A Report on Multilinear PCA Plus GTDA to Deal With Face Image

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.

This paper proposes a novel face super-resolution reconstruction (hallucination) technique, color face images reconstruction of RGB space with an error regression model in multi-linear principal component analysis (MPCA). From hallucination framework, many color face images are explained in RGB space. Then, they can be naturally described as tensors or multi-linear arrays. In this way, the error regression analysis is used to find the error estimation which can be obtained from the existi ng LR in tensor space. The framework consists of learning and hallucinating process. In learning process is from the mistakes in reconstruct face images of the training dataset by MPCA, then finding the relationship between input and error by regression analysis. In hallucinating process uses normal method by back-projection of MPCA, after that the result is corrected with the error estimation. In this contribution we show that our hallucination technique can be suitable for color face images both in RGB space. By using the MPCA subspace with error regression model, we can generate photorealistic color face images. Our approach is demonstrated by extensive experiments with high-quality hallucinated color faces. In addition, our experiments on face images from FERET database validate our algorithm

This paper presents a novel approach to solve the supervised dimensionality reduction problem and feature extraction by encoding an image object as a general tensor of 2-D/3-D order. In this paper a multilinear principal component analysis (MPCA) for tensor object feature extraction and then a multilinear discriminant analysis (MDA), to find the best subspaces have been proposed. It should be noted that both of the algorithms work with tensor objects so the structure of the objects has been never broken. Therefore we achieve a better result than the result of the traditional methods. The focus of these algorithms is avoiding the curse of dimensionality. Finally, a comprehensive experiments on ORL and FERET databases has been provided by encoding face images as 2-D or 3-D tensors to demonstrate that MPCA+MDA algorithm based on higher order tensors has the potential to outperform the traditional vector-based subspace learning algorithms such as Eigenface and Fisherface, especially in the cases with small sample sizes and curse of dimensionality dilemma.

Linear Discriminant Analysis (LDA) and Multilinear Principal Component Analysis (MPCA) are leading subspace methods for achieving dimension reduction based on supervised learning. Both LDA and MPCA use class labels of data samples to calculate subspaces onto which these samples are projected. Furthermore, both methods have been successfully applied to face recognition. Although LDA and MPCA share common goals and methodologies, in previous research they have been applied separately and independently. In this paper, we propose an extension of LDA to multiple factor frameworks. Our proposed method, Multifactor Discriminant Analysis, aims to obtain multilinear projections that maximize the between-class scatter while minimizing the withinclass scatter, which is the same core fundamental objective of LDA. Moreover, Multifactor Discriminant Analysis (MDA), like MPCA, uses multifactor analysis and calculates subject parameters that represent the characteristics of subjects and are invariant to other changes, such as viewpoints or lighting conditions. In this way, our proposed MDA combines the best virtues of both LDA and MPCA for face recognition.

This paper introduces a pioneering Hybrid Parallel Multi-linear Face Recognition algorithm that capitalizes on multi-linear methodologies, such as Multi-linear Principal Component Analysis (MPCA), Linear Discriminant Analysis (LDA), and Histogram of Oriented Gradients (HOG), to attain exceptional recognition performance. The Hybrid Feature Selection (HFS) algorithm is meticulously crafted to augment the classification performance on the CK+ and FERET datasets by amalgamating the strengths of feature extraction techniques and feature selection methods. HFS seamlessly incorporates Principal Component Analysis (PCA), Local Discriminant Analysis (LDA), and HOG. The primary aim of this algorithm is to autonomously identify a subset of the most distinctive features from the extracted feature pool, thus elevating classification accuracy, precision, recall, and F1-Score. By amalgamating these methodologies, the algorithm adeptly diminishes dimensionality while conserving pivotal features. Experimental trials on facial image datasets, CK+ and FERET, underscore the algorithm's supremacy in terms of accuracy and computational efficiency when contrasted with conventional linear techniques and even certain deep learning approaches. The proposed algorithm proffers an encouraging solution for real-world face recognition applications where precision and operational efficiency are of paramount significance.

Accurate detection of abnormal myocardium regions is essential for differential diagnosis of cardiovascular disease. However, to achieve this goal by image analysis will significantly increase the burden on radiologists who is already overwhelmed. To ease the time and energy-demanding process and enhance the reproducibility, we proposed a novel framework for automatic abnormal shape detection on left ventricular (LV) using MR images. Our proposed approach utilizes the features obtained by large deformation diffeomorphic metric mapping (LDDMM). To take advantage of 3D structural information, we introduce multilinear principal component analysis (MPCA) in the framework to reduce feature dimensions. Then we combine MPCA with linear discriminant analysis (LDA) to perform differential diagnosis. The performance of proposed framework is evaluated on patients’ images. In the classification of three common cardiovascular diseases, our proposed method outperformed traditional classifiers (Global point signature, Random Forest and XGBoost) with an accuracy of 94%. To further automatically detect the dysfunctional heart regions, we did a comparison on 3D morphology between the diseased subjects and healthy controls and performed an automatic visualization of the abnormal myocadiac regions. In conclusion, our proposed framework reserves the spatial information of the features generated through LDDMM registration and enables the 3D visualization of abnormal regions of LV. With the advance of our method, differential diagnosis is successfully performed on patients with different cardiovascular diseases.

Multilinear class-specific discriminant analysis

This paper presents emotion label estimation via tensor-based spatiotemporal visual attention analysis. It has been reported in the fields of psychology and neuroscience that human emotions are related to two elements, their visual attention change and objects included in a target image. Therefore, the proposed method focuses on the spatiotemporal change of visual attention of human gazing at objects in the target image and constructs two neural networks which enable the emotion label estimation considering both of the above two elements. Specifically, the proposed method newly constructs a fourth-order tensor, gaze and image tensor (GIT) whose modes correspond to the width, the height and the color channel of the target image and the time axis of visual attention which is used for representing the time change. Then the first network, which consists of general tensor discriminant analysis (GTDA) and extreme learning machine (ELM), estimates the emotion label from the fourth-order GIT with concerning their visual attention change. Furthermore, the second network, which consists of pre-trained convolutoinal neural network-based feature extraction, GTDA and ELM, enables the estimation from the second-order GIT including visual features obtained from objects focused at each time. Finally, the proposed method estimates emotion labels based on decision fusion of the outputs from the two networks. Experimental results show the effectiveness of the proposed method.

Objectives: Various interpretation and analytical approaches of oral and dental cavities have significantly got enough attention and consideration in imaging and imaging analysis as it led to numerous carious lesions. Prevailing cavities and caries finding approaches are not able to verify and scrutinize the carious lesions at the beginning level. It is an attempt which proposes to develop a unique and novel cavities identification approach which comprises three segments, namely (a) pre-processing, (b) feature extraction and (c) classification. Methodology: In the beginning, the quality of the image is enriched by numerous pre-processing techniques such as contrast improvement, grey thresholding and active contour. Subsequently, the features are found with the aid of “multi-linear principal component analysis (MPCA)”. Lastly, classification is done using neural network (NN), which is trained by the adaptive dragonfly algorithm (DA) algorithm. Results: The proposed MPCA model nonlinear programming with adaptive DA (MNP-ADA) yields the correct and scrutinized as well as classified outcome. It is compared with prevailing approaches in terms of numerous statistical measures, and it is proved superior over it. It can be used as an additional approach for enriching the diagnostic efficiency.KeywordsDental cariesFeaturesClassificationBEASFMPCANeural network

Although widely used, Multilinear PCA (MPCA), one of the leading multilinear analysis methods, still suffers from four major drawbacks. First, it is very sensitive to outliers and noise. Second, it is unable to cope with missing values. Third, it is computationally expensive since MPCA deals with large multi-dimensional datasets. Finally, it is unable to maintain the local geometrical structures due to the averaging process. This paper proposes a novel approach named Compressed Submanifold Multifactor Analysis (CSMA) to solve the four problems mentioned above. Our approach can deal with the problem of missing values and outliers via SVD-L1. The Random Projection method is used to obtain the fast low-rank approximation of a given multifactor dataset. In addition, it is able to preserve the geometry of the original data. Our CSMA method can be used efficiently for multiple purposes, e.g. noise and outlier removal, estimation of missing values, biometric applications. We show that CSMA method can achieve good results and is very efficient in the inpainting problem as compared to [1], [2]. Our method also achieves higher face recognition rates compared to LRTC, SPMA, MPCA and some other methods, i.e. PCA, LDA and LPP, on three challenging face databases, i.e. CMU-MPIE, CMU-PIE and Extended YALE-B.

Challenges in detecting machinery faults, particularly in multivariate sensor environments, necessitate advanced feature extraction and classification techniques. This study introduces a novel approach that combines Multilinear Principal Component Analysis (MPCA) with a 1D-Convolutional Neural Network (1D-CNN) for efficient fault detection. By constructing Frequency Domain (FD) tensors from multivariate sensor data and applying MPCA for dimensionality reduction, our methodology enhances the capabilities of a 1D-CNN in feature learning and fault classification. The efficacy of this approach is validated through experiments on a Machinery Fault Simulator (MFS) with acoustic and vibration sensors, demonstrating notable improvements in fault detection accuracy compared to benchmark methods. The study results demonstrate that the proposed approach exhibits high accuracy in identifying machine fault conditions and outperforms the benchmark methods. The findings of this study have significant inferences for machine fault detection and fill the gap of more effective and reliable techniques in this domain.

Gait recognition is a rising biometric technology which aims to distinguish people purely through the analysis of the way they walk, while the problem is that the dimensionality of the gait data is too high, so it is necessary to carry on dimensionality reduction task. Up to date, in the area of computer vision and pattern recognition, various dimensionality reduction algorithms have been employed for gait data, including the conventional vector representation based methods principal components analysis (PCA) and, locality preserving projection (LPP), and the recently proposed multi-linear subspace learning based approaches such as multilinear principal component analysis (MPCA). In this paper, inspired by the advantages of the tensor representation and manifold learning, we propose a novel sparse tensor discriminative locality alignment for human gait feature representation and dimensionality reduction algorithm, and subsequently apply the refined feature for gait recognition by a lazy classifier of the KNN. The proposed method adopts sparse multi-way projection based on the high-order version of discriminative locality alignment, by which the class separability is enhanced and the potential model overfitting is simultaneously avoided. Extensive experiments on the University of South Florida (USF) HumanID Gait Database show that the proposed method achieves better recognition rate compared with some existing classical dimensionality reduction algorithms.

In this study, we present individual identification using a third-order tensor-based multilinear FisherECG (MFECG). The MFECG is based on multilinear linear discriminant analysis (LDA) in the field of multilinear subspace learning (MSL). MSL performs feature extraction without rearranging input data into 1-D. Thus, the MSL can maintain the original correlation in structure. Also, since the compact features are extracted, the large tensor can be efficiently handled. However, linear subspace learning (LSL) must reorder the data into 1-D for feature extraction. That makes the dimension of the data become very large, which causes the problem of insufficient number of training data. Here, the 3-D tensor is formed by rearranging a 1-D electrocardiogram signal into a 2-D matrix and accumulating the 2-D matrices. The experimental results show that the tensor-based MFECG showed higher accuracies than PCA (Principal Component Analysis) and LDA of LSL.

Multilinear subspace analysis (MSA) is a promising methodology for pattern-recognition problems due to its ability in decomposing the data formed from the interaction of multiple factors. The MSA requires a large training set, which is well organized in a single tensor, which consists of data samples with all possible combinations of the contributory factors. However, such a "complete" training set is difficult (or impossible) to obtain in many real applications. The missing-value problem is therefore crucial to the practicality of the MSA but has been hardly investigated up to present. To solve the problem, this paper proposes an algorithm named M(2)SA, which is advantageous in real applications due to the following: 1) it inherits the ability of the MSA to decompose the interlaced semantic factors; 2) it does not depend on any assumptions on the data distribution; and 3) it can deal with a high percentage of missing values. M(2)SA is evaluated by face image modeling on two typical multifactorial applications, i.e., face recognition and facial age estimation. Experimental results show the effectiveness of M(2) SA even when the majority of the values in the training tensor are missing.

There is a growing interest in subspace learning techniques for face recognition; however, the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma. In this paper, we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order. First, we propose a discriminant tensor criterion, whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction. Then, a novel approach, called k-mode optimization, is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions. We call this algorithm multilinear discriminant analysis (MDA), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes, 2) for classification problems involving higher order tensors, the MDA algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem, and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k-mode optimization. We provide extensive experiments on ORL, CMU PIE, and FERET databases by encoding face images as second- or third-order tensors to demonstrate that the proposed MDA algorithm based on higher order tensors has the potential to outperform the traditional vector-based subspace learning algorithms, especially in the cases with small sample sizes.