Direction Of Maximum Variance Research Articles

Detecting and Monitoring Artisanal Mining Operations in Semi-Arid Terrain Using Multitemporal SAR Data for InSAR Coherence Estimation and Unsupervised Classification

Abstract. The impact of artisanal mining in sub-Saharan Africa and other developing countries are often huge as they leave trails of environmental and socio-economic effects on the people and the environment. 123 Multi-temporal SAR data acquired between 2019 and 2023 was used. SARPROZ was used to co-register the images and other preprocessing steps like radiometric and geometric correction to transform the images from SAR coordinates to geographic coordinates after generating all the interferograms. A stack of the 122 coherence map was created. Unsupervised classification was implemented on the stack. Principal component analysis of dimensionality reductions method yielded a far better result than the other unsupervised cluster methods attempted, it showed a very high classification accuracy of the terrain. The principal component analysis worked by computing the covariance matrix of the stacked coherence map then performed eigen-decomposition on it to yield eigenvectors and eigenvalues, The eigenvectors corresponding to the largest eigenvalues represent the principal components. These principal components capture the directions of maximum variance, and the eigenvectors provides a reduced-dimensional representation of the image stack which is then used to reconstruct an approximation of the original image that captures the essential features of the original SAR data. Backscatter intensity of the SAR images processed for this study period for unsupervised change detection and land cover classification, delineated the different features and classes based on long term coherence values.

Fast and Simple Statistical Shape Analysis of Pregnant Women Using Radial Deformation of a Cylindrical Template.

Non-rigid deformation of a template to fit 3D scans of human subjects is widely used to develop statistical models of 3D human shapes and poses. Complex optimization problems must be solved to use these models to parameterize scans of pregnant women, thus limiting their use in antenatal point-of-care tools in low-resource settings. Moreover, these models were developed using datasets that did not contain any 3D scans of pregnant women. In this study, we developed a statistical shape model of the torso of pregnant women at greater than 36 weeks of gestation using fast and simple vertex-based deformation of a cylindrical template constrained along the radial direction. The 3D scans were pre-processed to remove noisy outlier points and segment the torso based on anatomical landmarks. A cylindrical template mesh was then fitted onto the segmented scan of the torso by moving each vertex of in the direction of the radial vector. This process is computationally inexpensive taking only 14.80 seconds to deform a template with 9090 vertices. Principal component analysis (PCA) was performed on the deformed vertex co-ordinates to find the directions of maximum variance. The first 10 principal vectors of our model explained 79.03% of the total variance and reconstructed unseen scans with a mean error of 2.43 cm. We also used the PCA weights of the first 10 principal vectors to accurately predict anthropometric measurements of the pregnant women.

Determining the Orientation of a Magnetic Reconnection X Line and Implications for a 2D Coordinate System

AbstractAn LMN coordinate system for magnetic reconnection events is sometimes determined by defining N as the direction of the gradient across the current sheet and L as the direction of maximum variance of the magnetic field. The third direction, M, is often assumed to be the direction of zero gradient, and thus the orientation of the X line. But when there is a guide field, the X line direction may have a significant component in the L direction defined in this way. For a 2D description, a coordinate system describing such an event would preferably be defined using a different coordinate direction M′ oriented along the X line. Here we use a 3D particle‐in‐cell simulation to show that the X line is oriented approximately along the direction bisecting the asymptotic magnetic field directions on the two sides of the current sheet. We describe two possible ways to determine the orientation of the X line from spacecraft data, one using the minimum gradient direction from Minimum Directional Derivative analysis at distances of the order of the current sheet thickness from the X line, and another using the bisection direction based on the asymptotic magnetic fields outside the current sheet. We discuss conditions for validity of these estimates, and we illustrate these conditions using several Magnetospheric Multiscale (MMS) events. We also show that intersection of a flux rope due to secondary reconnection with the primary X line can destroy invariance along the X line and negate the validity of a two‐dimensional description.

Automated building damage detection on digital imagery using machine learning

Purpose. To develop an automated method based on machine learning for accurate detection of features of a damaged building on digital imagery. Methodology. This article presents an approach that employs a combination of unsupervised machine learning techniques, specifically Principal Component Analysis (PCA), K-means clustering, and Density-Based Spatial Clustering of Applications with Noise (DBSCAN), to identify building damage resulting from military conflicts. The PCA method is utilized to identify principal vectors representing the directions of maximum variance in the data. Subsequently, the K-means method is applied to cluster the feature vector space, with the predefined number of clusters reflecting the number of principal vectors. Each cluster represents a group of similar blocks of image differences, which helps to identify significant features associated with fractures. Finally, the DBSCAN method is employed to identify areas where points with similar characteristics are located. Subsequently, a binary fracture mask is generated, with pixels exceeding the threshold being identified as fractures. Findings. The introduced methodology attains an accuracy rate of 98.13 %, surpassing the performance of conventional methods such as DBSCAN, PCA, and K-means. Furthermore, the method exhibits a recall of 82.38 %, signifying its ability to effectively detect a substantial proportion of positive examples. Precision of 58.54 % underscores the methodology’s capability to minimize false positives. The F1 Score of 70.90 % demonstrates a well-balanced performance between precision and recall. Originality. DBSCAN, PCA and K-means methods have been further developed in the context of automated detection of building destruction in aerospace images. This allows us to significantly increase the accuracy and efficiency of monitoring territories, including those affected by the consequences of military aggression. Practical value. The results obtained can be used to improve automated monitoring systems for urban development and can also serve as the basis for the development of effective strategies for the restoration and reconstruction of damaged infrastructure.

Strategies for Producing Reliable Trends Forecasting of COVID-19 Pandemic in Malaysia using Dynamic Mode Decomposition

Dynamic Mode Decomposition (DMD) with time delay embedding is used to predict dynamic patterns in univariate time series. An important pattern that can be extracted using DMD is the trend or global change in a time series which is useful for producing reliable forecast. DMD utilizes the computationally effi cient singular value decomposition (SVD) to produce a low rank approximation of the linear operator that brings about the dynamic patterns in the time series. Trend in the time series is translated as dynamic modes of the operator with low frequencies. The time evolution of this low frequency pattern produces forecast of the time series. In this paper, we outline the strategies for extracting trend component from COVID-19 time series of Malaysia. It is discovered that, other than identifying modes with slow varying frequencies, we need to also resolve the time stamp delay, so that mean-square error of the reconstructed time series is minimal. Information of the magnitude and phase of DMD modes are useful to identify persistent patterns and remove nonstationary ones. We compare the performance of DMD with another SVD-based method which is the singular spectrum analysis (SSA) and our results highlight certain fundamental difference between these two methods. The forecasts from SSA tend to lean towards the direction of maximum variance, producing low reconstruction error but slow to detect sudden changes in the time series. On the other hand, forecasts from DMD captures the phases of dominant modes that dictates the overall global pattern, hence providing a better prediction of future dynamics of the time series.

Visual perception of surface roughness via maximum variance direction of image patches

Most existing visual roughness perception algorithms are pixel-wised operations, which lead to unstable roughness measurements. To address this problem, a novel visual roughness perception in the maximum variance direction of image patches is proposed in this article. Specifically, each patch is assumed to be a point in a multi-dimensional Euclidean space. To improve the signal-to-noise ratio of roughness, all points are projected onto its maximum variance direction based on principal component analysis. In this direction, the variance of these points is characterized as roughness. A new roughness metric dataset is constructed by scanned images of sandpapers with different mesh sizes to verify the effectiveness of the proposed algorithm. Experiments on the dataset show the proposed method outperforms many computer vision-based methods, such as the gray-level co-occurrence matrix approach and the approach.

A New Method of Fluxgate Magnetometer Offset Vector Determination in the Solar Wind Using Any Magnetic Field Variations

In-depth study of dynamic processes in the astrophysical plasma environment relies on high-precision measurement of the magnetic field. Fluxgate magnetometers (FGMs) are commonly used on spacecraft to measure the magnetic field. However, their zero offsets vary slowly with time, and therefore need regularly in-flight calibration. Traditional methods of calculating the zero offset are based on properties of Alfvén waves, mirror mode structures, or current sheets. Here, we develop a new method of calculating the zero offset using any interplanetary magnetic field (IMF) variations. We create an offset cube according to the possible range of the IMF strength. The average values of B L for the IMF variation events approximately obey the normal distribution if there are enough events, where B L is the magnetic field in the maximum variance direction. Any constant vector added to the natural magnetic field data of the events will make the standard deviation of the normal distribution larger. Thereby, the point is determined to be the zero offset so that the corresponding standard deviation at this point is the minimum in the offset cube. Our test results show that this method has a 95.5% probability of obtaining the zero offset with an error of less than 0.3 nT when 10–21 hr of data are used. Our method provides an option for the in-flight calibration of the spaceborne FGM in the solar wind when there are not enough Alfvén waves, mirror modes, or current sheets.

Quality‐relevant and process‐relevant fault monitoring based on GNPER and the fault quantification index for industrial processes

AbstractTraditional quality‐relevant fault monitoring methods focus on extracting the relationship between the global structural features of the process and quality variables but ignore the local features. At the same time, they lack the quantification of quality‐relevant faults. To solve these problems, a quality‐relevant and process‐relevant fault monitoring method and its fault quantification index based on global neighbourhood preserving embedding regression (GNPER) are proposed. First, by seeking the direction of maximum global variance, the global objective function is applied to neighbourhood preserving embedding algorithm, and the global neighbourhood preserving embedding (GNPE) model is established to fully extract the global and local information of process data. Second, on the basis of GNPE, through the idea of projection regression, the GNPER model is established to obtain mapping relationships among process variables and quality variables, and quality‐relevant subspace and process‐relevant subspace are extracted, the corresponding subspace statistics are established for fault monitoring. Finally, the fault quantification index is established for the faults in the two subspaces, which can provide more meaningful fault monitoring results. A numerical example, the hot rolling mill and the Tennessee Eastman (TE) process, verify the superiority and accuracy of the proposed method.

Cyclic Nonlinear Correlation Analysis for Time Series

Principal component analysis (PCA) and kernel PCA allow the decorrelation of data with respect to a basis that is found via variance maximization. However, these techniques are based on pointwise correlations. Especially in the context of time series analysis this is not optimal. We present a novel generalization of PCA that allows to imprint any desired correlation pattern. Thus the proposed method can be used to incorporate previously known statistical dependencies between input variables into the model which is increasing the overall performance. This is achieved by generalizing the projection onto the direction of maximum variance—as known from PCA—to a projection onto a multi-dimensional subspace. We focus on the use of cyclic correlation patterns, which is especially of interest in the domain of time series analysis. Beneath introducing the presented variation of PCA, we discuss the role of this method with respect to other well-known time series analysis techniques.

Fatigue life calculation of notched specimens by modified Wöhler curve method and theory of critical distance under multiaxial random loading

AbstractReformulation of a critical plane‐based multiaxial fatigue criterion named as Modified Wöhler Curve Method (MWCM) in the frequency domain is proposed; moreover, it is combined with the theory of critical distance (TCD) to implement vibration fatigue lifetime prediction of notched specimens subjected to complex multiaxial random loading. Firstly, a frequency‐domain formulation of the maximum variance method (MVM) is proposed for determining the critical plane with high computational efficiency. Then, a reference fatigue curve is defined through the frequency‐domain formulation of the reference stress ratio corresponding to the critical plane. Finally, the power spectral density (PSD) function of the resolved shear stress along the maximum variance direction is applied with the Bendat/Tovo–Benasciutti (TB) method to implement fatigue damage estimation of mechanical components. Both the time‐domain formulation and the proposed frequency‐domain formulation of the MWCM combined with the TCD are applied to the experimental results from the literature, concerning notched specimens made of 2024‐T4 aluminum alloy tested under various nonproportional bending‐torsion random vibration fatigue loading.

Small‐Scale Magnetic Structures: Cluster Observations

AbstractWithin the inner magnetosphere, the occurrence of plasma waves and/or magnetic field structures plays an important role in the dynamics of the particle populations, accelerating some particles to higher energies while scattering others. The 2013 Cluster Inner Magnetosphere Campaign was designed to investigate this process based on observations made at small separation scales. In addition, it provides an ideal opportunity for the study of small‐scale structures. This paper presents observations of previously unreported small‐scale magnetic field structures and investigates their characteristics and spatial properties. These structures, seen in the STAFF‐SC data set, are characterized by a rotation in the field direction and are observed to have spatial sizes of a few tens of kilometers, with a central core region around 10 km and are probably filamentary current structures. Using a variance analysis, it was determined that the maximum variance direction was close to being perpendicular to the external magnetic field. Based on the size of the central core region the current density is of the order of 10–40 . While they may affect the profile of these structures, data calibration effects were ruled out as their origin.

Capturing discrete latent structures: choose LDs over PCs.

High-dimensional biological data collection across heterogeneous groups of samples has become increasingly common, creating high demand for dimensionality reduction techniques that capture underlying structure of the data. Discovering low-dimensional embeddings that describe the separation of any underlying discrete latent structure in data is an important motivation for applying these techniques since these latent classes can represent important sources of unwanted variability, such as batch effects, or interesting sources of signal such as unknown cell types. The features that define this discrete latent structure are often hard to identify in high-dimensional data. Principal component analysis (PCA) is one of the most widely used methods as an unsupervised step for dimensionality reduction. This reduction technique finds linear transformations of the data which explain total variance. When the goal is detecting discrete structure, PCA is applied with the assumption that classes will be separated in directions of maximum variance. However, PCA will fail to accurately find discrete latent structure if this assumption does not hold. Visualization techniques, such as t-Distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP), attempt to mitigate these problems with PCA by creating a low-dimensional space where similar objects are modeled by nearby points in the low-dimensional embedding and dissimilar objects are modeled by distant points with high probability. However, since t-SNE and UMAP are computationally expensive, often a PCA reduction is done before applying them which makes it sensitive to PCAs downfalls. Also, tSNE is limited to only two or three dimensions as a visualization tool, which may not be adequate for retaining discriminatory information. The linear transformations of PCA are preferable to non-linear transformations provided by methods like t-SNE and UMAP for interpretable feature weights. Here, we propose iterative discriminant analysis (iDA), a dimensionality reduction technique designed to mitigate these limitations. iDA produces an embedding that carries discriminatory information which optimally separates latent clusters using linear transformations that permit post hoc analysis to determine features that define these latent structures.

A New Method to Calculate the Fluxgate Magnetometer Offset in the Interplanetary Magnetic Field: 2. Using Mirror Mode Structures

AbstractAccurate magnetic field measurement is of great significance to the development of space exploration. The fluxgate magnetometer (FGM) is a magnetic field measuring instrument commonly used on the spacecraft. The zero offset of the spaceborne FGM varies slowly with time, thus it needs to be regularly calibrated. Here, we develop a new method to determine the zero offset of the FGM using mirror mode structures. This method is based on an assumption that the magnetic depression of mirror mode structures is only in the maximum variance direction. We find that each mirror mode structure has an optimal offset line (OOL), which is determined by the minimum strength of the modified magnetic field in the plane perpendicular to the maximum variance direction in an offset cube. The OOL is approximately parallel to the maximum variance direction and passes through the zero offset in the offset cube. The common intersection of at least two non‐parallel OOLs can be regarded as the zero offset, which accuracy tends to be higher with more events. Our method can simultaneously use the mirror modes and Alfvén waves, and is able to be applied to many regions, such as solar wind, planetary magnetosheaths and magnetospheres.

An algorithm for fast critical plane search in computer‐aided engineering durability analysis under multiaxial random loadings: Application to the Carpinteri–Spagnoli–Vantadori spectral method

AbstractThis paper presents a new algorithm to implement the Carpinteri–Spagnoli–Vantadori (CSV) multiaxial fatigue criterion for random loading and to shorten the computation time. This goal is achieved after calculating the exact expressions of stress spectral moments in every rotated plane, which allow the maximum variance and expected maximum peak of normal/shear stress to be computed directly. This permits the new algorithm to determine the five rotations of the critical plane without using ‘for/end’ loops (which represent a slow numerical operation), although some information on stress signals examined is lost. Two examples are presented to demonstrate the advantages of the new algorithm in comparison with its standard version, which are particularly remarkable when considering the stress output of all finite element model nodes. The approach behind the new algorithm can be extended to other multiaxial spectral criteria that use angular rotations or direction cosines to locate the critical plane or the direction of maximum stress variance.

Modeling Non‐Force‐Free and Deformed Flux Ropes in Titan's Ionosphere

AbstractPrevious work at Titan presented a set of 85 flux ropes detected during Cassini flybys of Titan from 2005 to 2017. In that study a force‐free model was used to determine the radii and axial magnetic field of the flux ropes. In this work we apply non‐force‐free models. The non‐force‐free model shows an improvement in the number of flux ropes that can be fitted with a model, along with improved uncertainties and χ2 values. A number of asymmetries and features in the magnetometer data cannot be reproduced by either model; therefore, we deform the force‐free model to show that small deformations can replicate these features. One such deformation is to use an elliptical cross section, which replicates a plateau in magnetic field strength along with asymmetries on either side of the center of the flux ropes. Additionally, we explore the properties of bending a flux rope, where we find that minimum variance analysis becomes increasingly degenerate with bending, along with a slight bend causing the switching of the axial field direction from intermediate to maximum variance direction. We conclude that the flux ropes at Titan show aspects of developing flux ropes, compared to other planetary bodies, which exhibit more agreement to the force‐free assumptions of mature flux ropes.

A repeatable and robust local reference frame for 3D surface matching

Local reference frames (LRFs) have been widely used for 3D local surface description. In this work, we propose a repeatable LRF with strong robustness to different nuisances. Different from existing LRF methods, the proposed LRF uses a part of neighboring points within the support region to calculate the z-axis, and performs an effective feature transformation on the neighboring points to define the x-axis. Specifically, feature transformation is applied to the data on a projection plane based on three point distribution characteristics via weighted strategies. These characteristics include the z-height, the distance to the center and the average length to 1-ring neighbors, covariance analysis is then applied to the transformed points to obtain the eigenvector with the largest eigenvalue, which points towards the maximum variance direction. Using a sign disambiguation technique, the modified eigenvector is used to define the final x-axis. Furthermore, a scale strategy is proposed to improve the robustness of the LRF with respect to mesh decimation. The proposed LRF was rigorously tested on six public benchmark datasets consisting of three different application contexts, i.e., 3D shape retrieval, 3D object recognition and registration. Experiments show that our method achieves significantly higher repeatability and stronger robustness than the state-of-the-arts under Gaussian noise, shot noise and mesh resolution variation. Finally, the descriptor matching results on four typical datasets further demonstrate the effectiveness of our LRF.

Determining L‐M‐N Current Sheet Coordinates at the Magnetopause From Magnetospheric Multiscale Data

AbstractWe discuss methods to determine L‐M‐N coordinate systems for current sheet crossings observed by the Magnetospheric Multiscale (MMS) spacecraft mission during ongoing reconnection, where eL is the direction of the reconnecting component of the magnetic field, B, and eN is normal to the magnetopause. We present and test a new hybrid method, with eL estimated as the maximum variance direction of B (MVAB) and eN as the direction of maximum directional derivative of B, and then adjust these directions to be perpendicular. In the best case, only small adjustment is needed. Results from this method, applied to an MMS crossing of the dayside magnetopause at 1305:45 UT on 16 October 2015, are discussed and compared with those from other methods for which eN is obtained by other means. Each of the other evaluations can be combined with eL from MVAB in a generalized hybrid approach to provide an L‐M‐N system. The quality of the results is judged by eigenvalue ratios, constancy of directions using different data segments and methods, and expected sign and magnitude of the normal component of B. For this event, the hybrid method appears to produce eN accurate to within less than 10°. We discuss variance analysis using the electric current density, J, or the J × B force, which yield promising results, and minimum Faraday residue analysis and MVAB alone, which can be useful for other events. We also briefly discuss results from our hybrid method and MVAB alone for a few other MMS reconnection events.

Phase imaging and detection in pseudo-heterodyne scattering scanning near-field optical microscopy measurements.

When considering the pseudo-heterodyne mode for detection of the modulus and phase of the near field from scattering scanning near-field optical microscopy (s-SNOM) measurements, processing only the modulus of the signal may produce an undesired constraint in the accessible values of the phase of the near field. A two-dimensional analysis of the signal provided by the data acquisition system makes it possible to obtain phase maps over the whole [0, 2π) range. This requires post-processing of the data to select the best coordinate system in which to represent the data along the direction of maximum variance. The analysis also provides a quantitative parameter describing how much of the total variance is included within the component selected for calculation of the modulus and phase of the near field. The dependence of the pseudo-heterodyne phase on the mean position of the reference mirror is analyzed, and the evolution of the global phase is extracted from the s-SNOM data. The results obtained from this technique compared well with the expected maps of the near-field phase obtained from simulations.

Efficient Image Recognition Technique Using Invariant Moments and Principle Component Analysis

Image recognition is widely used in different application areas such as shape recognition, gesture recognition and eye recognition. In this research, we introduced image recognition using efficient invariant moments and Principle Component Analysis (PCA) for gray and color images using different number of invariant moments. We used twelve moments for each image of gray images and Hu’s seven moments for color images to decrease dimensionality of the problem to 6 PCA’s for gray and 5 PCA’s for color images and hence the recognition time. PCA is then employed to decrease dimensionality of the problem and hence the recognition time and this is our main objective. The PCA is derived from Karhunen-Loeve’s transformation. Given an N-dimensional vector representation of each image, PCA tends to find a K-dimensional subspace whose basis vectors correspond to the maximum variance direction in the original image space. This new subspace is normally lower dimensional (K N). Three known datasets are used. The first set is the known Flower dataset. The second is the Africans dataset, and the third is the Shapes dataset. All these datasets were used by many researchers.

On determining fluxgate magnetometer spin axis offsets from mirror mode observations

Abstract. In-flight calibration of fluxgate magnetometers that are mounted on spacecraft involves finding their outputs in vanishing ambient fields, the so-called magnetometer offsets. If the spacecraft is spin-stabilized, then the spin plane components of these offsets can be relatively easily determined, as they modify the spin tone content in the de-spun magnetic field data. The spin axis offset, however, is more difficult to determine. Therefore, usually Alfvénic fluctuations in the solar wind are used. We propose a novel method to determine the spin axis offset: the mirror mode method. The method is based on the assumption that mirror mode fluctuations are nearly compressible such that the maximum variance direction is aligned to the mean magnetic field. Mirror mode fluctuations are typically found in the Earth's magnetosheath region. We introduce the method and provide a first estimate of its accuracy based on magnetosheath observations by the THEMIS-C spacecraft. We find that 20 h of magnetosheath measurements may already be sufficient to obtain high-accuracy spin axis offsets with uncertainties on the order of a few tenths of a nanotesla, if offset stability can be assumed.