Local Principal Component Analysis Research Articles

Evaluation Methodology for Respiratory Signal Extraction from Clinical Cone-Beam CT (CBCT) using Data-Driven Methods

The absence of a ground truth for internal motion in clinical studies has always been a challenge to evaluate developed methods to extract respiratory motion especially during a 60-second cone-beam CT (CBCT) scan in Image-Guided Radiotherapy Treatment (IGRT). The unavailability of a gold standard has led this study to present a methodology to manually track respiratory motion on a clinically acquired CBCT projection data set over a 360° view angle. The tracked signal is then used as a reference to assess the performance of four data-driven methods in respiratory motion extraction, namely: the Amsterdam Shroud (AS), Local Principal Component Analysis (LPCA), Intensity Analysis (IA), and Fourier Transform (FT)-based methods that do not require additional equipment nor protocol to the existing treatment delivery. The assessment using this reference signal includes both quantitative and qualitative analysis. It is found out quantitatively that all four methods managed to extract respiratory signals that are highly correlated with the reference signal, with the LPCA method displaying the highest correlation coefficient value at 0.9108. Furthermore, the normalized root-mean-squared amplitude error of detected peaks and troughs within the signal from the LPCA method is also lowest at 1.6529 % compared to the other methods. This result is further supported by qualitative analysis via visual inspection of each extracted signal plotted with the reference signal on the same axes.

Identification with Face Recognition Methods in Real Life Applications

The development of technologies such as employment tracking systems, personal security, and the use of robots has led a lot of studies on face recognition systems. In the most of studies considering face recognition, recognition accuracies are very high, since training and testing images are selected randomly from the same databases. However, in real life applications, these images are not randomly selected from the same database. Because, these systems are trained during installation of the recognition system or when a new person needs to be introduced to the system. On the other hand, images used for predictions are uploaded to the system at other times. In this study, it is aimed to show that the accuracy rates of real-life face recognition systems differ from the systems trained and tested with randomly selected images as usually done in literature. To observe this difference in the first step, training and test images are selected randomly. In the second step, training and test images are divided according to the recording dates as in real life. Accuracy rates are evaluated by using linear discriminant analysis, local binary patterns and principal component analysis methods. Although the accuracies are very high for the first step, it is seen that the accuracies fell dramatically in the second step for all methods. Afterwards a new method is searched also in this study to increase these low accuracy rates. It is shown that usage of eye area images instead of face images has higher accuracy rates in all above methods for real life applications.

Real-Time Attendance and Feedback System

Face is the representation of one’s identity. Hence, we have proposed an automated student attendance system based on face recognition. Face recognition system is very useful in life applications especially for attendance system. In our proposed approach, firstly, video framing is performed by activating the camera through a user-friendly interface. In the pre-processing stage, scaling of the size of images is performed, if necessary, in order to prevent loss of information. In face recognition stage, enhanced local binary pattern (LBP) and principal component analysis (PCA) is applied correspondingly in order to extract the features from facial images. Another way of marking the attendance is fingerprint recognition. To mark the attendance students simply have to give the fingerprint impression in fingerprint scanner module. Finally, the attendance of the recognized student will be marked and saved in the excel file. The student who is not registered will also be able to register on the spot and notification will be given if students sign in more than once. Whenever seminar is completed then a link is sent on email. It includes the information in terms of feedback. When student fills the feedback form then analysis of overall session is done.

Local control editing paradigms for part‐based 3D face morphable models

AbstractWe propose an approach to construct realistic 3D facial morphable models (3DMM) that allows an intuitive facial attribute editing workflow. Current face modeling methods using 3DMM suffer from a lack of local control. We thus create a 3DMM by combining local part‐based 3DMM for the eyes, nose, mouth, ears, and facial mask regions. Our local principal component analysis (PCA)‐based approach uses a novel method to select the best eigenvectors from the local 3DMM to ensure that the combined 3DMM is expressive, while allowing accurate reconstruction. We provide different editing paradigms, all designed from the analysis of the data set. Some use anthropometric measurements from the literature and others allow the user to control the dominant modes of variation extracted from the data set. Our part‐based 3DMM is compact, yet accurate, and compared to other 3DMM methods, it provides a new trade‐off between local and global control. We tested our approach on a data set of 135 scans used to derive the 3DMM, plus 19 scans that served for validation. The results show that our part‐based 3DMM approach has excellent generative properties and allows the user intuitive local control.

Machine learning for integrating combustion chemistry in numerical simulations

A strategy based on machine learning is discussed to close the gap between the detailed description of combustion chemistry and the numerical simulation of combustion systems. Indeed, the partial differential equations describing chemical kinetics are stiff and involve many degrees of freedom, making their solving in three-dimensional unsteady simulations very challenging. It is discussed in this work how a reduction of the computing cost by an order of magnitude can be achieved using a set of neural networks trained for solving chemistry. The thermochemical database used for training is composed of time evolutions of stochastic particles carrying chemical species mass fractions and temperature according to a turbulent micro-mixing problem coupled with complex chemistry. The novelty of the work lies in the decomposition of the thermochemical hyperspace into clusters to facilitate the training of neural networks. This decomposition is performed with the Kmeans algorithm, a local principal component analysis is then applied to every cluster. This new methodology for combustion chemistry reduction is tested under conditions representative of a non-premixed syngas oxy-flame.

Fuzzy c-Varieties Clustering for Vertically Distributed Datasets

Fuzzy c-varieties (FCV) is a linear fuzzy clustering method, whose clustering criterion is constructed by replacing the fuzzy c-means (FCM) prototypes with linear varieties, and has been utilized for local principal component analysis. In this paper, the FCV iterative algorithm is modified for handling vertically distributed datasets under consideration of privacy preservation. A cryptographic calculation scheme is realized by utilizing the least square criterion without eigen solutions. The characteristics of the proposed algorithm is demonstrated through numerical experiments.

Assessing the Interplay of Shape and Physical Parameters by Unsupervised Nonlinear Dimensionality Reduction Methods

The article presents an exploratory study on the application to ship hydrodynamics of unsupervised nonlinear design-space dimensionality reduction methods, assessing the interaction of shape and physical parameters. Nonlinear extensions of the principal component analysis (PCA) are applied, namely local PCA (LPCA) and kernel PCA (KPCA). An artificial neural network approach, specifically a deep autoencoder (DAE) method, is also applied and compared with PCA-based approaches. The data set under investigation is formed by the results of 9000 potential flow simulations coming from an extensive exploration of a 27-dimensional design space, associated with a shape optimization problem of the DTMB 5415 model in calm water at 18 kn (Froude number, Fr = 25). Data include three heterogeneous distributed and suitably discretized parameters (shape modification vector, pressure distribution on the hull, and wave elevation pattern) and one lumped parameter (wave resistance coefficient), for a total of 9000 x 5101 elements. The reduced-dimensionality representation of shape and physical parameters is set to provide a normalized mean squared error smaller than 5%. The standard PCA meets the requirement using 19 principal components/parameters. LPCA and KPCA provide the most promising compression capability with 14 parameters required by the reduced-dimensionality parametrizations, indicating significant nonlinear interactions in the data structure of shape and physical parameters. The DAE achieves the same error with 17 components. Although the focus of the current work is on design-space dimensionality reduction, the formulation goes beyond shape optimization and can be applied to large sets of heterogeneous physical data from simulations, experiments, and real operation measurements.

Study of MILD combustion using LES and advanced analysis tools

A cylindrical confined combustor operating under MILD condition is investigated using LES. The combustion and its interaction with turbulence are modeled using two reactor based models, PaSR and EDC. Results show that the Partially Stirred Reactor (PaSR) model yields improved estimation for mean temperature and species mole fractions compared to Eddy Dissipation Concept (EDC). LES data are analysed using advanced post-processing methods such as the chemical Tangential Stretching Rate (TSR), balance analysis and local Principle Component (PCA) analysis. TSR can identify chemical explosive (ignition-like) and contractive (burnt) regions. With the balance analysis of the convective, diffusive and reactive terms in temperature equation, regions with substantial heat release coming from ignition or flame are identified. The local PCA analysis classifies the whole domain into clusters (regions with specific features) and provides the leading species in each cluster. The three analyses correlate well with one another and it is observed that the most chemically active region locates upstream (in the near-field). Also, both autoignition and flame-like structures play equally important roles in MILD combustion.

Tumor phase recognition using cone-beam computed tomography projections and external surrogate information.

Directly extracting the respiratory phase pattern of the tumor using cone-beam computed tomography (CBCT) projections is challenging due to the poor tumor visibility caused by the obstruction of multiple anatomic structures on the beam's eye view. Predicting tumor phase information using external surrogate also has intrinsic difficulties as the phase patterns between surrogates and tumors are not necessary to be congruent. In this work, we developed an algorithm to accurately recover the primary oscillation components of tumor motion using the combined information from both CBCT projections and external surrogates. The algorithm involved two steps. First, a preliminary tumor phase pattern was acquired by applying local principal component analysis (LPCA) on the cropped Amsterdam Shroud (AS) images. In this step, only the cropped image of the tumor region was used to extract the tumor phase pattern in order to minimize the impact of pattern recognition from other anatomic structures. Second, by performing multivariate singular spectrum analysis (MSSA) on the combined information containing both external surrogate signal and the original waveform acquired in the first step, the primary component of the tumor phase oscillation was recovered. For the phantom study, a QUASAR respiratory motion phantom with a removable tumor-simulator insert was employed to acquire CBCT projection images. A comparison between LPCA only and our method was assessed by power spectrum analysis. Also, the motion pattern was simulated under the phase shift or various amplitude conditions to examine the robustness of our method. Finally, anatomic obstruction scenarios were simulated by attaching a heart model, PVC tubes, and RANDO® phantom slabs to the phantom, respectively. Each scenario was tested with five real-patient breathing patterns to mimic real clinical situations. For the patient study, eight patients with various tumor locations were selected. The performance of our method was then evaluated by comparing the reference waveform with the extracted signal for overall phase discrepancy, expiration phase discrepancy, peak, and valley accuracy. In tests of phase shifts and amplitude variations, the overall peak and valley accuracy was -0.009±0.18sec, and no time delay was found compared to the reference. In anatomical obstruction tests, the extracted signal had 1.6±1.2 % expiration phase discrepancy, -0.12±0.28sec peak accuracy, and 0.01±0.15sec valley accuracy. For patient studies, the extracted signal using our method had -1.05±3.0 % overall phase discrepancy, -1.55±1.45% expiration phase discrepancy, 0.04±0.13sec peak accuracy, and -0.01±0.15sec valley accuracy, compared to the reference waveforms. An innovative method capable of accurately recognizing tumor phase information was developed. With the aid of extra information from the external surrogate, an improvement in prediction accuracy, as compared with traditional statistical methods, was obtained. It enables us to employ it as the ground truth for 4D-CBCT reconstruction, gating treatment, and other clinic implementations that require accurate tumor phase information.

Image Denoising Using Superpixel-Based PCA

Denoising is a fundamental task in image processing, aimed at estimating an unknown image from its noisy observation. In this paper, we develop a computationally simple paradigm for image denoising using superpixel grouping and principal component analysis (PCA) of similar patches within the superpixels. Our method comprises three steps. First, we perform a superpixel segmentation on the noisy images. Next, similar patches within the superpixels are grouped in order to preserve the local image structures. Finally, each group of similar patches is factorized by PCA transform and estimated by performing coefficient shrinkage in the PCA domain to remove the noise. The proposed method exploits the optimal energy compaction property of PCA on groups of similar patches in the least squares sense. The performance of our approach is experimentally verified on a variety of synthetic images at various noise levels, and on real world noisy images. Our proposed method achieves very competitive denoising performance, especially in preserving the fine image structures, compared with many existing denoising algorithms with respect to both objective measurement and visual evaluation. We also show that our proposed method is computationally more efficient than other local PCA based methods.

A time-varying diffusion index forecasting model

This paper introduces a novel forecasting method based on a time-varying diffusion index model, where both factor loadings and regression coefficients are allowed to be time-varying. We first obtain the local principal component analysis (PCA) estimators for the latent factors and then estimate the factor augmented forecasting regression with time-varying coefficients nonparametrically. A feasible forecast is proposed by combining the estimated factors and the nonparametric estimators of coefficients. A set of Monte Carlo simulations demonstrates better performance of our proposed method than the standard diffusion index forecasters based on rolling windows. An empirical application of forecasting US macroeconomic variables is provided.

Local eigenvalue decomposition for embedded Riemannian manifolds

Local Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the local extrinsic and intrinsic curvature. We show that the volume of domains on a submanifold of general codimension, determined by the intersection with higher-dimensional cylinders and balls in the ambient space, have asymptotic expansions in terms of the mean and scalar curvatures. Moreover, we propose a generalization of the classical third fundamental form to general submanifolds and prove that the local eigenvalue decomposition (EVD) of the covariance matrices have asymptotic expansions that contain the curvature information encoded by the traces of this tensor. This proves the general correspondence between the local EVD integral invariants and differential-geometric curvature for arbitrary embedded Riemannian submanifolds, found so far for curves and hypersurfaces only. Thus, we establish a key theoretical bridge, via covariance matrices at scale, for potential applications in manifold learning relating the statistics of point clouds sampled from Riemannian submanifolds to the underlying geometry.

Impact of the Partitioning Method on Multidimensional Adaptive-Chemistry Simulations

The large number of species included in the detailed kinetic mechanisms represents a serious challenge for numerical simulations of reactive flows, as it can lead to large CPU times, even for relatively simple systems. One possible solution to mitigate the computational cost of detailed numerical simulations, without sacrificing their accuracy, is to adopt a Sample-Partitioning Adaptive Reduced Chemistry (SPARC) approach. The first step of the aforementioned approach is the thermochemical space partitioning for the generation of locally reduced mechanisms, but this task is often challenging because of the high-dimensionality, as well as the high non-linearity associated to reacting systems. Moreover, the importance of this step in the overall approach is not negligible, as it has effects on the mechanisms’ level of chemical reduction and, consequently, on the accuracy and the computational speed-up of the adaptive simulation. In this work, two different clustering algorithms for the partitioning of the thermochemical space were evaluated by means of an adaptive CFD simulation of a 2D unsteady laminar flame of a nitrogen-diluted methane stream in air. The first one is a hybrid approach based on the coupling between the Self-Organizing Maps with K-Means (SKM), and the second one is the Local Principal Component Analysis (LPCA). Comparable results in terms of mechanism reduction (i.e., the mean number of species in the reduced mechanisms) and simulation accuracy were obtained for both the tested methods, but LPCA showed superior performances in terms of reduced mechanisms uniformity and speed-up of the adaptive simulation. Moreover, the local algorithm showed a lower sensitivity to the training dataset size in terms of the required CPU-time for convergence, thus also being optimal, with respect to SKM, for massive dataset clustering tasks.

Denoising of multi b-value diffusion-weighted MR images using deep image prior

The clinical value of multiple b-value diffusion-weighted (DW) magnetic resonance imaging (MRI) has been shown in many studies. However, DW-MRI often suffers from low signal-to-noise ratio, especially at high b-values. To address this limitation, we present an image denoising method based on the concept of deep image prior (DIP). In this method, high-quality prior images obtained from the same patient were used as the network input, and all noisy DW images were used as the network output. Our aim is to denoise all b-value DW images simultaneously. By using early stopping, we expect the DIP-based model to learn the content of images instead of the noise. The performance of the proposed DIP method was evaluated using both simulated and real DW-MRI data. We simulated a digital phantom and generated noise-free DW-MRI data according to the intravoxel incoherent motion model. Different levels of Rician noise were then simulated. The proposed DIP method was compared with the image denoising method using local principal component analysis (LPCA). The simulation results show that the proposed DIP method outperforms the LPCA method in terms of mean-squared error and parameter estimation. The results of real DW-MRI data show that the proposed DIP method can improve the quality of IVIM parametric images. DIP is a feasible method for denoising multiple b-value DW-MRI data.

Stable generalized finite element methods for elasticity crack problems

SummaryGeneralized or eXtended finite element methods (GFEM/XFEM) for crack problems have been studied extensively. The GFEM/XFEM are called extrinsic if additional functions are enriched at every node in certain domains, while they are called degree of freedom (DOF)‐gathering if the singular enriched functions are gathered using cutoff functions. The DOF‐gathering GFEM/XFEM save the additional DOFs compared with the extrinsic approach. Both extrinsic and DOF‐gathering GFEM/XFEM suffer from difficulties of stabilities in a sense that their scaled condition numbers (SCN) of stiffness matrices could be much larger than those of the standard FEM. A GFEM/XFEM is referred to as stable GFEM (SGFEM) if it reaches optimal convergence orders, and its SCN is of same order as that of FEM. An extrinsic SGFEM was established in Zhang et al for the Poisson crack problems. Objective of this article is to propose the SGFEM for elasticity crack problems; both extrinsic and DOF‐gathering schemes are addressed. The main idea is to modify the enriched functions by subtracting their FE interpolants, which was developed by Babuška and Banerjee. To remove local almost linear dependence introduced by multifold enrichments at one node, we propose a local principal component analysis technique to identify and analyze “contributions” of multifold enrichments at one node. Numerical studies demonstrate that the proposed SGFEM and DOF‐gathering SGFEM are of optimal convergence and have the SCNs of same order as in the FEM.

Comparison of data-driven respiratory signal extraction methods from cone-beam CT (CBCT)

In Cone-Beam CT (CBCT) imaging, respiratory motion needs to be considered to mitigate motion artifacts thus increasing the accuracy of reconstructed images. Data driven methods can be used to extract respiratory signal directly from projection data without requiring any additional equipment or surrogate devices. Digital phantoms provide an adequate option to evaluate developing methods prior to clinical implementation. In this study, four data driven methods are used to extract respiratory signal from simulated projections. An in-house 4D MRI-based CBCT digital phantom is used, where actual respiratory signal is available as ground truth. In comparing all four data driven methods, the respiratory signal extracted using the Local Principal Component Analysis (LPCA) method is found to be robust and yielded the highest correlation coefficient of 0.8644 compared to the ground truth.

A stable generalized finite element method (SGFEM) of degree two for interface problems

Generalized or Extended Finite Element Methods (GFEM/XFEM) of degree 1 for interface problems have been reported in the literature; they (i) yield optimal order of convergence, i.e., O(h) (h is a discretization parameter), (ii) are stable in a sense that conditioning is not worse than that of the standard FEM, and (iii) are robust in that the conditioning does not deteriorate as interface curves are close to boundaries of underlying elements. However, higher order GFEM/XFEM with the properties (i)–(iii) have not been successfully addressed yet. Various enrichment schemes for GFEM/XFEM based on D or DPk (D is a distance function or the absolute value of level set function, and Pk is the polynomial basis of degree k) have been reported recently to obtain higher order convergence, but they are not stable or robust in general; in fact, they even may not yield the optimal orders of convergence. In this paper, we propose a stable GFEM/XFEM of degree 2 (SGFEM2) for the interface problems, where we used the enrichment scheme based on D{1,x,y}, instead of D or D{1,x,y,x2,xy,y2} in the literature. We prove that the SGFEM2 yields the optimal order of convergence, i.e., O(h2), for the interface problems with curved (smooth) interfaces. A local principal component analysis technique has been proposed, which ensures that the SGFEM2 is stable and robust. Numerical experiments for straight and curved interfaces have been presented to illuminate these properties.

Finger vein biometric verification using block multi-scale uniform local binary pattern features and block two-directional two-dimension principal component analysis

Finger vein recognition has drawn increasing attention as one of the most popular and promising biometrics due to its high distinguishes ability, security and non-invasive procedure. The focus of this paper is on proposing new schemes based on finger vein patterns by employing block uniform local binary pattern and block two-directional two-dimension principal component analysis method in order to effectively reduce data redundancy. First, a block multi-scale uniform local binary pattern (MULBP) features operator based on improved circular neighborhood is employed to extract the local texture features of finger vein images effectively. Then two-directional two-dimension principal component analysis ((2D)2PCA) method is applied to finger vein recognition in this paper, which can effectively reduce the dimension of feature matrix and improve system performance. Furthermore, in order to avoid the disadvantage of (2D)2PCA method which cannot preserve some important local features, this paper adopts (2D)2PCA method based on block to preserve local information of image. The experimental results revealed that our proposed method achieved superior performance for the FV-USM finger vein database with a recognition rate of99.32 % and consistent performance for the Tianjin finger vein database with a recognition rate more than 99 %. Above results show that this new algorithm is effective and feasible in finger vein recognition system.

Nonlinear Fault Detection of Batch Processes Using Functional Local Kernel Principal Component Analysis

In order to guarantee and improve the product quality, the data-driven fault detection technique has been widely used in industry. For three-way datasets of batch process in industry process (i.e., batch × variable × time), a novel method named functional local kernel principal component analysis (FLKPCA) is proposed. Since the variables' trajectories often show functional nature and can be considered as smooth functions rather than just vectors. Firstly, the variables' trajectory is expressed as the combination of smooth basis functions using functional data analysis (FDA), which means that the datasets of batches process would be transformed from the three-ways array into two-ways function matrix. Then, kernel locality preserving projections (LKPCA) is used to perform dimensionality reduction on two-way function matrix directly. Different from kernel principal component analysis (KPCA). LKPCA aims at preserving the both local and global structure of the data in a new optimization objective. Consequently, FLKPCA could more effectively seek the potential information that hidden in the three-ways datasets. Lastly, the effectiveness of the proposed approach is illustrated by the benchmark of fed-batch penicillin fermentation process and the hot strip rolling process.

Local Binary Pattern Method (LBP) and Principal Component Analysis (PCA) for Periocular Recognition

Identification of identity through eye is gaining more and more importance. Commonly, the researchers approach the eye from any of three parts, the iris, the circumference around the eye, and the iris and its circumference. This study follows a holistic approach to identity identification by using the iris and whole periocular area and proposes a periocular recognition system (PRS) that has been developed using the Local Binary Pattern (LBP) technique combined with Principal Component Analysis (PCA) at the feature extraction stage and the k-nearest neighbors (k-NN) algorithm as a classifier at the classification stage. This system achieves identity recognition through three steps: pre-processing, feature extraction, and classification. Pre-processing is applied to the images so as to convert them to grayscale. In the feature extraction step, the LBP method is applied to extract the texture feature from the images and use it in PCA to reduce data dimensionality and obtain the relevant data so that only the important features are extracted. These two steps are applied both in the training phase and the testing phase of image processing. On the other hand, the testing data sets are processed using the k-NN classifier. The proposed PRS was tested on data drawn from the PolyU database using more than one basis of system experience. Specifically, the system performance was tested once on all 209 subjects present in the database and once on 140 subjects. This database also contains images taken in the visible (VIS) and near-infrared (NIR) regions of the electromagnetic radiation (EMR) spectrum. So, the system was tested on images taken in both regions separately for matching. As well, the proposed PRS benefited from the availability of images for the right and left perioculars. Performance was, therefore, tested on images of each side of the periocular area (the left and right sides) separately, as well as for the combination of the two sides. The identity recognition rates characteristic of the proposed PRS were most often higher than the recognition rates produced by systems reported in the literature. The highest recognition accuracy obtained from the proposed system, which is 98.21%, was associated with the 140-subject data sub-set.