Multilinear Principal Component Analysis Research Articles

Multilinear EigenECGs and FisherECGs for Individual Identification from Information Obtained by an Electrocardiogram Sensor

In this study, we present a third-order tensor-based multilinear eigenECG (MEECG) and multilinear Fisher ECG (MFECG) for individual identification based on the information obtained by an electrocardiogram (ECG) sensor. MEECG and MFECG are based on multilinear principal component analysis (MPCA) and multilinear linear discriminant analysis (MLDA) in the field of multilinear subspace learning (MSL), respectively. MSL directly extracts features without the vectorization of input data, while MSL extracts features without vectorizing the input data while maintaining most of the correlations shown in the original structure. In contrast with unsupervised linear subspace learning (LSL) techniques such as PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis), it is less susceptible to small-data problems because it learns more compact and potentially useful representations, and it can efficiently handle large tensors. Here, the third-order tensor is formed by reordering the one-dimensional ECG signal into a two-dimensional matrix, considering the time frame. The MSL consists of four steps. The first step is preprocessing, in which input samples are centered. The second step is initialization, in which eigen decomposition is performed and the most significant eigenvectors are selected. The third step is local optimization, in which input data is applied by eigenvectors from the second step, and new eigenvectors are calculated using the applied input data. The final step is projection, in which the resultant feature tensors after projection are obtained. The experiments are performed on two databases for performance evaluation. The Physikalisch-Technische Bundesanstalt (PTB)-ECG is a well-known database, and Chosun University (CU)-ECG is directly built for this study using the developed ECG sensor. The experimental results revealed that the tensor-based MEECG and MFECG showed good identification performance in comparison to PCA and LDA of LSL.

Dual process monitoring of metal-based additive manufacturing using tensor decomposition of thermal image streams

Additive manufacturing (AM) processes are subject to lower stability compared to their traditional counterparts. The process inconsistency leads to anomalies in the build, which hinders AM’s broader adoption to critical structural component manufacturing. Therefore, it is crucial to detect any process change/anomaly in a timely and accurate manner for potential corrective operations. Real-time thermal image streams captured from AM processes are regarded as most informative signatures of the process stability. Existing state-of-the-art studies on thermal image streams focus merely on in situ sensing, feature extraction, and their relationship with process setup parameters and material properties. The objective of this paper is to develop a statistical process control (SPC) approach to detect process changes as soon as it occurs based on predefined distribution of the monitoring statistics. There are two major challenges: 1) complex spatial interdependence exists in the thermal images and current engineering knowledge is not sufficient to describe all the variability, and 2) the thermal images suffer from a large data volume, a low signal-to-noise ratio, and an ill structure with missing data. To tackle these challenges, multilinear principal component analysis (MPCA) approach is used to extract low dimensional features and residuals. Subsequently, an online dual control charting system is proposed by leveraging multivariate T2 and Q control charts to detect changes in extracted low dimensional features and residuals, respectively. A real-world case study of thin wall fabrication using a Laser Engineered Net Shaping (LENS) process is used to illustrate the effectiveness of the proposed approach, and the accuracy of process anomaly detection is validated based on X-ray computed tomography information collected from the final build offline.

BEASF-Based Image Enhancement for Caries Detection Using Multidimensional Projection and Neural Network

Tooth caries or cavities diagnosing are concerned as the most significant research work, as this is the common oral disease suffered by humans. Many approaches have been proposed under the topics including demineralization and decaying as well. However, the imaging modalities often suffer from various critical or complex aspects that struggles the methods to attain accurate diagnosis. This article turns to introduce a new cavity diagnosis model with three phases: (i) pre-processing (ii) feature extraction (iii) classification. In the first phase, a new bi-histogram equalization with adaptive sigmoid functions (BEASF) is introduced to enhance the image quality followed by other enhancements models like grey thresholding and active contour. Then, the features are extracted using multilinear principal component analysis (MPCA). Further, the classification is done via neural network (NN) classifier. After the implementation, the proposed model compares its performance over other conventional methods like principal component analysis (PCA), linear discriminant analysis (LDA) and independent component analysis (ICA) and the performance of the approach is analyzed in terms of measures such as accuracy, sensitivity, specificity, precision, false positive rate (FPR), false negative rate (FNR), negative predictive value (NPV), false discovery rate (FDR), F1Score and Mathews correlation coefficient (MCC), and proves the superiority of proposed work.

Pattern Clustering of Hysteresis Time Series With Multivalued Mapping Using Tensor Decomposition

Many actuators and sensors made by smart materials have hysteresis feature which is a complex nonlinear phenomenon with multivalued mapping. Accurate identification of hysteresis pattern in those sensors and actuators is helpful for improving the modeling and control strategies of the systems. In this paper, a general framework of the pattern clustering of hysteretic time series is developed on the basis of tensor decomposition. First, high-dimensional multivariate data of hysteresis objects are transformed into three-order hysteresis tensors. Then the multilinear principal component analysis (MPCA) is utilized to reduce the dimensionality of hysteresis tensors. Afterward, a novel tensor ${k}$ -means clustering (CTKmeans) based on tensor distance and cycle variation feature initialization is developed for the clustering of tensor objects. In order to evaluate the performance of the proposed approach, the experiment of hysteresis feature test using polyvinylidene fluoride (PVDF)-based pressure sensors is implemented. The measured high-dimensional hysteresis time series of PVDF successively undergoes the procedures of filtering, segmentation, MPCA dimensionality reduction and CTKmeans clustering. The experimental results show that the MPCA can capture more significant inherent features of hysteresis objects than the principal component analysis (PCA) or the kernel PCA in the dimensionality reduction. In terms of tensor distance and cycle variation feature initialization, the CTKmeans outperforms the random-initialization-based tensor ${k}$ -means and standard ${k}$ -means in the clustering of hysteresis tensors. With the tensor decomposition approach of multivariate time series, the hysteresis objects with nonlinear multivalued mapping features can be effectively identified by the combination of MPCA and CTKmeans.

Speckle noise reduction of multi-frame optical coherence tomography data using multi-linear principal component analysis

Optical coherence tomography (OCT) is an important interferometric diagnostic technique extensively applied in medical sciences. However, OCT images inevitably suffer from speckle noise, which reduces the accuracy of the diagnosis of ocular diseases. To deal with this problem, a speckle noise reduction method based on multi-linear principal component analysis (MPCA) is presented to denoise multi-frame OCT data. To well preserve local image features, nonlocal similar 3D blocks extracted from the data are first grouped using k-means++ clustering method. MPCA transform is then performed on each group and the transform coefficients are shrunk to remove speckle noise. Finally, the filtered OCT volume is obtained by inverse MPCA transform and aggregation. Experimental results show that the proposed method outperforms other compared approaches in terms of both speckle noise reduction and fine detail preservation.

Face Hallucination with Linear Regression Model in Semi-Orthogonal Multilinear PCA Method

In this paper, we propose a new face hallucination technique, face images reconstruction in HSV color space with a semi-orthogonal multilinear principal component analysis method. This novel hallucination technique can perform directly from tensors via tensor-to-vector projection by imposing the orthogonality constraint in only one mode. In our experiments, we use facial images from FERET database to test our hallucination approach which is demonstrated by extensive experiments with high-quality hallucinated color faces. The experimental results assure clearly demonstrated that we can generate photorealistic color face images by using the SO-MPCA subspace with a linear regression model.

Prediction of sensitivity to gefitinib/erlotinib for EGFR mutations in NSCLC based on structural interaction fingerprints and multilinear principal component analysis

BackgroundNon-small cell lung cancer (NSCLC) with activating EGFR mutations, especially exon 19 deletions and the L858R point mutation, is particularly responsive to gefitinib and erlotinib. However, the sensitivity varies for less common and rare EGFR mutations. There are various explanations for the low sensitivity of EGFR exon 20 insertions and the exon 20 T790 M point mutation to gefitinib/erlotinib. However, few studies discuss, from a structural perspective, why less common mutations, like G719X and L861Q, have moderate sensitivity to gefitinib/erlotinib.ResultsTo decode the drug sensitivity/selectivity of EGFR mutants, it is important to analyze the interaction between EGFR mutants and EGFR inhibitors. In this paper, the 30 most common EGFR mutants were selected and the technique of protein-ligand interaction fingerprint (IFP) was applied to analyze and compare the binding modes of EGFR mutant-gefitinib/erlotinib complexes. Molecular dynamics simulations were employed to obtain the dynamic trajectory and a matrix of IFPs for each EGFR mutant-inhibitor complex. Multilinear Principal Component Analysis (MPCA) was applied for dimensionality reduction and feature selection. The selected features were further analyzed for use as a drug sensitivity predictor. The results showed that the accuracy of prediction of drug sensitivity was very high for both gefitinib and erlotinib. Targeted Projection Pursuit (TPP) was used to show that the data points can be easily separated based on their sensitivities to gefetinib/erlotinib.ConclusionsWe can conclude that the IFP features of EGFR mutant-TKI complexes and the MPCA-based tensor object feature extraction are useful to predict the drug sensitivity of EGFR mutants. The findings provide new insights for studying and predicting drug resistance/sensitivity of EGFR mutations in NSCLC and can be beneficial to the design of future targeted therapies and innovative drug discovery.

A wavelet tensor fuzzy clustering scheme for multi-sensor human activity recognition

With the increasing number of wearable sensors and mobile devices, human activity recognition (HAR) based on multiple sensors has attracted more and more attention in recent years. On account of the diversity of human actions, the analysis of multivariate signals of activities is still a challenging task. Clustering is an unsupervised classification technique which can directly work on unlabeled data and automatically identify unknown activities. Therefore, a new wavelet tensor fuzzy clustering scheme (WTFCS) for multi-sensor activity recognition is proposed in this paper. Firstly, feature tensors of multiple activity signals are constructed using the discrete wavelet packet transform (DWPT). Then Multilinear Principal Component Analysis (MPCA) is utilized to reduce the dimensionality of feature tensors so as to keep the inherent data structure. On the basis of the principal feature initialization and the tensor fuzzy membership, a new fuzzy clustering (PTFC) is developed to identify different activity feature tensor groups. Finally, the open HAR dataset (DSAD) is used to verify the efficiency of the WTFCS. Clustering results of seventeen activities of eight subjects show that potential useful features of human activities can be captured through combining DWPT-based feature extraction with MPCA-based dimensionality reduction. The PTFC is capable of discriminating various human activities effectively. Its correctness rate of activity recognition is higher than those of fuzzy c-means clustering and the fuzzy clustering based on the tensor distance.

RTensor: An R Package for Multidimensional Array (Tensor) Unfolding, Multiplication, and Decomposition

rTensor is an R package designed to provide a common set of operations and decompositions for multidimensional arrays (tensors). We provide an S4 class that wraps around the base 'array' class and overloads familiar operations to users of 'array', and we provide additional functionality for tensor operations that are becoming more relevant in recent literature. We also provide a general unfolding operation, for which the k-mode unfolding and the matrix vectorization are special cases of. Finally, package rTensor implements common tensor decompositions such as canonical polyadic decomposition, Tucker decomposition, multilinear principal component analysis, t-singular value decomposition, as well as related matrix-based algorithms such as generalized low rank approximation of matrices and popular value decomposition.

Online multilinear principal component analysis

Abstract Recently, the problem of extracting tensor object feature is studied and a very elegant solution, multilinear principal component analysis (MPCA), is proposed, which is motivated as a tool for tensor object dimension reduction and feature extraction by operating directly on the original tensor data. However, the original MPCA is an offline learning method and not suitable for processing online data since it generates the best projection matrices by learning on the whole training data set at once. In this study, we propose an online multilinear principal component analysis (OMPCA) algorithm and prove that the sequence generated by OMPCA converges to a stationary point of the total tensor scatter maximizing problem. Experiment results of an OMPCA-based support higher-order tensor machine for classification, show that OMPCA significantly lowers the time of dimension reduction with little sacrifice of recognition accuracy.

Integrating angle-frequency domain synchronous averaging technique with feature extraction for gear fault diagnosis

Abstract Gear fault diagnosis relies heavily on the scrutiny of vibration responses measured. In reality, gear vibration signals are noisy and dominated by meshing frequencies as well as their harmonics, which oftentimes overlay the fault related components. Moreover, many gear transmission systems, e.g., those in wind turbines, constantly operate under non-stationary conditions. To reduce the influences of non-synchronous components and noise, a fault signature enhancement method that is built upon angle-frequency domain synchronous averaging is developed in this paper. Instead of being averaged in the time domain, the signals are processed in the angle-frequency domain to solve the issue of phase shifts between signal segments due to uncertainties caused by clearances, input disturbances, and sampling errors, etc. The enhanced results are then analyzed through feature extraction algorithms to identify the most distinct features for fault classification and identification. Specifically, Kernel Principal Component Analysis (KPCA) targeting at nonlinearity, Multilinear Principal Component Analysis (MPCA) targeting at high dimensionality, and Locally Linear Embedding (LLE) targeting at local similarity among the enhanced data are employed and compared to yield insights. Numerical and experimental investigations are performed, and the results reveal the effectiveness of angle-frequency domain synchronous averaging in enabling feature extraction and classification.

Ranking Tensor Subspaces in Weighted Multilinear Principal Component Analysis

Multilinear principal component analysis (MPCA) has been applied for tensor decomposition and dimensionality reduction in image databases modeled through higher order tensors. Despite the well-known attractive properties of MPCA, the traditional approach does not incorporate prior information in order to steer its subspace computation. In this paper, we propose a method to explicitly incorporate such semantics in the MPCA framework to allow an automatic selective treatment of the variables that compose the patterns of interest. The method relies on spatial weights calculated, in this work, by separating hyperplanes and Fisher criterion. In this way, we can perform feature extraction and dimensionality reduction taking advantage of high level information in the form of labeled data. Besides, the corresponding tensor components are ranked in order to identify the principal weighted tensor subspaces for classification tasks. In the computational results we consider gender and facial expression experiments to illustrate the capabilities of the method for dimensionality reduction, classification and reconstruction of face images.

Multilinear Spatial Discriminant Analysis for Dimensionality Reduction

In the last few years, great efforts have been made to extend the linear projection technique (LPT) for multidimensional data (i.e., tensor), generally referred to as the multilinear projection technique (MPT). The vectorized nature of LPT requires high-dimensional data to be converted into vector, and hence may lose spatial neighborhood information of raw data. MPT well addresses this problem by encoding multidimensional data as general tensors of a second or even higher order. In this paper, we propose a novel multilinear projection technique, called multilinear spatial discriminant analysis (MSDA), to identify the underlying manifold of high-order tensor data. MSDA considers both the nonlocal structure and the local structure of data in the transform domain, seeking to learn the projection matrices from all directions of tensor data that simultaneously maximize the nonlocal structure and minimize the local structure. Different from multilinear principal component analysis (MPCA) that aims to preserve the global structure and tensor locality preserving projection (TLPP) that is in favor of preserving the local structure, MSDA seeks a tradeoff between the nonlocal (global) and local structures so as to drive its discriminant information from the range of the non-local structure and the range of the local structure. This spatial discriminant characteristic makes MSDA have more powerful manifold preserving ability than TLPP and MPCA. Theoretical analysis shows that traditional MPTs, such as multilinear linear discriminant analysis, TLPP, MPCA, and tensor maximum margin criterion, could be derived from the MSDA model by setting different graphs and constraints. Extensive experiments on face databases (ORL, CMU PIE, and the extended Yale-B) and the Weizmann action database demonstrate the effectiveness of the proposed MSDA method.

Decision-level fusion for single-view gait recognition with various carrying and clothing conditions

Gait recognition is one of the latest and attractive biometric techniques, due to its potential in identification of individuals at a distance, unobtrusively and even using low resolution images. In this paper we focus on single lateral view gait recognition with various carrying and clothing conditions. Such a system is needed in access control applications whereby a single view is imposed by the system setup. The gait data is firstly processed using three gait representation methods as the features sources; Accumulated Prediction Image (API) and two new gait representations namely; Accumulated Flow Image (AFI) and Edge-Masked Active Energy Image (EMAEI). Secondly, each of these methods is tested using three matching classification schemes; image projection with Linear Discriminant Functions (LDF), Multilinear Principal Component Analysis (MPCA) with K-Nearest Neighbor (KNN) classifier and the third method: MPCA plus Linear Discriminant Analysis (MPCA+LDA) with KNN classifier. Gait samples are fed into the MPCA and MPCALDA algorithms using a novel tensor-based form of the gait images. This arrangement results into nine recognition sub-systems. Decisions from the nine classifiers are fused using decision-level (majority voting) scheme. A comparison between unweighted and weighted voting schemes is also presented. The methods are evaluated on CASIA B Dataset using four different experimental setups, and on OU-ISIR Dataset B using two different setups. The experimental results show that the classification accuracy of the proposed methods is encouraging and outperforms several state-of-the-art gait recognition approaches reported in the literature.

Development of a New Three-Dimensional Fluorescence Spectroscopy Method Coupling with Multilinear Pattern Recognition to Discriminate the Variety and Grade of Green Tea

According to the different types and contents of amino acids in green tea, a new method was proposed for green tea classification and quality evaluation based on excitation-emission matrix (EEM) fluorescence spectroscopy coupled with multilinear pattern recognition in this work. Amino acids in green tea samples were first derived with formaldehyde and acetyl acetone solution. Derivatives of green teas were then scanned with a three-dimensional fluorescence spectrometry. Multilinear pattern recognition methods, including multilinear principal component analysis (M-PCA), self-weight alternative trilinear decomposition (SWATLD), and multilinear partial least squares discriminant analysis (N-PLS-DA) methods, were used to decompose the EEM data sets. All of these multilinear pattern recognition methods showed the clustering tendency for five different kinds of green tea. Compared with the other two methods, N-PLS-DA got more accurate and reliable classification result because it made full use of all the fluorescence information of the derivative green tea samples. At the same time, this method also revealed the possibility of evaluating the grade of green tea.

Analysis of human motion variation patterns using UMPCA

The rapid development of motion capture technologies has greatly increased the use of human motion data in many applications. This has increased the demand to have an effective means to systematically analyze those massive data in order to understand human motion variation patterns. This paper studies one typical type of motion data, which are recorded as multi-stream trajectories of human joints. Such a high dimensional multi-stream data structure makes it difficult to directly perform visual comparisons or simply apply conventional methods such as PCA to capture the variation of human motion patterns. In this paper, a high order array (tensor) is suggested for data representation, based on which the Uncorrelated Multilinear Principal Component Analysis (UMPCA) is applied to analyze the variation of human motion patterns. A simulation study is presented to show the superiority of UMPCA over PCA in preserving the cross-correlation among multi-stream trajectories. The effectiveness of UMPCA is also demonstrated using a case study for analyzing vehicle ingress test data.

Multilinear principal component analysis for statistical modeling of cylindrical surfaces: a case study

This paper focuses the problem of modeling manufactured surfaces for statistical process control. The application of Multilinear principal component analysis (MPCA) is introduced. MPCA is the generalization of the regular principal component analysis where the input can be not only vectors, but also tensors. The objective of this work is basically to explore the MPCA, as well as some basic concepts of multilinear algebra, for modeling manufactured surfaces. A real case study concerning cylindrical surfaces obtained by a lathe-turning process is taken as reference. The measurements related to a specific surface are stored in a matrix addressed by 2 index variables, while the observed data set related to several surfaces is stored in a 3rd-order tensor addressed by 3 indexes. Since the targeted application involves only the use of 3rd-order tensors of real entries, in this study the implementation of MPCA is limited to this specific case. Although a specific geometry is used herein as reference case study, any 2.5-dimensional surface (i.e. where scalar measurements are sampled for each item by using a fixed grid of two spatial index variables) can be modeled with the proposed MPCA-based approach.

Facial descriptor for Kinect depth using inner–inter-normal components local binary patterns and tensor histograms

RGB-D data collected from Microsoft Kinect are an easily available media providing the additional depth information besides RGB, which has great potentials in improving the performance of the facial analysis applications. In this paper, we focus on facial descriptor extraction from depth channel. First, we design a facial shape descriptor based on local binary patterns encoding from surface normal. The novelty lies in that it considers local structures involved in both inner component and inter-components of surface normal. Second, we propose a tensor representation for histogram arrays embedded in multidimensional space and further use multilinear principal component analysis to obtain an optimal trade-off between efficacy and efficiency. The experiments conducted on two publicly available databases, named CurtinFaces and Eurecom, have demonstrated the promising results achieved by proposed schemes on identity and ethnicity classification.

Sparse tensor canonical correlation analysis for micro-expression recognition

A micro-expression is considered a fast facial movement that indicates genuine emotions and thus provides a cue for deception detection. Due to its promising applications in various fields, psychologists and computer scientists, particularly those focus on computer vision and pattern recognition, have shown interest and conducted research on this topic. However, micro-expression recognition accuracy is still low. To improve the accuracy of such recognition, in this study, micro-expression data and their corresponding Local Binary Pattern (LBP) (Ojala et al., 2002) [1] code data are fused by correlation analysis. Here, we propose Sparse Tensor Canonical Correlation Analysis (STCCA) for micro-expression characteristics. A sparse solution is obtained by the regularized low rank matrix approximation. Experiments are conducted on two micro-expression databases, CASME and CASME 2, and the results show that STCCA performs better than the Three-dimensional Canonical Correlation Analysis (3D-CCA) without sparse resolution. The experimental results also show that STCCA performs better than three-order Discriminant Tensor Subspace Analysis (DTSA3) with discriminant information, smaller projected dimensions and a larger training set sample size. The experiments also showed that Multi-linear Principal Component Analysis (MPCA) is not suitable for micro-expression recognition because the eigenvectors corresponding to smaller eigenvectors are discarded, and those eigenvectors include brief and subtle motion information.

Support Tensor Machines for Classification of Hyperspectral Remote Sensing Imagery

In recent years, the support vector machines (SVMs) have been very successful in remote sensing image classification, particularly when dealing with high-dimensional data and limited training samples. Nevertheless, the vector-based feature alignment of the SVM can lead to an information loss in representation of hyperspectral images, which intrinsically have a tensor-based data structure. In this paper, a new multiclass support tensor machine (STM) is specifically developed for hyperspectral image classification. Our newly proposed STM processes the hyperspectral image as a data cube and then identifies the information classes in tensor space. The multiclass STM is developed from a set of binary STM classifiers using the one-against-one parallel strategy. As a part of our tensor-based processing chain, a multilinear principal component analysis (MPCA) is used for preprocessing, in order to reduce the tensorial data redundancy and, at the same time, preserve the tensorial structure information in sparse and high-order subspaces. As a result, the contributions of this work are twofold: a new multiclass STM model for hyperspectral image classification is developed, and a tensorial image interpretation framework is constructed, which provides a system consisting of tensor-based feature representation, feature extraction, and classification. Experiments with four hyperspectral data sets, covering agricultural and urban areas, are conducted to validate the effectiveness of the proposed framework. Our experimental results show that the proposed STM and MPCA-STM can achieve better results than traditional SVM-based classifiers.