Subspace Projection Research Articles

Tensor local linear embedding with global subspace projection optimisation

In this paper, a novel tensor dimensionality reduction (TDR) approach is proposed, which maintains the local geometric structure of tensor data by tensor local linear embedding and explores the global feature by optimising global subspace projection. Firstly, we analyse the local linear feature of tensor data for learning the linear separable embedding of the tenor data. Furthermore, a global subspace projection distance minimisation strategy is introduced to extract the global characteristic of the tensor data. The aim of this strategy is to find an optimal low-dimensional subspace for TDR. In particular, two novel TDR algorithms are developed by the ensemble of tensor local feature preservation and global subspace projection distance minimisation, which express the subspace projection optimisation as an iteration optimisation problem and a Rayleigh quotient problem, respectively. The extensive experimental results on tensor data classification and clustering have demonstrated the proposed algorithms performed well.

Low-Complexity Robust Adaptive Beamforming Based on INCM Reconstruction via Subspace Projection.

Adaptive beamforming is sensitive to steering vector (SV) and covariance matrix mismatches, especially when the signal of interest (SOI) component exists in the training sequence. In this paper, we present a low-complexity robust adaptive beamforming (RAB) method based on an interference–noise covariance matrix (INCM) reconstruction and SOI SV estimation. First, the proposed method employs the minimum mean square error criterion to construct the blocking matrix. Then, the projection matrix is obtained by projecting the blocking matrix onto the signal subspace of the sample covariance matrix (SCM). The INCM is reconstructed by replacing part of the eigenvector columns of the SCM with the corresponding eigenvectors of the projection matrix. On the other hand, the SOI SV is estimated via the iterative mismatch approximation method. The proposed method only needs to know the priori-knowledge of the array geometry and angular region where the SOI is located. The simulation results showed that the proposed method can deal with multiple types of mismatches, while taking into account both low complexity and high robustness.

Autonomic Nervous System characterization in hyperbaric environments considering respiratory component and non-linear analysis of Heart Rate Variability

Objectives: an evaluation of Principal Dynamic Mode (PDM) and Orthogonal Subspace Projection (OSP) methods to characterize the Autonomic Nervous System (ANS) response in three different hyperbaric environments was performed. Methods: ECG signals were recorded in two different stages (baseline and immersion) in three different hyperbaric environments: (a) inside a hyperbaric chamber, (b) in a controlled sea immersion, (c) in a real reservoir immersion. Time-domain parameters were extracted from the RR series of the ECG. From the Heart Rate Variability signal (HRV), classic Power Spectral Density (PSD), PDM (a non-linear analysis of HRV which is able to separate sympathetic and parasympathetic activities) and OSP (an analysis of HRV which is able to extract the respiratory component) methods were used to assess the ANS response. Results: PDM and OSP parameters follows the same trend when compared to the PSD ones for the hyperbaric chamber dataset. Comparing the three hyperbaric scenarios, significant differences were found: i) heart rate decreased and RMSSD increased in the hyperbaric chamber and the controlled dive, but they had the opposite behavior during the uncontrolled dive; ii) power in the OSP respiratory component was lower than power in the OSP residual component in cases a and c; iii) PDM and OSP methods showed a significant increase in sympathetic activity during both dives, but parasympathetic activity increased only during the uncontrolled dive. Conclusions: PDM and OSP methods could be used as an alternative measurement of ANS response instead of the PSD method. OSP results indicate that most of the variation in the heart rate variability cannot be described by changes in the respiration, so changes in ANS response can be assigned to other factors. Time-domain parameters reflect vagal activation in the hyperbaric chamber and in the controlled dive because of the effect of pressure. In the uncontrolled dive, sympathetic activity seems to be dominant, due to the effects of other factors such as physical activity, the challenging environment, and the influence of breathing through the scuba mask during immersion. In sum, a careful description of the changes in all the possible factors that could affect the ANS response between baseline and immersion stages in hyperbaric environments is needed for better interpretation of the results.

MCSP-SSS: A Domain Adaptive Framework for High-Accuracy Sensor Data Classification

Due to sensor drift, instrumental variation, or change of measurement object, the distributions of the datasets (domains) acquired by the sensors are often different. A domain adaptive framework called MCSP-SSS is proposed to reduce the distribution discrepancy across domains for high-accuracy sensor data classification. The framework consists of two key parts: Multi-Constraint Subspace Projection (MCSP) and Source Sample Selection (SSS). MCSP is a subspace-projection-based approach, which introduces four constraints to get an optimized projection matrix: Principal Component Analysis (PCA) is used to reduce the redundancy of features; Mean Distribution Discrepancy (MDD) is applied to minimize the difference between source and target data; Hilbert-Schmidt Independence Criterion (HSIC) is adopted to maximizing the dependence between features and labels; A so-called weighted-within-class scatter matrix is introduced to minimize the within-class variance to avoid samples with different labels to overlap in the subspace. SSS is designed to remove the outliers in projected source samples so as to reduce distribution discrepancy between the source and target samples projected by MCSP. Experimental results show that our framework can achieve the best accuracies in all classification tasks in comparison with other state-of-the-art approaches. The accuracy of MCSP-SSS is 3.57 percentage points (pps) higher on average than that of the second best approach for single-source domain adaptation, and 7.00 pps for multi-source domain adaptation. Source code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/threedteam/tsc_subspace_projection</uri> .

Random subspace and random projection nearest neighbor ensembles for high dimensional data

The random subspace and the random projection methods are investigated and compared as techniques for forming ensembles of nearest neighbor classifiers in high dimensional feature spaces. The two methods have been empirically evaluated on three types of high-dimensional datasets: microarrays, chemoinformatics, and images. Experimental results on 34 datasets show that both the random subspace and the random projection method lead to improvements in predictive performance compared to using the standard nearest neighbor classifier, while the best method to use depends on the type of data considered; for the microarray and chemoinformatics datasets, random projection outperforms the random subspace method, while the opposite holds for the image datasets. An analysis using data complexity measures, such as attribute to instance ratio and Fisher’s discriminant ratio, provide some more detailed indications on what relative performance can be expected for specific datasets. The results also indicate that the resulting ensembles may be competitive with state-of-the-art ensemble classifiers; the nearest neighbor ensembles using random projection perform on par with random forests for the microarray and chemoinformatics datasets.

Application of Dirichlet Process and Support Vector Machine Techniques for Mapping Alteration Zones Associated with Porphyry Copper Deposit Using ASTER Remote Sensing Imagery

The application of machine learning (ML) algorithms for processing remote sensing data is momentous, particularly for mapping hydrothermal alteration zones associated with porphyry copper deposits. The unsupervised Dirichlet Process (DP) and the supervised Support Vector Machine (SVM) techniques can be executed for mapping hydrothermal alteration zones associated with porphyry copper deposits. The main objective of this investigation is to practice an algorithm that can accurately model the best training data as input for supervised methods such as SVM. For this purpose, the Zefreh porphyry copper deposit located in the Urumieh-Dokhtar Magmatic Arc (UDMA) of central Iran was selected and used as training data. Initially, using ASTER data, different alteration zones of the Zefreh porphyry copper deposit were detected by Band Ratio, Relative Band Depth (RBD), Linear Spectral Unmixing (LSU), Spectral Feature Fitting (SFF), and Orthogonal Subspace Projection (OSP) techniques. Then, using the DP method, the exact extent of each alteration was determined. Finally, the detected alterations were used as training data to identify similar alteration zones in full scene of ASTER using SVM and Spectral Angle Mapper (SAM) methods. Several high potential zones were identified in the study area. Field surveys and laboratory analysis were used to validate the image processing results. This investigation demonstrates that the application of the SVM algorithm for mapping hydrothermal alteration zones associated with porphyry copper deposits is broadly applicable to ASTER data and can be used for prospectivity mapping in many metallogenic provinces around the world.

Three-dimensional transient electromagnetic response of multiple grounded-wire sources

Multiple grounded-wire sources combination are proposed to improve the signal strength and resolution of the transient electromagnetic method. Multi-source excitation from the different direction was executed to identify the conductive body in the subsurface and achieve refined detection of the target body. The vector finite element method based on the rational Krylov subspace projection algorithm was used to calculate transient response of the target bodies. The voltage response calculated by our algorithm was compared with that calculated by the integral equation method and the results agreed well with them. We designed different grounded-wire combinations, including a single source, pairs of sources, and groups of three and four sources, and analyzed induced EMF and the secondary field response of one conductive body. It indicates that multi-source transient method can obtain stronger signals, which is beneficial to the discovery of deep weak anomalies. Finally, we established two adjacent conductive block bodies and compared their electromagnetic response for the different source combination. The results showed that multiple-source transient electromagnetic response anomaly amplitude and lateral resolution are superior to those of a single source. Multi-channel diagram for multiple sources have two obvious peaks, especially for three sources and four sources, but the induced EMF from a single source does not differentiate between the two conductive bodies in the horizontal direction. Multiple grounded-wire source combinations are used not only for the surface transient electromagnetic method but can also be extended to the grounded electrical-source airborne transient electromagnetic survey.

Technical aspects of cardiorespiratory estimation using subspace projections and cross entropy

Background. Respiratory sinus arrhythmia (RSA) is a form of cardiorespiratory coupling. Its quantification has been suggested as a biomarker to diagnose different diseases. Two state-of-the-art methods, based on subspace projections and entropy, are used to estimate the RSA strength and are evaluated in this paper. Their computation requires the selection of a model order, and their performance is strongly related to the temporal and spectral characteristics of the cardiorespiratory signals. Objective. To evaluate the robustness of the RSA estimates to the selection of model order, delays, changes of phase and irregular heartbeats as well as to give recommendations for their interpretation on each case. Approach. Simulations were used to evaluate the model order selection when calculating the RSA estimates introduced before, as well as three different scenarios that can occur in signals acquired in non-controlled environments and/or from patient populations: the presence of irregular heartbeats; the occurrence of delays between heart rate variability (HRV) and respiratory signals; and the changes over time of the phase between HRV and respiratory signals. Main results. It was found that using a single model order for all the calculations suffices to characterize RSA correctly. In addition, the RSA estimation in signals containing more than 5 irregular heartbeats in a period of 5 min might be misleading. Regarding the delays between HRV and respiratory signals, both estimates are robust. For the last scenario, the two approaches tolerate phase changes up to 54°, as long as this lasts less than one fifth of the recording duration. Significance. Guidelines are given to compute the RSA estimates in non-controlled environments and patient populations.

Two-Step Approach to Processing Raw Strain Monitoring Data for Damage Detection of Structures under Operational Conditions.

Strain data of structural health monitoring is a prospective to be made full use of, because it reflects the stress peak and fatigue, especially sensitive to local stress redistribution, which is the probably damage in the vicinity of the sensor. For decoupling structural damage and masking effects caused by operational conditions to eliminate the adverse impacts on strain-based damage detection, small time-scale structural events, i.e., the short-term dynamic strain responses, are analyzed in this paper by employing unsupervised modeling. A two-step approach to successively processing the raw strain monitoring data in the sliding time window is presented, consisting of the wavelet-based initial feature extraction step and the decoupling step to draw damage indicators. The principal component analysis and a low-rank property-based subspace projection method are adopted as two alternative decoupling methodologies. The approach’s feasibility and robustness are substantiated by analyzing the strain monitoring data from a customized truss experiment to successfully remove the masking effects of operating loads and identify local damages even concerning accommodating situations of missing data and limited measuring points. This work also sheds light on the merit of a low-rank property to separate structural damages from masking effects by comparing the performances of the two optional decoupling methods of the distinct rationales.

Laguerre-Gramian-based structure-preserving model order reduction for second-order form systems

A new structure-preserving model order reduction technique based on Laguerre-Gramian for second-order form systems is presented in this article. The main task of the proposed approach is to use the Laguerre polynomial expansion of the matrix exponential function to obtain the approximate low-rank decomposition of the Gramians for the equivalent first-order representation of the original second-order form system. The approximate balanced system is generated by a balancing transformation which is directly computed from the expansion coefficients of impulse responses in the space spanned by Laguerre polynomials, without computing the full Gramians for the first-order representation. Then, the reduced second-order model is constructed by truncating the states with small approximate Hankel singular values (HSVs). The above method has a disadvantage that it may unexpectedly result in unstable systems although the original one is stable. Therefore, modified reduction procedure combined with the dominant subspace projection method is presented to alleviate the limitation. Finally, two numerical experiments are provided to demonstrate the effectiveness of the algorithms.

HYPERSPECTRAL IMAGE CLASSIFICATION BASED ON MANIFOLD DATA ANALYSIS AND SPARSE SUBSPACE PROJECTION

Aiming at the problem of "dimension disaster" in hyperspectral image classification, a method of dimension reduction based on manifold data analysis and sparse subspace projection (MDASSP) is proposed. The sparse coefficient matrix is established by the new method, and the sparse subspace projection is carried out by the optimization method. To keep the geometric structure of the manifold, the objective function is regularized by the manifold learning method. The new method combines sparse coding and manifold learning to generate features with better classification ability. The experimental results show that the new method is better than other methods in the case of small samples.

Exploring attention mechanisms based on summary information for end-to-end automatic speech recognition

Recent studies have confirmed that attention mechanisms with location constraint strategy are helpful to reduce the misrecognition caused by incorrect alignments in attention-based end-to-end automatic speech recognition (E2E ASR) systems. The significant advantage of these mechanisms is that they consider the monotonicity of the alignment by employing a location constraint vector. This vector is directly obtained from historical attention scores for most such attention mechanisms. However, an unreasonable vector may become an additional interference when an inaccurate historical attention score occurs. Moreover, the subsequent process of attention scoring will be affected by the interference continuously. To address the problem, we obtain a reasonable location constraint vector from the matching relationship between the historical output information and the summary information, where the summary information includes content and temporal information about speech sequence. We further propose an enhanced location constrained attention mechanism, i.e., summary constrained (SC) attention mechanism, to generate the vector by a matching relationship-based neural network. We use a summary subspace embedding learned by a linear subspace projection to represent the summary information. Furthermore, considering the complementarity of the SC and typical location constrained attention mechanisms, a fused attention mechanism is used to generate a more reasonable vector by combining the two mechanisms. The SC and fused attention mechanisms-based E2E ASR systems were evaluated on a Switchboard conversational telephone speech recognition. The experimental results show that our mechanisms obtained the relative reductions of 10.6% and 16.7% in the word error rate compared with the baseline system.

A Novel Underdetermined Blind Source Separation Method Based on OPTICS and Subspace Projection

In recent years, the problem of underdetermined blind source separation (UBSS) has become a research hotspot due to its practical potential. This paper presents a novel method to solve the problem of UBSS, which mainly includes the following three steps: Single source points (SSPs) are first screened out using the principal component analysis (PCA) approach, which is based on the statistical features of signal time-frequency (TF) points. Second, a mixing matrix estimation method is proposed that combines Ordering Points To Identify the Clustering Structure (OPTICS) with an improved potential function to directly detect the number of source signals, remove noise points, and accurately calculate the mixing matrix vector; it is independent of the input parameters and offers great accuracy and robustness. Finally, an improved subspace projection method is used for source signal recovery, and the upper limit for the number of active sources at each mixed signal is increased from m−1 to m. The unmixing process of the proposed algorithm is symmetrical to the actual signal mixing process, allowing it to accurately estimate the mixing matrix and perform well in noisy environments. When compared to previous methods, the source signal recovery accuracy is improved. The method’s effectiveness is demonstrated by both theoretical and experimental results.

HPS meets AMPS: how soft hair dissolves the firewall

We build on the observation by Hawking, Perry and Strominger that a global black hole space-time supports a large number of soft hair degrees of freedom to shed new light on the firewall argument by Almheiri, Marolf, Polchinski, and Sully. We propose that the soft hair Goldstone mode is encoded in a classical transition function that connects the asymptotic and near horizon region. The entropy carried by the soft hair is part of the black hole entropy and encoded in the outside geometry. We argue that the infalling observer automatically measures the classical value of the soft mode before reaching the horizon and that this measurement implements a code subspace projection that enables the reconstruction of interior operators. We use the soft hair dynamics to introduce an observer dependent notion of the firewall and show that for an infalling observer it recedes inwards into the black hole interior: the observer never encounters a firewall before reaching the singularity. Our results indicate that the HPS black hole soft hair plays an essential role in dissolving the AMPS firewall.

Dimensionality reduction based on multi-local linear regression and global subspace projection distance minimum

Dimensionality reduction based on multi-local linear regression and global subspace projection distance minimum

Divide-and-Merge the embedding space for cross-modality person search

This study considers the problem of text-based person search, which aims to find the corresponding person of a given text description in an image gallery. Existing methods usually learn a similarity mapping of local parts between image and text, or embed the whole image and text into a unified embedding space. However, the relevance between local and the whole is largely underexplored. In this paper, we design a Divide-and-Merge Embedding (DME) learning framework for text-based person search. DME explicitly 1) models the relations between local parts and global embedding, 2) incorporates local details into global embedding. Specifically, we design a Feature Dividing Network (FDN) to embed the input into K locally guided semantic representations by self-attentive embedding, each representation depicts a local part of the person. Then, we propose a Relevance based Subspace Projection (RSP) method for merging diverse local representations to a compact global embedding. RSP helps the model to obtain discriminative embedding by jointly minimizing the redundancy of local parts and maximizing the relevance between local parts and global embedding. Extensive experimental results on three challenging benchmarks, i.e., CUHK-PEDES, CUB and Flowers datasets, have demonstrated the effectiveness of the proposed method.

Parametric reduced order models based on a Riemannian barycentric interpolation

AbstractA new strategy for constructing parametric Galerkin reduced order models is presented in this article. This strategy is achieved thanks to the Riemannian manifold, quotient of the set of full‐rank matrices by the orthogonal group. Starting from a set of training parametrized subspaces of the same dimension, namely obtained by the proper orthogonal decomposition, the projection subspace for a new untrained parameter value is sought as the Karcher barycenter of the data points. The principal advantage of this strategy is that it leads to parametric reduced order models that are naturally flexible with respect to parameter variations. This property is a result of the simple expressions of the geodesic exponential and logarithmic mappings involved in the calculations of the approximated projection subspace. Confrontation with the usual interpolation in the tangent space to the Grassmann manifold is carried out for the flow problem past a circular cylinder and the flow in a lid‐driven cavity. Comparable results in terms of accuracy are obtained, while the proposed approach is shown to be computationally cheaper by allowing real‐time update of Galerkin projections.

Cardiopulmonary coupling indices to assess weaning readiness from mechanical ventilation

The ideal moment to withdraw respiratory supply of patients under Mechanical Ventilation at Intensive Care Units (ICU), is not easy to be determined for clinicians. Although the Spontaneous Breathing Trial (SBT) provides a measure of the patients’ readiness, there is still around 15–20% of predictive failure rate. This work is a proof of concept focused on adding new value to the prediction of the weaning outcome. Heart Rate Variability (HRV) and Cardiopulmonary Coupling (CPC) methods are evaluated as new complementary estimates to assess weaning readiness. The CPC is related to how the mechanisms regulating respiration and cardiac pumping are working simultaneously, and it is defined from HRV in combination with respiratory information. Three different techniques are used to estimate the CPC, including Time-Frequency Coherence, Dynamic Mutual Information and Orthogonal Subspace Projections. The cohort study includes 22 patients in pressure support ventilation, ready to undergo the SBT, analysed in the 24 h previous to the SBT. Of these, 13 had a successful weaning and 9 failed the SBT or needed reintubation –being both considered as failed weaning. Results illustrate that traditional variables such as heart rate, respiratory frequency, and the parameters derived from HRV do not differ in patients with successful or failed weaning. Results revealed that HRV parameters can vary considerably depending on the time at which they are measured. This fact could be attributed to circadian rhythms, having a strong influence on HRV values. On the contrary, significant statistical differences are found in the proposed CPC parameters when comparing the values of the two groups, and throughout the whole recordings. In addition, differences are greater at night, probably because patients with failed weaning might be experiencing more respiratory episodes, e.g. apneas during the night, which is directly related to a reduced respiratory sinus arrhythmia. Therefore, results suggest that the traditional measures could be used in combination with the proposed CPC biomarkers to improve weaning readiness.

A Domain Adaptation Sparse Representation Classifier for Cross-Domain Electroencephalogram-Based Emotion Classification.

The brain-computer interface (BCI) interprets the physiological information of the human brain in the process of consciousness activity. It builds a direct information transmission channel between the brain and the outside world. As the most common non-invasive BCI modality, electroencephalogram (EEG) plays an important role in the emotion recognition of BCI; however, due to the individual variability and non-stationary of EEG signals, the construction of EEG-based emotion classifiers for different subjects, different sessions, and different devices is an important research direction. Domain adaptation utilizes data or knowledge from more than one domain and focuses on transferring knowledge from the source domain (SD) to the target domain (TD), in which the EEG data may be collected from different subjects, sessions, or devices. In this study, a new domain adaptation sparse representation classifier (DASRC) is proposed to address the cross-domain EEG-based emotion classification. To reduce the differences in domain distribution, the local information preserved criterion is exploited to project the samples from SD and TD into a shared subspace. A common domain-invariant dictionary is learned in the projection subspace so that an inherent connection can be built between SD and TD. In addition, both principal component analysis (PCA) and Fisher criteria are exploited to promote the recognition ability of the learned dictionary. Besides, an optimization method is proposed to alternatively update the subspace and dictionary learning. The comparison of CSFDDL shows the feasibility and competitive performance for cross-subject and cross-dataset EEG-based emotion classification problems.

A strong adaptive piecewise model order reduction method for large-scale dynamical systems with viscoelastic damping

This paper develops a novel and strong adaptive piecewise model order reduction (PMOR) method for large-scale dynamical systems with viscoelastic damping. Based on polynomial least squares approximations, the system is piecewise approximated by several kth-order (k≥2) dynamical systems in a wide target frequency band, in which the orders are adaptively determined with a curvature-based method. Then the convergent reduced-order models (ROMs) of the approximate systems are obtained gradually. In the above process, for each approximate system, the orthonormal basis is constructed iteratively via the kth-order Arnoldi method to span a projection subspace. To accelerate the convergence, an influence coefficient method and an order-dependent method are proposed to automatically determine the initial order of the ROM and the order increments, respectively. More importantly, a proposed error estimation strategy can predict all forms of estimated relative errors. According to the study of these forms, a comparison-selection method is presented to determine the final ROM for the whole target band interval by interval. Four examples comprehensively validate the strong adaptive ability, high efficiency and wide applicability of the PMOR method.