Subspace-based Approach Research Articles

A Hybrid Hubspace-RNN based approach for Modelling of Non-Linear Batch Processes

The manuscript addresses the problem of developing a modelling strategy that can accurately capture the dynamics of a non-linear batch process, demonstrated on a uni-axial rotational molding process. To this end, this work presents a strategy that utilizes the nonlinear modeling capability of a recurrent neural network (RNN) model, while leveraging the rigor of subspace-based approaches. The proposed modeling strategy is as follows: a subspace identification algorithm is first utilized on all the training batches to obtain the state sequence for these batches. Then the state sequences from all the training batches and the corresponding input sequences are given as the output and the input to a neural network, respectively. This step essentially builds a non-linear state space model, albeit using the state trajectory identified by the subspace model. The output equation obtained from the above-mentioned subspace identification step along with the newly obtained non-linear state equation is now ready to be used for predicting the output trajectory of the system. The results from the experiments illustrate the improved prediction performance of a model obtained by the proposed hybrid Subspace-RNN approach in comparison to both a subspace-based approach and an RNN-based approach.

Deep Learning-Aided Signal Enumeration for Lens Antenna Array

This work investigates a data-driven approach to detect the number of incoming signals for a lens antenna array (LAA). First, the energy-focusing property of an electromagnetic (EM) lens is utilized to generate an input spectrum, which can be used to enumerate both the multipath and independent signals. Next, we present the deep learning (DL)-assisted sharp peak recognition method referred to as the power spectrum-based convolutional neural network (PSCNet). Unlike classical techniques, such as constant false alarm rate (CFAR) detection, this data-driven detector can count received signals adaptively based on the LAA power spectrum without requiring any initial configurations. In addition, the PSCNet outperforms other state-of-the-art subspace-based detectors, even under challenging conditions, such as a low signal-to-noise ratio (SNR), a small observation size, and angular ambiguity. For the training phase, we propose a pretrained-model reusing strategy and an input pre-processing approach referred to as the power spectrum shortening (PSS) to alleviate the training burden and achieve lower complexity compared to fully retraining all isolated networks. The simulation results demonstrate that our proposed sharp peak-recognition algorithm not only accomplishes the improved signal enumeration performance but also requires lower computational resources than other subspace-based approaches.

Augmented Covariance Matrix Reconstruction for DOA Estimation Using Difference Coarray

As is well known, nonuniform linear arrays have significant advantages in array aperture and degrees of freedom over uniform linear arrays. Using their difference coarrays, subspace-based approaches can be utilized to perform underdetermined and high-resolution direction-of-arrival (DOA) estimation. However, the subspace-based approaches depend on the covariance matrix reconstruction in the coarray domain, which are not statistically efficient when the number of sources is more than one and less than the number of sensors. In this paper, to overcome this drawback, we devise an augmented covariance matrix reconstruction algorithm for DOA estimation in the coarray domain. The proposed algorithm recovers the complete augmented covariance matrix by solving a rank-minimization problem. But unlike the conventional schemes, it exploits the estimation error distribution of the incomplete augmented covariance matrix to derive the constraint condition of the rank-minimization problem. Based on the reconstructed augmented covariance matrix, we can enhance the DOA estimation performance for multiple source scenario at high signal-to-noise ratio. Although our algorithm is developed based on the non-consecutive coarray, it is also suitable for the consecutive coarray. Numerical results demonstrate the superiority of the proposed algorithm over several existing approaches.

Subspace-Based Learning for Automatic Dysarthric Speech Detection

To assist the clinical diagnosis and treatment of speech dysarthria, automatic dysarthric speech detection techniques providing reliable and cost-effective assessment are indispensable. Based on clinical evidence on spectro-temporal distortions associated with dysarthric speech, we propose to automatically discriminate between healthy and dysarthric speakers exploiting spectro-temporal subspaces of speech. Spectro-temporal subspaces are extracted using singular value decomposition, and dysarthric speech detection is achieved by applying a subspace-based discriminant analysis. Experimental results on databases of healthy and dysarthric speakers for different languages and pathologies show that the proposed subspace-based approach using temporal subspaces is more advantageous than using spectral subspaces, also outperforming several state-of-the-art automatic dysarthric speech detection techniques.

Hierarchical density decompositions for abnormal event diagnosis in serially correlated non-Gaussian systems

Processes in industrial practice often represent dynamic systems, which is a result of controller feedback, the presence of process noise and measured or unmeasured disturbances. To monitor dynamic systems that produce serially/time-based correlated data records, the literature has proposed numerous multivariate techniques that rely on (i) time-lagged arrangements of the recorded variables and (ii) subspace-based approaches. Proposed techniques, however, may not accurately and reliably describe to what extent process variables are affected by abnormal events, which compromises the identification of potential root causes. To address this, this paper employs a state space model to describe the inherent serial correlation and introduces a joint probability density function for this model. The density function can be hierarchically decomposed into the product of multiple low-dimensional conditional densities to reduce complexity and to detect and preanalyze anomalous behavior. Using the low-dimensional densities, a correction scheme to optimally describe the effect of an abnormal event upon particular process variables is proposed. A second important benefit of the hierarchical decomposition is that no assumptions are imposed on the distribution of the random error component of the state space models. Application studies to a simulation process and recorded data from two industrial processes demonstrate that, compared to conventional methods, the hierarchical decomposition can substantially improve the diagnosis of abnormal process behavior.

Direction-of-Arrival Estimation Based on Quantized Matrix Recovery

Usually, the problem of direction-of-arrival (DOA) estimation in antenna array systems assumes that the measurement quantization has infinite resolution or the quantization error is insignificant and thus can be simply absorbed into the noise. However, in modern systems such as large-scale antenna arrays, low-resolution analog-to-digital converter (ADC) has been widely reported to reduce the hardware cost and circuit power consumption. Hence, the quantization should be seriously treated to ensure satisfactory DOA estimation performance. To this end, we propose to formulate a constrained maximum likelihood optimization problem to recover the noiseless array measurement matrix, which is low-rank, from quantized noisy measurements. On this basis, we apply traditional subspace-based approaches to determine the DOAs. Numerical examples are carried out to illustrate the effectiveness of the proposed method.

System Identification Based on Output-Only Decomposition and Subspace Appropriation

Output-only identification methods have been developed on a stochastic framework, but for the first time, a subspace-based approach is proposed without using geometric and statistical tools. This aids the computational efforts to be significantly reduced and the range of input sources to be extended in a much realistic manner for future output-only analyses. The approach encompasses any input type and can properly work for systems excited by inputs with finite periods. It is demonstrated that the row space of the output sequences spanned by column vectors of the decomposed orthonormal matrix is sufficient to reconstruct the observations. The transient and steady-state portions of the output row space, afterward, can be captured to reconstruct an integrated innovation model. The advantages of the algorithm are highlighted through several numerical and experimental examples comparing with the traditional subspace identification algorithms.

Abundance-Indicated Subspace for Hyperspectral Classification With Limited Training Samples

The imbalance between the (often limited) number of available training samples and the high data dimensionality, together with the presence of mixed pixels, often complicates the classification of remotely sensed hyperspectral data. In this paper, we tackle these problems by developing a new method that combines spectral unmixing and classification techniques in a subspace-based approach. The proposed method is developed under the assumption that the spectral signature of a land cover class is associated with a given set of pure spectral signatures (called endmembers in spectral unmixing terminology), which define a low-dimensional subspace with clear physical meaning. We aim to exploit this relationship to learn the class-dependent subspaces and integrate them with a multinomial logistic regression procedure. Experiments on synthetic datasets and real hyperspectral images show that our method is able to obtain competitive performances in comparison with other approaches, particularly when very limited training sets are available.

A New Non-Parametric Subspace-Based Approach for Unit Root Test

A new non-parametric subspace-based approach is introduced for unit root test in AR(1) process. The proposed approach contains block-bootstrap and spectrum properties of a time series as well as statistical testing methodology. The simulation result validates the proposed test and indicates its superiority compared with other existent procedures.

A Frequency-Domain SPICE Approach to High-Resolution Time Delay Estimation

We propose a frequency-domain sparse iterative covariance-based estimation (FD-SPICE) approach for the high-resolution time delay estimation of spread spectrum signals. The conventional correlation method fails to resolve the signals in the case where they are spaced within a Rayleigh resolution limit and further processing should be applied to the correlation outputs in order to improve performance. SPICE is one of the most prominent candidates for further processing since it has various advantages over subspace-based approaches. SPICE is implemented normally in the time domain like other sparse signal reconstruction-based approaches. However, the time-domain SPICE (TD-SPICE) approach suffers from a severe performance degradation in coherent signal cases, as in direction-of-arrival estimation. We develop an FD-SPICE approach which makes use of the Fourier transform bins of the correlation output samples to form a sample covariance matrix. Numerical examples demonstrate the superiority of FD-SPICE over TD-SPICE, especially in coherent signal cases.

Multiview Clustering via Unified and View-Specific Embeddings Learning.

Multiview clustering, which aims at using multiple distinct feature sets to boost clustering performance, has a wide range of applications. A subspace-based approach, a type of widely used methods, learns unified embedding from multiple sources of information and gives a relatively good performance. However, these methods usually ignore data similarity rankings; for example, example A may be more similar to B than C, and such similarity triplets may be more effective in revealing the data cluster structure. Motivated by recent embedding methods for modeling knowledge graph in natural-language processing, this paper proposes to mimic different views as different relations in a knowledge graph for unified and view-specific embedding learning. Moreover, in real applications, it happens so often that some views suffer from missing information, leading to incomplete multiview data. Under such a scenario, the performance of conventional multiview clustering degenerates notably, whereas the method we propose here can be naturally extended for incomplete multiview clustering, which enables full use of examples with incomplete feature sets for model promotion. Finally, we demonstrate through extensive experiments that our method performs better than the state-of-the-art clustering methods.

Matched shrunken subspace detectors for hyperspectral target detection

In this paper, we propose a new approach, called the matched shrunken subspace detector (MSSD), to target detection from hyperspectral images. The MSSD is developed by shrinking the abundance vectors of the target and background subspaces in the hypothesis models of the matched subspace detector (MSD), a popular subspace-based approach to target detection. The shrinkage is achieved by introducing simple l2-norm regularisation (also known as ridge regression or Tikhonov regularisation). We develop two types of MSSD, one with isotropic shrinkage and termed MSSD-i and the other with anisotropic shrinkage and termed MSSD-a. For these two new methods, we provide both the frequentist and Bayesian derivations. Experiments on a real hyperspectral imaging dataset called Hymap demonstrate that the proposed MSSD methods can outperform the original MSD for hyperspectral target detection.

Principal component analysis based signal-to-noise ratio improvement for inchoate faulty signals: Application to ball bearing fault detection

This paper addresses the development of an algorithm that can improve the signal-to-noise ratio (SNR) in inchoate faulty signals. The removal of noise and preservation of fault information components cannot be easily achieved. Many techniques for SNR improvement in healthy signals rely on frequency bands. Such techniques have been proven to be efficient in improving the SRN by filtering out frequency bands (FoFBs). However, these techniques cannot reduce noise and preserve fault information when dealing with inchoate faulty signals. Thus, a feature extraction technique based on statistical parameters, which are free from Gaussian noise, is proposed in this paper. The proposed signal subspace-based approach for SNR improvement in inchoate faulty signals is based on a modified principal component analysis (PCA), in which the optimal subspace is selected via a cumulative percent of variance (CPV) criterion and the test statistic condition of the true information loss, which has the tendency to alleviate the impact of Gaussian and non-Gaussian noise and provides useful time domain analysis for non-stationary signals such as vibration, in which spectral contents vary with respect to time. Furthermore, the modified PCA algorithm is combined with a low-pass filter (LPF) to achieve an optimum balance between noise reduction efficiency and the conservation of inchoate fault information. The proposed PCA-LPF algorithm is compared with different filters under different noise levels to find the most efficient approach in terms of optimizing the trade-off between noise reduction efficiency and precision of inchoate fault information conservation, with the final goal of improving the fault detection capability. Further, the performance of the proposed PCA-LPF algorithm was demonstrated with an experimental study on vibration-based ball bearing fault detection.

Sparsity-based narrowband interference mitigation in ultra wide-band communication for 5G and beyond

In real operating environments, the performance of low power large bandwidth ultra wide-band (UWB) communication systems suffers due to narrowband interference (NBI) from high power narrowband interferers. Since noise is not spectrally white in the presence of NBI in UWB systems, conventional matched filter based receivers are not optimum in such scenarios. Although NBI mitigation methods have been proposed using NBI subspace and/or limiters for UWB systems, subspace-based approaches are usually not feasible due to no apriori knowledge of the NBI subspace in a real scenario, and the limiter-based approach is also non-optimum. In this paper, we propose a sparsity-based NBI mitigation method that exploits distinct characteristics of UWB signals and NBI, and does not require a limiter. Improved performance of the proposed receiver has been validated via time hopping binary phase shift keying (TH-BPSK) UWB signal transmission in both additive white Gaussian noise and multipath fading channels.

New Approaches to Direction-of-Arrival Estimation With Sensor Arrays in Unknown Nonuniform Noise

It is known that classical subspace-based direction-of-arrival (DOA) estimation algorithms are not straightforwardly applicable to scenarios with unknown spatially nonuniform noise. Among the state-of-the-art solutions, this problem is tackled by iterative subspace estimation algorithms to incorporate subspace-based approaches or nonlinear optimization routines to bypass the direct identification of subspaces. In this paper, the problem of DOA estimation in nonuniform noise is revisited by devising two computationally efficient proposals. It is proved herein that, if the signals are uncorrelated, the signal and noise subspaces can be directly obtained from the eigendecomposition of a reduced array covariance matrix. On the other hand, when the signals are correlated, the estimation of the noise covariance matrix is formulated into a rank minimization problem which can be approximately solved by semidefinite programming. In both cases, the signal and noise subspaces are easy to compute without iterations. Consequently, classical subspace-based algorithms can be employed to determine the DOAs. Numerical examples are provided to demonstrate the performance and applicability of the proposed methods.

Weighted Data-Driven Fault Detection and Isolation: A Subspace-Based Approach and Algorithms

Well-established theory of subspace system identification and model-based fault detection and isolation (FDI) enable the birth of subspace-based data-driven FDI approach. In this paper, we develop subspace-based FDI approach with a scheme of weighted historical and operating data. We propose two kinds of weighted data-driven fault detection algorithms and present fault isolation algorithm and its modified version incorporated with forgetting factors. Analysis of sensitivity and precision shows the weighted algorithms can obtain more accurate results without loss of sensitivity. Effectiveness and improvements of the proposed algorithms are validated on the widely used benchmark platform of Tennessee-Eastman process (TEP).

A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System

Massive MIMO has been recognized as a promising technology to meet the demand for higher data capacity for mobile networks in 2020 and beyond. Although promising, each base station needs accurate estimation of the channel state information (CSI), either through feedback or channel reciprocity schemes in order to achieve the benefits of massive MIMO in practice. Time division duplex (TDD) has been suggested as a better mode to acquire timely CSI in massive MIMO systems. The use of non-orthogonal pilot schemes, proposed for channel estimation in multi-cell TDD networks, is considered as a major source of pilot contamination in the literature due to the limitations of coherence time. Given the importance of pilot contamination in massive MIMO systems, we provide an extensive survey on pilot contamination, and identify other possible sources of pilot contamination, which include hardware impairment and non-reciprocal transceivers. We review established theories that have analyzed the effect of pilot contamination on the performance of massive MIMO systems, particularly on achievable rates. Next, we categorize the different proposed mitigation techniques for pilot contamination using the following taxonomy: pilot-based approach and subspace-based approach. Finally, we highlight the open issues, such as training overhead, deployment scenario, computational complexity, use of channel reciprocity, and conclude with broader perspective and a look at future trends in pilot contamination in massive MIMO systems.

Classification of Hyperspectral Images Using Subspace Projection Feature Space

A concern in hyperspectral image classification is the high number of required training samples. When traditional classifiers are applied, feature reduction (FR) techniques are the most common approaches to deal with this problem. Subspace-based classifiers, which are developed based on high-dimensional space characteristics, are another way to handle the high dimension of hyperspectral images. In this letter, a novel subspace-based classification approach is proposed and compared with basic and improved subspace-based classifiers. The proposed classifier is also compared with traditional classifiers that are accompanied by an FR technique and the well-known support vector machine classifier. Experimental results prove the efficiency of the proposed method, especially when a limited number of training samples are available. Furthermore, the proposed method has a very high level of automation and simplicity, as it has no parameters to be set.

Subspace-Based Support Vector Machines for Hyperspectral Image Classification

Hyperspectral image classification has been a very active area of research in recent years. It faces challenges related with the high dimensionality of the data and the limited availability of training samples. In order to address these issues, subspace-based approaches have been developed to reduce the dimensionality of the input space in order to better exploit the (limited) training samples available. An example of this strategy is a recently developed subspace-projection-based multinomial logistic regression technique able to characterize mixed pixels, which are also an important concern in the analysis of hyperspectral data. In this letter, we extend the subspace-projection-based concept to support vector machines (SVMs), a very popular technique for remote sensing image classification. For that purpose, we construct the SVM nonlinear functions using the subspaces associated to each class. The resulting approach, called SVMsub, is experimentally validated using a real hyperspectral data set collected using the National Aeronautics and Space Administration's Airborne Visible/Infrared Imaging Spectrometer. The obtained results indicate that the proposed algorithm exhibits good performance in the presence of very limited training samples.

A Grassmann graph embedding framework for gait analysis

Abstract Gait recognition is important in a wide range of monitoring and surveillance applications. Gait information has often been used as evidence when other biometrics is indiscernible in the surveillance footage. Building on recent advances of the subspace-based approaches, we consider the problem of gait recognition on the Grassmann manifold. We show that by embedding the manifold into reproducing kernel Hilbert space and applying the mechanics of graph embedding on such manifold, significant performance improvement can be obtained. In this work, the gait recognition problem is studied in a unified way applicable for both supervised and unsupervised configurations. Sparse representation is further incorporated in the learning mechanism to adaptively harness the local structure of the data. Experiments demonstrate that the proposed method can tolerate variations in appearance for gait identification effectively.