3624 but also pave the way for future research employing noise-reduction techniques to analyze nonlinearity in observed dynamical systems.

Enhanced Multilinear PCA for Efficient Image Analysis and Dimensionality Reduction: Unlocking the Potential of Complex Image Data

This paper presents an Enhanced Multilinear Principal Component Analysis (EMPCA) algorithm, an improved variant of the traditional Multilinear Principal Component Analysis (MPCA) tailored for efficient dimensionality reduction in high-dimensional data, particularly in image analysis tasks. EMPCA integrates random singular value decomposition to reduce computational complexity while maintaining data integrity. Additionally, it innovatively combines the dimensionality reduction method with the Mask R-CNN algorithm, enhancing the accuracy of image segmentation. Leveraging tensors, EMPCA achieves dimensionality reduction that specifically benefits image classification, face recognition, and image segmentation. The experimental results demonstrate a 17.7% reduction in computation time compared to conventional methods, without compromising accuracy. In image classification and face recognition experiments, EMPCA significantly enhances classifier efficiency, achieving comparable or superior accuracy to algorithms such as Support Vector Machines (SVMs). Additionally, EMPCA preprocessing exploits latent information within tensor structures, leading to improved segmentation performance. The proposed EMPCA algorithm holds promise for reducing image analysis runtimes and advancing rapid image processing techniques.

Enhanced utility estimation algorithm for discrete choice models in travel demand forecasting

Abstract Recent data-driven discrete choice models in travel demand forecasting have achieved improved predictability. However, such prediction improvements come at the cost of black-box models and lost transparency in travel demand forecasting, which makes scenario testing and transportation planning difficult (if not impossible). Furthermore, these predictability gains have often been modest compared to handcrafted parsimonious models, which benefit from enhanced behavioural interpretability and transparency. This paper introduces a novel bi-level model and estimation framework (DUET) to enhance predictability in traditional utility-based discrete choice models. The proposed model improves the specification process by identifying effective variable transformations and interactions in utility functions. Utilising a genetic algorithm, the upper level of our framework selects feasible functional forms from an extensive array, while the lower level applies iterative singular value decomposition and maximum likelihood estimation to optimise model parameters and prevent overfitting. This approach ensures superior predictability through a general utility functional form that considers extensive variable interactions. Case studies on both synthetic data and the Swissmetro dataset highlight the framework’s effectiveness in improving model performance and uncovering critical behavioural patterns and latent trends. Notably, incorporating interactions among variables in Swissmetro data, our model demonstrates a 6.5% improvement in the Brier score (probabilistic prediction accuracy) compared to the state-of-the-art deep neural network-based discrete choice model.Lastly, our results on transport mode choice data align with existing literature, indicating that younger individuals are less sensitive to travel costs. This confirms the need for targeted pricing policies to encourage public transit use among different age groups.

Compressed sensing based off-grid calibration for microwave imaging with random illuminations under low SNR

ABSTRACT Recently, microwave imaging (MWI) based on randomized fields has shown promising potential in practical scenes. However, the off-grid error and low signal-to-noise ratio (SNR) measurements remain a challenge for the imaging process. In this paper, we proposed a compressed sensing (CS) based off-grid calibration method for MWI with random illuminations under low SNR environment. A noisy mismatched imaging model with off-grid error is firstly established. Under the framework of CS, the off-grid error is corrected by genetic algorithm (GA) and singular value decomposition (SVD) is conducted to enhance the SNR of echo signal. In the inversion, the OMP algorithm is used due to its high computational efficiency. At last, the effectiveness of the proposed method is verified based on the numerical data. Compared to the existing algorithms, the proposed approach is able to achieve satisfactory results in both off-grid calibration and noise suppression. Besides, the imaging performance versus the number of measurements, SNR, off-grid level and sparsity is discussed. The proposed method provides a new clue for off-grid MWI in low SNR scenarios.

The exploitation of eigenspectra in electrochemical impedance spectroscopy: Reconstruction of spectra from sparse measurements

Electrochemical Impedance Spectroscopy (EIS) represents one of the most widely utilized techniques for the characterization of solid oxide cells (SOCs) and stacks in contemporary research. This work examines patterns in a set X of over 2.600 EIS measurements conducted on SOC stack level to identify a low-dimensional representation of the data. Besides the efficient training of data-driven models in such, this work primarily focuses on enabling the reconstruction of complete spectra from sampling the impedance at a limited number of relevant frequencies, thus significantly reducing the measurement time. By applying singular value decomposition, a reconstruction matrix can be developed containing a set of r patterns to sufficiently describe all the EIS in X. Based on these patterns, a set of r/2 tailored frequencies can be determined. For every permutation of measurement conditions in X and for r between four and twelve, the reconstruction results are comprehensively discussed utilizing EIS measurements conducted on a holdout SOC stack and thus not being part of the data set X. Furthermore, EIS containing varying faults and artificially distorted EIS are used to also capture unforeseen behavior. Depending on the measurement conditions accurate reconstructions can be reported for r=6, i.e. three tailored frequencies.

Singular value decomposition of near-field electromagnetic data for compressing and accelerating deep neural networks in the prediction of geometric parameters for through silicon via array

Singular value decomposition of near-field electromagnetic data for compressing and accelerating deep neural networks in the prediction of geometric parameters for through silicon via array

Color image watermarking scheme based on singular value decomposition of split quaternion matrices

Color image watermarking scheme based on singular value decomposition of split quaternion matrices

A reconstruction method for dam monitoring data based on improved singular value decomposition

A reconstruction method for dam monitoring data based on improved singular value decomposition

Analysis of Different Noise Reduction Effects of Ground Penetrating Radar Image of Cavity Behind Tunnel Primary Support Based on Singular Value Decomposition and Wavelet Transform

The cavity behind the lining structure is a typical disease in tunnel engineering. Cavity seriously affects the interaction between lining and surrounding rock, resulting in uneven bearing of lining structure and stress concentration, which can easily induce lining concrete cracking, water leakage and other diseases. Accurate identification of lining structure cavities is the key to ensure the normal operation of the tunnel. However, the ground penetrating radar detection images of lining cavities often contain interference signals such as background noise, which seriously affects the accuracy and clarity of cavity detection. The application effects of wavelet transform and singular value decomposition in image denoising and resolution of tunnel lining cavity ground penetrating radar are studied. Under this background, the model test of regular and irregular cavity detection behind tunnel lining is carried out, in which the irregular cavity is located in the surrounding rock environment of filling soil to simulate the real situation of tunnel. The measured images of lining cavity under different working conditions are obtained, and the image denoising analysis is carried out. The results show that singular value decomposition can effectively suppress noise. The ground penetrating radar image after singular value decomposition denoising is clearer, and the image resolution is effectively improved, thus realizing the accurate identification of cavity diseases behind the primary support of the tunnel

Multi-modal denoised data-driven milling chatter detection using an optimized hybrid neural network architecture

Chatter, a type of self-excited vibration, deteriorates surface quality and reduces tool life and machining efficiency. Chatter detection serves as an effective approach to achieve stable cutting. To address the low accuracy in chatter detection caused by the limitations of both one-dimensional temporal and two-dimensional image modal information, this study proposes a multi-modal denoised data-driven milling chatter detection method using an optimized hybrid neural network architecture. A data denoising model combining Complementary Ensemble Empirical Mode Decomposition (CEEMD) and Singular Value Decomposition (SVD) is established. The Ivy algorithm is employed to optimize the hyperparameters of CEEMD-SVD. Multi-modal data features of different machining states are then obtained using time–frequency domain methods and Markov transition field methods. Sensitivity analysis of time–frequency domain features is conducted using Pearson correlation coefficient analysis. A hybrid neural network model (DBMA) for chatter detection is constructed by integrating dual-scale parallel convolutional neural networks, bidirectional gated recurrent units, and multi-head attention mechanisms. The Ivy algorithm is utilized to optimize the hyperparameters of DBMA. The t-SNE algorithm is employed to visualize features extracted from different network layers of the chatter detection model. Results demonstrate that effective denoising of machining signals and the use of multi-modal data can significantly improve the accuracy of state detection. Compared with other methods, the proposed model exhibits superior stability and robustness.

Automated Scattering Media Estimation in Peplography Using SVD and DCT

In this paper, we propose automation of estimating scattering media information in peplography using singular value decomposition (SVD) and discrete cosine transform (DCT). Conventional scattering media-removal methods reduce light scattering in images utilizing a variety of image-processing techniques and machine learning algorithms. However, under conditions of heavy scattering media, they may not clearly visualize the object information. Peplography has been proposed as a solution to this problem. Peplography is capable of visualizing the object information by estimating the scattering media information and detecting the ballistic photons from heavy scattering media. Following that, 3D information can be obtained by integral imaging. However, it is difficult to apply this method to real-world situations since the process of scattering media estimation in peplography is not automated. To overcome this problem, we use automatic scattering media-estimation methods using SVD and DCT. They can estimate the scattering media information automatically by truncating the singular value matrix and Gaussian low-pass filter in the frequency domain. To evaluate our proposed method, we implement the experiment with two different conditions and compare the result image with the conventional method using metrics such as structural similarity (SSIM), feature similarity (FSIMc), gradient magnitude similarity deviation (GMSD), and learned perceptual image path similarity (LPIPS).

P-765. Enhancing Tuberculosis (TB) Surveillance with Artificial Intelligence: Utilizing Latent Semantic Indexing (LSI) to Automatically Detect TB Cases

Abstract Background Reducing TB surveillance incurs significant costs, as effective control and societal impact minimization rely on robust, ongoing surveillance systems that integrate and analyze comprehensive data for prompt action. Our study supports integrating artificial intelligence (LSI) into TB and other notifiable disease monitoring frameworks to improve trackingFigure 1Binary Matrix of 125 Terms: Presence vs. Absence of Root Keywords Retrieved from the Patient ElectronicRecord for the LSI Automatic Retrieval System.Binary Matrix of 125 Terms: Presence vs. Absence of Root Keywords Retrieved from the Patient Electronic Record for the LSI Automatic Retrieval System. Methods In 2024, we developed a novel application within Datamart A.R.G.U.S.—Assistant for Recovery and Guarding of Urgent and Epidemiological Sentinels—a cloud-based platform hosted on AWS and developed by our team. This application integrates with hospital systems (MV) and laboratory systems (MATRIX and GAL) to enhance the surveillance of healthcare-associated infections (HAI) and notifiable diseases. Data from both hospital and outpatient care are encoded into a binary matrix of 125 terms (root keywords) extracted from patient electronic records. This matrix is then processed using Singular Value Decomposition (SVD) within an LSI-based information retrieval system (Fig. 1). In our model, each patient is represented as a point in a 125-dimensional hyperdimensional space. When projected into three-dimensional space, this framework allows for effective clustering and classification of notifiable Diseases (Fig. 2), specifically TB (Fig. 3).Figure 2:3D Visualization of High-Dimensional Data: Comparing Mandatory Notifiable Diseases versus Non-Notifiable Diseases. Both patient types are well separated in the space, enabling automatic clustering and classification.3D Visualization of High-Dimensional Data: Comparing Mandatory Notifiable Diseases versus Non-Notifiable Diseases. Both patient types are well separated in the space, enabling automatic clustering and classification. Results The LSI-based matrix was constructed using data from January 2023 to February 2024, encompassing a sample of 17,895 cases (lines) across 125 presence versus absence terms, with each case classified as either a notifiable or non-notifiable disease. The 125-dimensional matrix was reduced to 28 factors using SVD. The sensitivity and specificity of the Euclidean distance were better than those of cosine similarity when automatically identifying TB cases in 1,970 independent queries (Fig. 4).Figure 3:3D Visualization of High-Dimensional Data: Comparing Tuberculosis versus Other Mandatory Notifiable Diseases versus Non-Notifiable Diseases. The three types of patients are well separated in the space, enabling automatic clustering and classification.3D Visualization of High-Dimensional Data: Comparing Tuberculosis versus Other Mandatory Notifiable Diseases versus Non-Notifiable Diseases. The three types of patients are well separated in the space, enabling automatic clustering and classification. Conclusion Artificial Intelligence (LSI), significantly enhances the surveillance of TB and other notifiable diseases by enabling real-time, automated case identification up to one day prior (D-1). This advancement allows surveillance personnel to complete their tasks more efficiently, thereby preventing outbreaks and reducing the risk of unforeseen fatalities.Figure 4:Performance Comparison of Cosine vs. Euclidean Distance Metrics in Automatically Identifying TB Cases Using LSI: Euclidean Distance Demonstrates Superior Accuracy and Has Been Integrated into Datamart A.R.G.U.S. for Real-Time Identification of TB and Other Notifiable Diseases as of the Previous Workday (D-1).Performance Comparison of Cosine vs. Euclidean Distance Metrics in Automatically Identifying TB Cases Using LSI: Euclidean Distance Demonstrates Superior Accuracy and Has Been Integrated into Datamart A.R.G.U.S. for Real-Time Identification of TB and Other Notifiable Diseases as of the Previous Workday (D-1). Disclosures All Authors: No reported disclosures

Re-scaling images using a SVD-based approach

There are many instances in computer science where computational operations must be performed on matrices of different sizes. In the field of machine learning, particularly when interpreting images, it is often necessary to resize and re-scale images to achieve higher resolutions. While there are various methods for this, they typically involve fitting a simple linear or cubic model to scale the image. The singular value decomposition (SVD) is a powerful tool for dimension reduction and projection. Our proposed state-of-the-art method leverages the capabilities of SVD to create a technique for re-scaling images. This method is primarily based on modifications of the eigenvectors derived from SVD. Previous work has shown that by editing only these Eigenvectors, it is possible to minimize error propagation through the images. When applied to several well-known image processing tasks, it is possible to scale an image with reduced error compared to the current state-of-the-art methods. Additionally, we show that our method can improve the results of machine learning approaches.

A Compact Stepped Frequency Continuous Waveform Through-Wall Radar System Based on Dual-Channel Software-Defined Radio

Software-defined radio (SDR) has high flexibility and low cost. It conforms to the miniaturization, lightweight, and digitization trends in through-wall radar systems. Stepped frequency continuous waveform (SFCW) is commonly used in through-wall radar, which has high resolution and strong anti-interference ability. This article develops an SFCW through-wall radar system based on a dual-channel SDR platform. Without changing hardware structure and complicated accessories, a phase compensation method of solving the phase incoherence problem in a low-cost dual-channel SDR platform is proposed. In addition, this article proposes a wall clutter mitigation approach by means of singular value decomposition (SVD) and principal component analysis (PCA) framework for through-wall applications. This approach can process the wall clutter and noise ‌efficiently,‌ and then extract the target subspace to obtain location information. The experimental results indicate that the proposed windowing-based SVD-PCA approach is effective for the developed radar system, which can ensure the accuracy of through-wall detection. It is also superior to the traditional methods in terms of the image quality of range profiles or signal-to-noise ratio (SNR).

Orientation – invariant limb action recognition method for human-robot interaction

PurposeThis study aims to address the issue that existing methods for limb action recognition typically assume a fixed wearing orientation of inertial sensors, which is not the case in real-world human-robot interaction due to variations in how operators wear it, installation errors, and sensor movement during operation.Design/methodology/approachTo address the resulting decrease in recognition accuracy, this paper introduced a data transformation algorithm that integrated the Euclidean norm with singular value decomposition. This algorithm effectively mitigates the impact of orientation errors on data collected by inertial sensors. To further enhance recognition accuracy, this paper proposed a method for extracting features that incorporate both time-domain and time-frequency domain features, markedly improving the algorithm’s robustness. This paper used five classifiers to conduct comparative experiments on action recognition. Finally, this paper built an experimental human-robot interaction platform.FindingsThe experimental results demonstrate that the proposed method achieved an average action recognition accuracy of 96.4%, conclusively proving its effectiveness. This approach allows for the recognition of data from sensors placed in any orientation, using only training samples conducted at an orientation.Originality/valueThis study addresses the challenge of reduced accuracy in limb action recognition caused by sensor misorientation. The human-robot interaction system developed in this paper was experimentally verified to effectively and efficiently guide the industrial robot to perform tasks based on the operator’s limb actions.

Model-based perfusion reconstruction with time separation technique in cone-beam CT dynamic liver perfusion imaging.

The success of embolization, a minimally invasive treatment of liver cancer, could be evaluated in the operational room with cone-beam CT by acquiring a dynamic perfusion scan to inspect the contrast agentflow. The reconstruction algorithm must address the issues of low temporal sampling and higher noise levels inherent in cone-beam CT systems, compared to conventional CT. Therefore, a model-based perfusion reconstruction based on the time separation technique (TST) was applied. TST uses basis functions to model time attenuation curves. These functions are either analytical or based on prior knowledge (PK), extracted using singular value decomposition of the classical CT perfusion data of animal subjects. To explore how well the PK can model perfusion dynamics and what the potential limitations are, the dynamic cone-beam CT (CBCT) perfusion scan was simulated from a dynamic CT perfusion scan under different noise levels. The TST method was compared to staticreconstruction. It was demonstrated on this simulated dynamic CBCT perfusion scan that a set consisting of only four basis functions results in perfusion maps that preserve relevant information, denoise the data, and outperform static reconstruction under higher noise levels. TST with PK would not only outperform static reconstruction but also the TST with analytical basis functions. Furthermore, it has been shown that only eight CBCT rotations, unlike previously assumed ten, are sufficient to obtain the perfusion maps comparable to the reference CT perfusion maps. This contributes to saving dose and reconstruction time. The real dynamic CBCT perfusion scan, reconstructed under the same conditions as the simulated scan, shows potential for maintaining the accuracy of the perfusion maps. By visual inspection, the embolized region was matching to that in corresponding CT perfusionmaps. CBCT reconstruction of perfusion scan data using the TST method has shown promising potential, outperforming static reconstructions and potentially saving dose by reducing the necessary number of acquisition sweeps. Further analysis of a larger cohort of patient data is needed to draw final conclusions regarding the expected advantages of theTST.

Dynamical reversibility and a new theory of causal emergence based on SVD

The theory of causal emergence (CE) with effective information (EI) posits that complex systems can exhibit CE, where macro-dynamics show stronger causal effects than micro-dynamics. A key challenge of this theory is its dependence on coarse-graining method. In this paper, we introduce a fresh concept of approximate dynamical reversibility derived from the singular value decomposition(SVD) of the Markov chain and establish a novel framework for CE based on this. We find that the essence of CE lies in the presence of redundancy, represented by irreversible and correlated information pathways within the Markov dynamics. Therefore, CE can be quantified as the potential maximal efficiency increase for dynamical reversibility or information transmission. We also demonstrate a strong correlation between the approximate dynamical reversibility and EI, establishing an equivalence between the SVD and EI maximization frameworks for quantifying CE, supported by theoretical insights and numerical examples from Boolean networks, cellular automata, and complex networks. Importantly, our SVD-based CE framework is independent of specific coarse-graining techniques and effectively captures the fundamental characteristics of the dynamics.

Deep Autoencoder Framework for Classifying Damage Mechanisms in Repaired CFRP

This study investigates the classification of damage modes in adhesively bonded carbon fiber-reinforced plastic (CFRP) composites, a critical factor in advancing lightweight automotive design. Adhesive bonding, replacing traditional riveting, improves structural integrity while reducing weight and CO2 emissions. Mechanical testing on CFRP composites was performed, and acoustic emission (AE) signals were collected to evaluate damage mechanisms. A deep autoencoder (DAE) framework was developed to automate damage characterization by reducing AE signal dimensionality through singular value decomposition (SVD) and classifying features using the k-means algorithm. This approach effectively identified three primary damage modes: matrix cracking, interfacial debonding, and fiber breakage. Traditional AE features, such as entropy and amplitude were also classified and validated using spectral analysis. The DAE-based strategy demonstrated superior capability in real-time damage mode differentiation. Fractographic analysis confirmed crack growth in the adhesive layer, leading to interfacial debonding, fiber-matrix separation, and eventual fiber rupture. These findings highlight the DAE framework’s effectiveness in enhancing damage mode characterization, offering valuable insights for optimizing the structural performance of bonded CFRP composites in automotive applications.