Version Of Principal Component Analysis Research Articles

Resource-efficient quantum principal component analysis

Principal component analysis (PCA) is an important dimensionality reduction method in machine learning and data analysis. Recently, the quantum version of PCA has been established to diagonalize quantum states. Although these quantum algorithms promise quantum advantages, they require substantial resources beyond the reach of state-of-the-art quantum technologies. This work aims to reduce resource requirements and improve the efficiency of quantum PCA. Assuming that the quantum state is accessed through a purified quantum query model and a sampling model, we propose quantum algorithms that use minimal resource requirements for ancillary qubits to reveal properties of eigenvectors and eigenvalues of a state. In particular, we show that estimating eigenvalue λ with error ε and success probability larger than λ(1−η) requests a query complexity O~(ϵ−1) and a sample complexity O~(ϵ−2η−1) , respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in 1/ϵ for quantum PCA. As applications, we discuss estimating the minimum relative entropy of entanglement of bipartite pure-states and performing quantum state discrimination tasks. We show that quantum speedups are maintained when the pure state has a low Schmidt number and states of discrimination have a low rank. This study opens up a new quantum PCA method for high-dimensional quantum data analysis and discusses its application in quantum information processing tasks.

Optimizing data aggregation and clustering in Internet of things networks using principal component analysis and Q-learning

The Internet of things (IoT) is a wireless network designed to perform specific tasks and plays a crucial role in various fields such as environmental monitoring, surveillance, and healthcare. To address the limitations imposed by inadequate resources, energy, and network scalability, this type of network relies heavily on data aggregation and clustering algorithms. Although various conventional studies have aimed to enhance the lifespan of a network through robust systems, they do not always provide optimal efficiency for real-time applications. This paper presents an approach based on state-of-the-art machine-learning methods. In this study, we employed a novel approach that combines an extended version of principal component analysis (PCA) and a reinforcement learning algorithm to achieve efficient clustering and data reduction. The primary objectives of this study are to enhance the service life of a network, reduce energy usage, and improve data aggregation efficiency. We evaluated the proposed methodology using data collected from sensors deployed in agricultural fields for crop monitoring. Our proposed approach (PQL) was compared to previous studies that utilized adaptive Q-learning (AQL) and regional energy-aware clustering (REAC). Our study outperformed in terms of both network longevity and energy consumption and established a fault-tolerant network.

An improved deep learning approach for speech enhancement

Single-channel speech enhancement refers to the task of improving the quality and intelligibility of a speech signal in a noisy environment. Time-domain and time-frequency-domain methods are two main categories of approaches for speech enhancement. In this paper, we propose a approach based on a cross-domain framework. This framework utilizes our knowledge of the spectrogram and overcomes some of the limitations faced by time-frequency domain methods. First, we apply the intrinsic mode functions of the empirical mode decomposition and an improved version of principal component analysis. Then, we design a cross-domain learning framework to determine the correlations along the frequency and time axes. At low SNR = -5 dB, the effectiveness of our proposed approach is demonstrated by its performance based on objective and subjective measures. With average scores of -0.49, 2.47, 2.44, and 0.68 for SegSNR, PESQ, Cov, and STOI, respectively. The results highlight the success of our approach in addressing low SNR conditions.

Improvement of variables interpretability in kernel PCA

BackgroundKernel methods have been proven to be a powerful tool for the integration and analysis of high-throughput technologies generated data. Kernels offer a nonlinear version of any linear algorithm solely based on dot products. The kernelized version of principal component analysis is a valid nonlinear alternative to tackle the nonlinearity of biological sample spaces. This paper proposes a novel methodology to obtain a data-driven feature importance based on the kernel PCA representation of the data.ResultsThe proposed method, kernel PCA Interpretable Gradient (KPCA-IG), provides a data-driven feature importance that is computationally fast and based solely on linear algebra calculations. It has been compared with existing methods on three benchmark datasets. The accuracy obtained using KPCA-IG selected features is equal to or greater than the other methods’ average. Also, the computational complexity required demonstrates the high efficiency of the method. An exhaustive literature search has been conducted on the selected genes from a publicly available Hepatocellular carcinoma dataset to validate the retained features from a biological point of view. The results once again remark on the appropriateness of the computed ranking.ConclusionsThe black-box nature of kernel PCA needs new methods to interpret the original features. Our proposed methodology KPCA-IG proved to be a valid alternative to select influential variables in high-dimensional high-throughput datasets, potentially unravelling new biological and medical biomarkers.

Measuring financial soundness around the world: A machine learning approach

We use a fully data-driven approach and information provided by the IMF’s financial soundness indicators to measure the condition of a country’s financial system around the world. Given the nature of the measurement problem, we apply different versions of principal component analysis (PCA) to deal with the presence of strong cross-sectional and time dependence in the data due to unobserved common factors. Using this comprehensive sample and various statistical methods, we produce an alternative data-driven measure of financial soundness that provides policy makers and financial institutions with a monitoring and policy tool that is easy to implement and update. We validate our index by using alternative macroeconomic factors, confirming its predictive power. Our index captures important aspects of financial intermediation around the world.

A synthetic review of some recent extensions of ComDim

AbstractThe simultaneous analysis of several data matrices related to the same set of samples can be done with the use of multiblock methods. Common components and specific weights analysis (CCSWA), also called ComDim, is one method enabling the analysis of such data. CCSWA, which is a multiblock version of principal components analysis (PCA), is particularly interesting as it can easily be modified and transformed, either by replacing its PCA‐based data decomposition by another multivariate method, such as independent components analysis or partial least‐squares regression, for example, or by segmenting the data matrices before multiblock analysis, or both. These modifications aim at improving the models and their interpretation. This article will give a concise description of ComDim and then a presentation of several recent extensions of the method, showing its usefulness as both a supervised and a non‐supervised method.

Redundancy Analysis to Reduce the High-Dimensional Near-Infrared Spectral Information to Improve the Authentication of Olive Oil

The high price of marketing of extra virgin olive oil (EVOO) requires the introduction of cost-effective and sustainable procedures that facilitate its authentication, avoiding fraud in the sector. Contrary to classical techniques (such as chromatography), near-infrared (NIR) spectroscopy does not need derivatization of the sample with proper integration of separated peaks and is more reliable, rapid, and cost-effective. In this work, principal component analysis (PCA) and then redundancy analysis (RDA)—which can be seen as a constrained version of PCA—are used to summarize the high-dimensional NIR spectral information. Then PCA and RDA factors are contemplated as explanatory variables in models to authenticate oils from qualitative or quantitative analysis, in particular, in the prediction of the percentage of EVOO in blended oils or in the classification of EVOO or other vegetable oils (sunflower, hazelnut, corn, or linseed oil) by the use of some machine learning algorithms. As a conclusion, the results highlight the potential of RDA factors in prediction and classification because they appreciably improve the results obtained from PCA factors in calibration and validation.

An ℓp theory of PCA and spectral clustering

Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations of individual principal component scores that yield low-dimensional embedding of samples. That hinders the analysis of various spectral methods. In this paper, we first develop an ℓp perturbation theory for a hollowed version of PCA in Hilbert spaces which provably improves upon the vanilla PCA in the presence of heteroscedastic noises. Through a novel ℓp analysis of eigenvectors, we investigate entrywise behaviors of principal component score vectors and show that they can be approximated by linear functionals of the Gram matrix in ℓp norm, which includes ℓ2 and ℓ∞ as special cases. For sub-Gaussian mixture models, the choice of p giving optimal bounds depends on the signal-to-noise ratio, which further yields optimality guarantees for spectral clustering. For contextual community detection, the ℓp theory leads to simple spectral algorithms that achieve the information threshold for exact recovery and the optimal misclassification rate.

A Visual Analytics Approach for Hardware System Monitoring with Streaming Functional Data Analysis.

Many real-world applications involve analyzing time-dependent phenomena, which are intrinsically functional, consisting of curves varying over a continuum (e.g., time). When analyzing continuous data, functional data analysis (FDA) provides substantial benefits, such as the ability to study the derivatives and to restrict the ordering of data. However, continuous data inherently has infinite dimensions, and for a long time series, FDA methods often suffer from high computational costs. The analysis problem becomes even more challenging when updating the FDA results for continuously arriving data. In this paper, we present a visual analytics approach for monitoring and reviewing time series data streamed from a hardware system with a focus on identifying outliers by using FDA. To perform FDA while addressing the computational problem, we introduce new incremental and progressive algorithms that promptly generate the magnitude-shape (MS) plot, which conveys both the functional magnitude and shape outlyingness of time series data. In addition, by using an MS plot in conjunction with an FDA version of principal component analysis, we enhance the analyst's ability to investigate the visually-identified outliers. We illustrate the effectiveness of our approach with two use scenarios using real-world datasets. The resulting tool is evaluated by industry experts using real-world streaming datasets.

A neural network regularization method to address variance inflation in autoencoders

There exist various machine learning techniques which can be used to reduce the dimensionality of original data while minimizing the information loss. Principal component analysis (PCA) is one of the most well known such techniques, which transforms the original correlated variables into uncorrelated variables called principal components. Although PCA is known to preserve the total variance of the original data during the transformation, there are some cases with a potential of variance inflation, where the total variance of principal components becomes much larger than that of original variables. It is important to prevent variance inflation, as it can negatively affect the performance of other application systems (e.g. process monitoring systems) which are designed on the basis of principal component with inflated variances. Variance inflation also has a high potential to occur during the training of autoencoder, a special type of neural network performing nonlinear version of PCA. Although there are several neural network regularization methods available to alleviate the problem of variance inflation, none of them is tailored to do such task. To this end, in this work, an alternative neural network regularization method is proposed, which can strongly regulate the total variance in the feature space. Using the Tennessee Eastman process as an illustrative example, the proposed regularization method is compared with the existing ones in terms of neural network overfitting, variance inflation, and training time.

Comparing global seismic tomography models using varimax principal component analysis

Abstract. Global seismic tomography has greatly progressed in the past decades, with many global Earth models being produced by different research groups. Objective, statistical methods are crucial for the quantitative interpretation of the large amount of information encapsulated by the models and for unbiased model comparisons. Here we propose using a rotated version of principal component analysis (PCA) to compress the information in order to ease the geological interpretation and model comparison. The method generates between 7 and 15 principal components (PCs) for each of the seven tested global tomography models, capturing more than 97 % of the total variance of the model. Each PC consists of a vertical profile, with which a horizontal pattern is associated by projection. The depth profiles and the horizontal patterns enable examining the key characteristics of the main components of the models. Most of the information in the models is associated with a few features: large low-shear-velocity provinces (LLSVPs) in the lowermost mantle, subduction signals and low-velocity anomalies likely associated with mantle plumes in the upper and lower mantle, and ridges and cratons in the uppermost mantle. Importantly, all models highlight several independent components in the lower mantle that make between 36 % and 69 % of the total variance, depending on the model, which suggests that the lower mantle is more complex than traditionally assumed. Overall, we find that varimax PCA is a useful additional tool for the quantitative comparison and interpretation of tomography models.

Cluster analysis with cellwise trimming and applications for the robust clustering of curves

In this work, we propose a robust cluster analysis methodology based on cellwise trimming as an extension to a robust version of Principal Component Analysis. This new approach is more reasonable than traditional casewise trimming when the dimension is not small. This type of trimming avoids an unnecessary loss of information when only a few cells of the entirely trimmed observations are atypical. We propose an algorithm to apply this approach. This algorithm is particularized to the case of functional cluster analysis. We provide simulations and applications using real data sets to illustrate the proposed methodology.

The Truth behind the Zeros: A New Approach to Principal Component Analysis of the Neuropsychiatric Inventory

Psychiatric syndromes in dementia are often derived from the Neuropsychiatric Inventory (NPI) using principal component analysis (PCA). The validity of this statistical approach can be questioned, since the excessive proportion of zeros and skewness of NPI items may distort the estimated relations between the items. We propose a novel version of PCA, ZIBP-PCA, where a zero-inflated bivariate Poisson (ZIBP) distribution models the pairwise covariance between the NPI items. We compared the performance of the method to classical PCA under zero-inflation using simulations, and in two dementia-cohorts (N = 830, N = 1349). Simulations showed that component loadings from PCA were biased due to zero-inflation, while the loadings of ZIBP-PCA remained unaffected. ZIBP-PCA obtained a simpler component structure of “psychosis,” “mood” and “agitation” in both dementia-cohorts, compared to PCA. The principal components from ZIBP-PCA had component loadings as follows: First, the component interpreted as “psychosis” was loaded by the items delusions and hallucinations. Second, the “mood” component was loaded by depression and anxiety. Finally, the “agitation” component was loaded by irritability and aggression. In conclusion, PCA is not equipped to handle zero-inflation. Using the NPI, PCA fails to identify components with a valid interpretation, while ZIBP-PCA estimates simple and interpretable components to characterize the psychopathology of dementia.

Concrete Preliminary Damage Inspection by Classification of Terrestrial Laser Scanner Point Clouds through Systematic Threshold Definition

This paper presents a novel approach for automatic, preliminary detection of damage in concrete structures using ground-based terrestrial laser scanners. The method is based on computation of defect-sensitive features such as the surface curvature, since the surface roughness changes strongly if an area is affected by damage. A robust version of principal component analysis (PCA) classification is proposed to distinguish between structural damage and outliers present in the laser scanning data. Numerical simulations were conducted to develop a systematic point-wise defect classifier that automatically diagnoses the location of superficial damage on the investigated region. The method provides a complete picture of the surface health of concrete structures. It has been tested on two real datasets: a concrete heritage aqueduct in Brooks, Alberta, Canada; and a civil pedestrian concrete structure. The experiment results demonstrate the validity and accuracy of the proposed systematic framework for detecting and localizing areas of damage as small as 1 cm or less.

An efficient data processing approach for frequency modulated thermal wave imaging for inspection of steel material

Non-destructive testing & evaluation (NDT&E) plays a vital role in industrial quality control. Among various NDT&E modalities, active thermal NDT&E gained its importance due to its inherent merits such as remote, whole-field, fast and quantitative inspection capabilities. Of various thermal NDT&E schemes, recently proposed pulse compression favorable frequency modulated thermal wave imaging (FMTWI) became popular due to its enhanced defect detection sensitivity along with improved test resolution. This paper presents noise rejection capabilities of FMTWI with principal component analysis (PCA) based post-processing schemes. PCA based post-processing helps in efficient interpretation of the thermographic data by removing artefacts and producing few significant images depicting sub-surface defects in the test specimen. The results obtained by PCA can be made more interpretable by using sparser version of PCA (SPCA). In this paper, SPCA based thermographic data processing technique is proposed in which SPCA has been considered in two different ways. Firstly it has been implemented to induce sparsity in empirical orthogonal functions (EOFs) which improves spatial contrast over the defective regions. Secondly, it has been used to modify principal components (PCs) (time series components) to obtain resultant images by projecting thermographic data on modified PCs which manages to enhance the signal to noise ratio (SNR). The sub-surface defect detection capabilities of the proposed methods are studied by a matched filter based pre-processing scheme which reduces the computational cost and memory usage also. The performance of the proposed methods has been evaluated on the experimental investigation of the mild steel specimen having flat bottom holes as defects.

Jan Steen\u2019s ground layers analysed with Principal Component Analysis

In-depth technical and art historical research into Jan Steen’s (ca. 1626–1679) oeuvre has been a focus at the Mauritshuis since 2012, as part of the Partners in Science collaboration with Shell. The aim of this project is to shed light on the chronology of Steen’s oeuvre based on the materials he used, since only 10% of his circa 450 works are dated. Steen worked in different cities within the Netherlands (Haarlem, The Hague, Delft, Leiden and Warmond), each with a distinct artistic community. So far 39 paintings from the Mauritshuis and many other collections in and outside the Netherlands have been analysed. This paper focuses on the ground layers in Steen’s paintings. Cross sections were taken of each painting and analysed using SEM-EDX. Principal Component Analysis (PCA) on the resulting dataset was used to find correlations between variables and clustering of samples. Special versions of PCA were explored to analyse pigment identifications and to allow data fusion of this binary data with the quantitative elemental analyses, which is not trivial with normal PCA. The statistical analyses allowed us to group paintings linking them to the different cities where Steen worked and to see outliers in terms of the ground layer composition. Interestingly, the present survey also revealed that apart from commercially prepared grounds, Steen also used grounds prepared in his own studio.

Kernel Principal Component Analysis Allowing Sparse Representation and Sample Selection

Kernel principal component analysis (KPCA) is a kernelized version of principal component analysis (PCA). A kernel principal component is a superposition of kernel functions. Due to the number of kernel functions equals the number of samples, each component is not a sparse representation. Our purpose is to sparsify coefficients expressing in linear combination of kernel functions, two types of sparse kernel principal component are proposed in this paper. The method for solving sparse problem comprises two steps: (a) we start with the Pythagorean theorem and derive an explicit regression expression of KPCA and (b) two types of regularization $l_1$-norm or $l_{2,1}$-norm are added into the regression expression in order to obtain two different sparsity form, respectively. As the proposed objective function is different from elastic net-based sparse PCA (SPCA), the SPCA method cannot be directly applied to the proposed cost function. We show that the sparse representations are obtained in its iterative optimization by conducting an alternating direction method of multipliers. Experiments on toy examples and real data confirm the performance and effectiveness of the proposed method.

A Trimmed Clustering-Based l1-Principal Component Analysis Model for Image Classification and Clustering Problems with Outliers

Different versions of principal component analysis (PCA) have been widely used to extract important information for image recognition and image clustering problems. However, owing to the presence of outliers, this remains challenging. This paper proposes a new PCA methodology based on a novel discovery that the widely used l1-PCA is equivalent to a two-groups k-means clustering model. The projection vector of the l1-PCA is the vector difference between the two cluster centers estimated by the clustering model. In theory, this vector difference provides inter-cluster information, which is beneficial for distinguishing data objects from different classes. However, the performance of l1-PCA is not comparable with the state-of-the-art methods. This is because the l1-PCA can be sensitive to outliers, as the equivalent clustering model is not robust to outliers. To overcome this limitation, we introduce a trimming function to the clustering model and propose a trimmed-clustering based l1-PCA (TC-PCA). With this trimming set formulation, the TC-PCA is not sensitive to outliers. Besides, we mathematically prove the convergence of the proposed algorithm. Experimental results on image classification and clustering indicate that our proposed method outperforms the current state-of-the-art methods.

Realistic fluid representation by anisotropic particle

This paper presents a novel method for tracking multiphase fluid surfaces more accurately using the particle level-set (PLS) method with anisotropic instead of spherical particles. We create an anisotropic particle by considering the distribution of particles. To construct the anisotropic particles, we use the weighted version of principal component analysis and adopt the distribution of particles from the directional derivatives. This represents the fluid surface accurately, but the search for neighbor particles requires to calculate singular value decomposition with a high computational cost. Therefore, we devised a new method that uses directional derivatives to generate the anisotropic particles. This reduces the computational costs significantly but still allows the fluid interface to be tracked more accurately. Compared to the PLS method, our approach provides more detailed surfaces, corrects numerical dissipation, and preserves the volume of the fluid. Furthermore, we present particle-based fluid simulations with a surface reconstruction that uses anisotropic particles.

A random version of principal component analysis in data clustering

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance/correlation matrix of the analyzed data. However, to properly work with high-dimensional data sets, PCA poses severe mathematical constraints on the minimum number of different replicates, or samples, that must be included in the analysis. Generally, improper sampling is due to a small number of data respect to the number of the degrees of freedom that characterize the ensemble. In the field of life sciences it is often important to have an algorithm that can accept poorly dimensioned data sets, including degenerated ones. Here a new random projection algorithm is proposed, in which a random symmetric matrix surrogates the covariance/correlation matrix of PCA, while maintaining the data clustering capacity. We demonstrate that what is important for clustering efficiency of PCA is not the exact form of the covariance/correlation matrix, but simply its symmetry.