Conventional Principal Component Analysis Research Articles

Data driven surrogate signal extraction for dynamic PET using selective PCA: time windows versus the combination of components.

Respiratory motion correction is beneficial in PET, as it can reduce artefacts caused by motion and improve quantitative accuracy. Methods of motion correction are commonly based on a respiratory trace obtained through an external device (like the Real Time Position Management System) or a data driven method, such as those based on dimensionality reduction techniques (for instance PCA). PCA itself being a linear transformation to the axis of greatest variation. Data driven methods have the advantage of being non-invasive, and can be performed post-acquisition. However, their main downside being that they are adversely affected by the tracer kinetics of the dynamic PET acquisition. Therefore, they are mostly limited to static PET acquisitions. This work seeks to extend on existing PCA-based data-driven motion correction methods, to allow for their applicability to dynamic PET imaging. The methods explored in this work include; a moving window approach (similar to the Kinetic Respiratory Gating method from Schleyer et al.), extrapolation of the principal component from later time points to earlier time points, and a method to score, select, and combine multiple respiratory components. The resulting respiratory traces were evaluated on 22 data sets from a dynamic 18FFDG study on patients with Idiopathic Pulmonary Fibrosis. This was achieved by calculating their correlation with a surrogate signal acquired using a Real Time Position Management System. The results indicate that all methods produce better surrogate signals than when applying conventional PCA to dynamic data (for instance, a higher correlation with a gold standard respiratory trace). Extrapolating a late time point principal component produced more promising results than using a moving window. Scoring, selecting, and combining components held benefits over all other methods. This work allows for the extraction of a surrogate signal from dynamic PET data earlier in the acquisition and with a greater accuracy than previous work. This potentially allows for numerous other methods (for instance, respiratory motion correction) to be applied to this data (when they otherwise could not be previously used).

Deep Learning-enhanced Hyperspectral Imaging for the Rapid Identification and Classification of Foodborne Pathogens

Background: Bacterial cellulose (BC) is a versatile biomaterial with numerous applications, and the identification of bacterial strains that produce it is of great importance. This study explores the effectiveness of a Stacked Autoencoder (SAE)-based deep learning method for the classification of bacterial cellulose-producing bacteria. Objective: The primary objective of this research is to assess the potential of SAE-based classification models in accurately identifying and classifying bacterial cellulose-producing bacteria, with a particular focus on strain GZ-01. objective: The primary objective of this research is to assess the potential of SAE-based classification models in accurately identifying and classifying bacterial cellulose-producing bacteria, with a particular focus on strain GZ-01. Methods: Strain GZ-01 was isolated and subjected to a comprehensive characterization process, including morphological observations, physiological and biochemical analysis, and 16S rDNA sequencing. These methods were employed to determine the identity of strain GZ-01, ultimately recognized as Acetobacter Okinawa. The study compares the performance of SAE-based classification models to traditional methods like Principal Component Analysis (PCA). Results: The SAE-based classifier exhibits outstanding performance, achieving an impressive accuracy of 94.9% in the recognition and classification of bacterial cellulose-producing bacteria. This approach surpasses the efficacy of conventional PCA in handling the complexities of this classification task. Conclusion: The findings from this research highlight the immense potential of utilizing nanotechnology- driven data analysis methods, such as Stacked Autoencoders, in the realm of bacterial cellulose research. These advanced techniques offer a promising avenue for enhancing the efficiency and accuracy of bacterial cellulose-producing bacteria classification, which has significant implications for various applications in biotechnology and materials science.

Robust Fault Detection in Monitoring Chemical Processes Using Multi-Scale PCA with KD Approach

Effective fault detection in chemical processes is of utmost importance to ensure operational safety, minimize environmental impact, and optimize production efficiency. To enhance the monitoring of chemical processes under noisy conditions, an innovative statistical approach has been introduced in this study. The proposed approach, called Multiscale Principal Component Analysis (PCA), combines the dimensionality reduction capabilities of PCA with the noise reduction capabilities of wavelet-based filtering. The integrated approach focuses on extracting features from the multiscale representation, balancing the need to retain important process information while minimizing the impact of noise. For fault detection, the Kantorovich distance (KD)-driven monitoring scheme is employed based on features extracted from Multiscale PCA to efficiently detect anomalies in multivariate data. Moreover, a nonparametric decision threshold is employed through kernel density estimation to enhance the flexibility of the proposed approach. The detection performance of the proposed approach is investigated using data collected from distillation columns and continuously stirred tank reactors (CSTRs) under various noisy conditions. Different types of faults, including bias, intermittent, and drift faults, are considered. The results reveal the superior performance of the proposed multiscale PCA-KD based approach compared to conventional PCA and multiscale PCA-based monitoring methods.

Robust and Sparse Principal Component Analysis With Adaptive Loss Minimization for Feature Selection.

Principal component analysis (PCA) is one of the most successful unsupervised subspace learning methods and has been used in many practical applications. To deal with the outliers in real-world data, robust principal analysis models based on various measure are proposed. However, conventional PCA models can only transform features to unknown subspace for dimensionality reduction and cannot perform features' selection task. In this article, we propose a novel robust PCA (RPCA) model to mitigate the impact of outliers and conduct feature selection, simultaneously. First, we adopt σ -norm as reconstruction error (RE), which plays an important role in robust reconstruction. Second, to conduct feature selection task, we apply l2,0 -norm constraint to subspace projection. Furthermore, an efficient iterative optimization algorithm is proposed to solve the objective function with nonconvex and nonsmooth constraint. Extensive experiments conducted on several real-world datasets demonstrate the effectiveness and superiority of the proposed feature selection model.

Perturbation analysis on PCA plus graph embedding methods and PCA plus exponential graph embedding methods

PCA plus graph embedding (PCA+GE) methods are popular techniques for dimensionality reduction and face recognition. In these methods, the principal component analysis (PCA) is used first, and then some graph embedding methods are applied. In practice, the data is often perturbed or contaminated, and it has been found that PCA is sensitive to noise, which may affect the accuracy of the subsequent classification. Moreover, the PCA+GE methods can be unstable after data perturbation. To the best of our knowledge, however, there are few results on perturbation analysis of this type of methods. In this work, we show the reason from a matrix perturbation analysis point of view. The main aim of this paper is to look for the reasons that cause the instability. To overcome the difficulty of instability, a framework of PCA plus exponential graph embedding methods is proposed to take the place of the conventional PCA plus graph embedding methods. The computational cost of the proposed methods is comparable to that of the original counterparts, and our methods are much more stable in terms of recognition accuracy. Numerical experiments show the effectiveness of our theoretical results, and demonstrate the efficiency of the new methods on some real-world data sets.

Functional PCA and deep neural networks-based Bayesian inverse uncertainty quantification with transient experimental data

This work focuses on developing an inverse uncertainty quantification (IUQ) process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the IUQ of TRACE physical model parameters using the FEBA benchmark transient experimental data on peak cladding temperatures during reflooding. The quantity-of-interest (QoI) is time-dependent peak cladding temperature (PCT) profiles. Conventional PCA can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information in the PCT profiles before conventional PCA is applied for dimensionality reduction. The resulting PC scores are then used to build DNN-based surrogate models to significantly reduce the computational cost in Markov Chain Monte Carlo sampling, while the code/interpolation uncertainty is accounted for using Bayesian neural networks. We compared four IUQ processes with different dimensionality reduction methods and surrogate models. The proposed approach has demonstrated the best performance in reducing the dimensionality of the transient PCT profiles. This approach also produces the posterior distributions of the physical model parameters with which the model predictions have the best agreement with the experimental data.

Pivotal-Aware Principal Component Analysis.

A conventional principal component analysis (PCA) frequently suffers from the disturbance of outliers, and thus, spectra of extensions and variations of PCA have been developed. However, all the existing extensions of PCA derive from the same motivation, which aims to alleviate the negative effect of the occlusion. In this article, we design a novel collaborative-enhanced learning framework that aims to highlight the pivotal data points in contrast. As for the proposed framework, only a part of well-fitting samples are adaptively highlighted, which indicates more significance during training. Meanwhile, the framework can collaboratively reduce the disturbance of the polluted samples as well. In other words, two contrary mechanisms could work cooperatively under the proposed framework. Based on the proposed framework, we further develop a pivotal-aware PCA (PAPCA), which utilizes the framework to simultaneously augment positive samples and constrain negative ones by retaining the rotational invariance property. Accordingly, extensive experiments demonstrate that our model has superior performance compared with the existing methods that only focus on the negative samples.

Supervised Principal Component Regression for Functional Responses with High Dimensional Predictors

We propose a supervised principal component regression method for relating functional responses with high-dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected integrated residual sum of squares, which directly makes use of the association between the functional response and the predictors. Minimizing the integrated residual sum of squares gives the supervised principal components, which is equivalent to solving a sequence of nonconvex generalized Rayleigh quotient optimization problems. We reformulate the nonconvex optimization problems into a simultaneous linear regression with a sparse penalty to deal with high dimensional predictors. Theoretically, we show that the reformulated regression problem can recover the same supervised principal subspace under certain conditions. Statistically, we establish nonasymptotic error bounds for the proposed estimators when the covariate covariance is bandable. We demonstrate the advantages of the proposed method through numerical experiments and an application to the Human Connectome Project fMRI data. Supplementary materials for this article are available online.

Raman identification of adulteration in poly-alpha-olefin synthetic lubricant using principal component analysis and two-dimensional correlation spectroscopy

Poly-alpha-olefin (PAO) synthetic lubricating oil provides significant advantages over mineral oil. Highly discerning methods of PAO adulteration with inexpensive mineral oil is crucial to promote energy conservation and emission reduction and safeguard the rights of consumers. In this research, conventional principal component analysis (PCA), modified principal component analysis (MPCA) and two-dimensional correlation spectroscopy (2D-COS) with temperature as perturbation factor were used for Raman identification of PAO adulteration with 5 %, 20 % and 50 % mineral oil (150 N). The influence of spectrum normalization on identification was also studied. When using maximum intensity normalization, the modified principal component analysis is more efficient than the conventional PCA and can distinguish the adulterated oil from the authentic PAO even when the adulteration ratio decreases to 5 %. Comparably, the conventional PCA can distinguish the adulteration with 5 % mineral oil by using peak area normalization. These results suggest that the area normalization is prior to the maximum intensity normalization for PCA identification, as attributed to that the maximum intensity normalization might weaken the intensity difference of strongest peak among different samples. By either peak area or maximum intensity normalization, the difference between the authentic and the adulterated PAO can be detected by synchronous 2D-COS, in which both the autocorrelation peak at 2843 cm−1 and the negative cross correlation peak at (2843, 2935 cm−1) become weakened along with the increase of adulteration ratio. This work can provide important technical support to ensure the safe operation of equipment and crack down on the illegal trade of counterfeit synthetic lubricants.

Supervised categorized principal component analysis for imagined speech classification via applying singular value decomposition on a symmetry matrix

The dimension of the feature vectors for performing the imagined speech is large. Hence, it is required to reduce their dimension as well as perform the classification simultaneously. This is a categorized principal component analysis (CatPCA) problem. However, the conventional CatPCA methods are unsupervised learning methods and the design of the unitary matrix in the conventional principal component analysis (PCA) algorithms is only based on the PCA approach. Therefore, the classification performance is limited. This paper proposes a supervised CatPCA approach for performing the imagined speech classification. Also, the objective function of an optimization problem for designing the unitary matrix is formulated based on both the PCA algorithm and the k means algorithm. To find the analytical solution of the optimization problem, a property on computing the singular value decomposition (SVD) of a symmetric matrix is employed. Then, the design of the cluster centers in the k means algorithm is formulated as a quadratic programming. Finally, the above two procedures are iterated until the algorithm converges. Since the analytical solutions of these two optimization problems can be derived analytically, the required computational power for finding the solution of the optimization problem is low. To demonstrate the effectiveness of our proposed CatPCA algorithm, the Track 3 of the International brain computer interface (BCI) Competition Database is employed as the dataset for performing the performance evaluation. The computer numerical simulation results show that our proposed CatPCA algorithm yields the higher classification accuracy compared to PCA variants and the dimension reduction related algorithms. Also, the required execution time of our proposed method is lower than those of the states of the arts methods. This demonstrates the effectiveness and the efficiency of our proposed CatPCA algorithm.

Unsupervised deep learning framework for data-driven gating in positron emission tomography.

Physiological motion, such as respiratory motion, has become a limiting factor in the spatial resolution of positron emission tomography (PET) imaging as the resolution of PET detectors continue to improve. Motion-induced misregistration between PET and CT images can also cause attenuation correction artifacts. Respiratory gating can be used to freeze the motion and to reduce motion induced artifacts. In this study, we propose a robust data-driven approach using an unsupervised deep clustering network that employs an autoencoder (AE) to extract latent features for respiratory gating. We first divide list-mode PET data into short-time frames. The short-time frame images are reconstructed without attenuation, scatter, or randoms correction to avoid attenuation mismatch artifacts and to reduce image reconstruction time. The deep AE is then trained using reconstructed short-time frame images to extract latent features for respiratory gating. No additional data are required for the AE training. K-means clustering is subsequently used to perform respiratory gating based on the latent features extracted by the deep AE. The effectiveness of our proposed Deep Clustering method was evaluated using physical phantom and real patient datasets. The performance was compared against phase gating based on an external signal (External) and image based principal component analysis (PCA) with K-means clustering (Image PCA). The proposed method produced gated images with higher contrast and sharper myocardium boundaries than those obtained using the External gating method and Image PCA. Quantitatively, the gated images generated by the proposed Deep Clustering method showed larger center of mass (COM) displacement and higher lesion contrast than those obtained using the other two methods. The effectiveness of our proposed method was validated using physical phantom and real patient data. The results showed our proposed framework could provide superior gating than the conventional External method and Image PCA.

A Consideration of the Recognition Taguchi Method Using High-Dimensional Principal Component Analysis

The Recognition-Taguchi (RT) method has been proposed for evaluating binary data such as image data. Additionally, the RT-PC method can be applied to continuous-type data when the variables have different units. The RT-PC method uses the principal component analysis (PCA); however, applying PCA to high-dimensional data causes complications in the estimation accuracy of the eigenvalue and eigenvector. Therefore, a method based on the sparse PCA is proposed in this context instead of the conventional PCA. However, previous studies have not investigated the assumption that the anomaly-detection performance of the RT-PC method is based on a typical high-dimensional PCA. In this study, we introduce the noise-reduction and cross-data (CD) matrix methods to the RT-PC method and evaluate their performance using Monte Carlo simulation. The RT-CD method uses the calculation process of the CD matrix method instead of PCA. The simulation analysis results show a better performance in the pattern of inner anomalies when compared to the RT-PC method. The RT-NR method uses the calculation process of the noise-reduction method in the RT-PC method instead of PCA. Finally, the RT-NR and RT-PC methods are observed to exhibit the same anomaly-detection performance.

Fault detection for NOx emission process in thermal power plants using SIP-PCA

With the era of big data, data-driven models are increasingly vital to just-in-time decision support in pollution emission management and planning. This article aims to evaluate the usability of the proposed data-driven model to monitor NOx emission from a coal-fired boiler process using easily measured process variables. As the emission process is highly complex, process variables interact with each other, and they cannot guarantee that all the variables in the actual operation obey the Gaussian distributions. As conventional principal component analysis (PCA) can only extract variance information, a novel data-driven model is proposed, called survival information potential-based PCA (SIP-PCA) model, is proposed in this work. First, an improved PCA model is established based on the SIP performance index. SIP-PCA can extract more information in the latent space from the process variables following the non-Gaussian distributions. Then, the control limits for fault detection are determined based on the kernel density estimation method. Finally, the proposed algorithm is successfully applied to a real NOx emission process. By monitoring the operation of process variables, possible failures can be detected as soon as possible. Fault isolation and system reconstruction can be implemented in time, preventing NOx emissions from exceeding its standard.

An enhanced temporal algorithm- coupled optimized adaptive sparse principal component analysis methodology for fault diagnosis of chemical processes

Principal component analysis (PCA) is a classic fault diagnosis method widely used in chemical process data modeling. However, the limitation of PCA to handle dynamic and time-variant data has been progressively exposed with the ever-increasing development of artificial intelligence technologies and applications of automation systems in the chemical industry. In this paper, an enhanced temporal algorithm-coupled optimized adaptive sparse PCA (ETA-OASPCA) methodology is proposed with the aim to improve the conventional PCA method by introducing temporal state computation and dynamic adaptive sparsity. The ETA is constructed to extract the state transitions of the time-variant process data by introducing the “Transition” and “Hold”, acquire the region of interest by employing a Maximum Fuzzy c-means (MFCM) method, and then use the region time prediction automaton to label the possible abnormal states. The introduction of dynamic adaptive sparsity in PCA, achieved by presenting an iterative interior point optimization method to update the dynamic sparse penalty term, can impose sparsity constraints on dynamic data calculations, thus enhancing the interpretability of the PCA model. The effectiveness of the proposed method was validated through its application in the Eastman Tennessee process, showing that an average fault detection rate, false alarm rate, and latency of 99.4%, 0.37%, and 4.11 mins can be achieved, respectively.

An enhanced principal component analysis method with Savitzky–Golay filter and clustering algorithm for sensor fault detection and diagnosis

Sensors are critical components of heating, ventilation, and air-conditioning systems. Sensor faults can impact control regulations, resulting in an uncomfortable indoor environment and energy wastage. To detect and identify sensor faults quickly, this study proposes an enhanced principal component analysis (PCA) method using the Savitzky–Golay (SG) filter and density-based spatial clustering of applications with noise (DBSCAN) algorithm. First, the DBSCAN algorithm is used to automatically divide the dataset into sub-datasets with different working conditions to reduce the interference information and concentrate the information of each training set. Then, each sub-dataset is smoothed using the SG algorithm to reduce the effects of data fluctuations. The processed dataset is used to build a sub-PCA model that ultimately identifies and locates faults. The proposed strategy is validated using field operating data for 20 air-handling unit (AHU) systems, as obtained from a large commercial building. The fault detection performances of multiple strategies are compared and analysed under different degrees of bias in single AHU and multiple AHU systems. The verification results show that the proposed DBSCAN-SG-PCA model offers significant improvements in fault detection accuracy and fault identification sensitivity over the conventional PCA method. Compared with the SG-PCA model, the proposed model reduces the amount of data required for fault detection by an average of 13.7%, and the Youden index is increased by an average of 0.21. Furthermore, the fault detection accuracy of the proposed model is ±0.7 °C.

Forecasting high levels of PM<SUB>10</SUB> in Korea based on the principal expectile component regression

As the level of fine dust has risen sharply recently, many studies has been conducted to analyze the data. Since exposure to fine dust is related to the occurrence of cardiovascular diseases and respiratory, it can make the mortality rate increase. Therefore, it is important to predict the extreme level of fine dust. In this paper, we consider a regression model based on the principal expectile analysis. Compare to the conventional principal component analysis, principal expectile analysis can capture variations around the tail of the data. By so doing, we predict ‘Bad’ cases of the PMSUB10/SUB level of 25 districts in Seoul, South Korea and compare the results with the classical principal component regression. From the results, we observe that the proposed model predicts the extreme level of fine dust better than the existing model.

Seismic Image Dip Estimation by Multiscale Principal Component Analysis

Dip estimation of geological structures plays an important role in geophysical applications. Principal component analysis (PCA) is a common approach to estimating local dips by decomposing the local gradients of a seismic migration image and obtaining its principal eigenvector. However, PCA is difficult to obtain robust and high-resolution dip estimations for low signal-to-noise ratio (SNR) migration images, while multiscale schemes in digital image processing can achieve a better compromise between noise robustness and dip resolution. Therefore, we propose to adopt a multiscale PCA (MPCA) method coupled with a propagation-weight-based fusion mechanism for seismic dip estimation of low SNR migration image. MPCA consists of three steps: 1) constructing an image pyramid by repeating the low-pass filter from fine to coarse scales; 2) estimating the dip using the PCA method at each scale of the image pyramid; and 3) fusing the multiscale dip estimations using propagation weights from coarse to fine scales. We test the MPCA method on an omnidirectional dip pattern and three seismic migration images and compare with the conventional PCA and multiscale methods. The results demonstrate that MPCA yields robust and high-resolution dip estimations for low SNR seismic migration images.

NetSHy: network summarization via a hybrid approach leveraging topological properties.

Biological networks can provide a system-level understanding of underlying processes. In many contexts, networks have a high degree of modularity, i.e. they consist of subsets of nodes, often known as subnetworks or modules, which are highly interconnected and may perform separate functions. In order to perform subsequent analyses to investigate the association between the identified module and a variable of interest, a module summarization, that best explains the module's information and reduces dimensionality is often needed. Conventional approaches for obtaining network representation typically rely only on the profiles of the nodes within the network while disregarding the inherent network topological information. In this article, we propose NetSHy, a hybrid approach which is capable of reducing the dimension of a network while incorporating topological properties to aid the interpretation of the downstream analyses. In particular, NetSHy applies principal component analysis (PCA) on a combination of the node profiles and the well-known Laplacian matrix derived directly from the network similarity matrix to extract a summarization at a subject level. Simulation scenarios based on random and empirical networks at varying network sizes and sparsity levels show that NetSHy outperforms the conventional PCA approach applied directly on node profiles, in terms of recovering the true correlation with a phenotype of interest and maintaining a higher amount of explained variation in the data when networks are relatively sparse. The robustness of NetSHy is also demonstrated by a more consistent correlation with the observed phenotype as the sample size decreases. Lastly, a genome-wide association study is performed as an application of a downstream analysis, where NetSHy summarization scores on the biological networks identify more significant single nucleotide polymorphisms than the conventional network representation. R code implementation of NetSHy is available at https://github.com/thaovu1/NetSHy. Supplementary data are available at Bioinformatics online.

Theoretical derivation of interval principal component analysis

Principal Component Analysis is a well-known method that can be used for dimensionality reduction, a useful technique in the Big Data era. There have been a series of proposed adaptations of the Principal Component Analysis method for interval-valued symbolic data, all of which have the downside of having intermediate steps that deal with conventional data. In this work, we put forward an interval Principal Component Analysis that only deals with symbolic data by developing a theoretical framework that allows for the definition of symbolic principal components. This framework provides the mathematical tools needed to use the symbolic principal components to transform the original data in a way that is mathematically coherent with the remainder of the framework and defines the principal components as solutions to maximisation problems, similarly to what is done in conventional Principal Component Analysis. After the theoretical foundations are laid down, we explore real-world data from the telecommunications sector, in an attempt to detect Internet redirection attacks in real-time. In particular, we use our symbolic method to improve and simplify an anomaly detection method that has been proposed in the literature for conventional data.

Semantic Interpretation for Convolutional Neural Networks: What Makes a Cat a Cat?

The interpretability of deep neural networks has attracted increasing attention in recent years, and several methods have been created to interpret the "black box" model. Fundamental limitations remain, however, that impede the pace of understanding the networks, especially the extraction of understandable semantic space. In this work, the framework of semantic explainable artificial intelligence(S-XAI) is introduced, which utilizes a sample compression method based on the distinctive row-centered principal component analysis (PCA) that is different from the conventional column-centered PCA to obtain common traits of samples from the convolutional neural network (CNN), and extracts understandable semantic spaces on the basis of discovered semantically sensitive neurons and visualization techniques. Statistical interpretation of the semantic space is also provided, and the concept of semantic probability is proposed. The experimental results demonstrate that S-XAI is effective in providing a semantic interpretation for the CNN, and offers broad usage, including trustworthiness assessment and semantic sample searching.