Popular Principal Component Analysis Research Articles

Designing an Embedded Feature Selection Algorithm for a Drowsiness Detector Model Based on Electroencephalogram Data.

Driver fatigue reduces the safety of traditional driving and limits the widespread adoption of self-driving cars; hence, the monitoring and early detection of drivers' drowsiness plays a key role in driving automation. When representing the drowsiness indicators as large feature vectors, fitting a machine learning model to the problem becomes challenging, and the problem's perspicuity decreases, making dimensionality reduction crucial in practice. For this reason, we propose an embedded feature selection algorithm that can be later utilized as a building block in the system development of a neural network-based drowsiness detector. We have adopted a technique: a so-called Feature Prune Layer is placed in front of the first layer in the architecture; as a result, its weights change regarding the importance of the corresponding input features and are deleted iteratively until the desired number is reached. We test the algorithm on EEG data, as it is one of the best indicators of drowsiness based on the literature. The proposed FS algorithm is able to reduce the original feature set by 95% with only 1% degradation in precision, while the precision increases by 1.5% and 2.7% respectively when selecting the top 10% and top 20% of the initial features. Moreover, the proposed method outperforms the widely popular Principal Component Analysis and the Chi-squared test when reducing the original feature set by 95%: it achieves 24.3% and 3.2% higher precision respectively.

Data-driven streamline stiffener path optimization (SSPO) for sparse stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures

The homogenization-based streamline stiffener path optimization (SSPO) method was previously proposed by the authors for stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures. The applications are limited to densely distributed stiffeners with no significant scale effect in the homogenization process, which is revealed in this work. A data-driven SSPO method, which is inspired by the popular principal component analysis (PCA) in data processing, is proposed for sparse stiffener layout design. With several referential layouts as input, the PCA generates a sequence of principal layouts. Together with weighting factors and distortion techniques, using only a small number of dominant principal layouts is enough to represent most possible synthesized layouts, which significantly reduces the number of design variables while preserving and extending a large design space. This strategy is further enhanced with a detailed modeling technique based on multiple point constraints (MPCs) to automate the modeling process. The data-driven SSPO method can be integrated with either gradient-based or artificial intelligence (AI) algorithms due to the small number of design variables. A flexible objective target, to maximize the critical buckling load or minimize the structural weight, can be used since the structural responses are evaluated on the detailed model. Numerical examples demonstrate the effectiveness of the proposed method in optimizing the layout of sparsely distributed stiffeners.

Dimensionality Reduction using PCA and K-Means Clustering for Breast Cancer Prediction

Breast cancer is the most important cause of death among women. A prediction of breast cancer in early stage provides a greater possibility of its cure. It needs a breast cancer prediction tool that can classify a breast tumor whether it was a harmful malignant tumor or un-harmful benign tumor. In this paper, two algorithms of machine learning, namely Support Vector Machine and Extreme Gradient Boosting technique will be compared for classification purpose. Prior to the classification, the number of data attribute will be reduced from the raw data by extracting features using Principal Component Analysis. A clustering method, namely K-Means is also used for dimensionality reduction besides the Principal Component Analysis. This paper will present a comparison among four models based on two dimensionality reduction methods combined with two classifiers which applied on Wisconsin Breast Cancer Dataset. The comparison will be measured by using accuracy, sensitivity and specificity metrics evaluated from the confusion matrices. The experimental results have indicated that the K-Means method, which is not usually used for dimensionality reduction can perform well compared to the popular Principal Component Analysis.

Dimension reduction in radio maps based on the supervised kernel principal component analysis

Differently from most existing studies either directly eliminating redundant WiFi APs with trivial importance or adopting unsupervised dimension reduction methods, e.g. principal component analysis (PCA), this paper employs a supervised approach to take the full advantage of the information available for building radio maps, i.e. location labels attached to fingerprints, to compress original radio maps. Specifically, in the offline phase, the supervised kernel PCA (SKPCA) method is employed to derive a nonlinear and optimal embedding in a low-dimensional subspace; in the online phase, any sample vector containing received signal strengths can be projected onto the optimal subspace in real-time for further localization processing. Experiments are carried out not only in a real environment but also using an open dataset. It is shown that the compressed radio maps based on SKPCA have much smaller sizes than their original radio maps, but achieve similar localization performance and significantly outperform the other two popular PCA- based unsupervised dimension reduction methods, i.e. PCA and PCA-MLE.

Structured Sparse Principal Components Analysis With the TV-Elastic Net Penalty.

Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover the dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, PCA's interpretability remains limited. Indeed, the components produced by PCA are often noisy or exhibit no visually meaningful patterns. Furthermore, the fact that the components are usually non-sparse may also impede interpretation, unless arbitrary thresholding is applied. However, in neuroimaging, it is essential to uncover clinically interpretable phenotypic markers that would account for the main variability in the brain images of a population. Recently, some alternatives to the standard PCA approach, such as sparse PCA (SPCA), have been proposed, their aim being to limit the density of the components. Nonetheless, sparsity alone does not entirely solve the interpretability problem in neuroimaging, since it may yield scattered and unstable components. We hypothesized that the incorporation of prior information regarding the structure of the data may lead to improved relevance and interpretability of brain patterns. We therefore present a simple extension of the popular PCA framework that adds structured sparsity penalties on the loading vectors in order to identify the few stable regions in the brain images that capture most of the variability. Such structured sparsity can be obtained by combining, e.g., and total variation (TV) penalties, where the TV regularization encodes information on the underlying structure of the data. This paper presents the structured SPCA (denoted SPCA-TV) optimization framework and its resolution. We demonstrate SPCA-TV's effectiveness and versatility on three different data sets. It can be applied to any kind of structured data, such as, e.g., -dimensional array images or meshes of cortical surfaces. The gains of SPCA-TV over unstructured approaches (such as SPCA and ElasticNet PCA) or structured approach (such as GraphNet PCA) are significant, since SPCA-TV reveals the variability within a data set in the form of intelligible brain patterns that are easier to interpret and more stable across different samples.

Kernel principal component analysis for multimedia retrieval

Principal component analysis (PCA) is an important tool in many areas including data reduction and interpretation, information retrieval, image processing, and so on. Kernel PCA has recently been proposed as a nonlinear extension of the popular PCA. The basic idea is to first map the input space into a feature space via a nonlinear map and then compute the principal components in that feature space. This paper illustrates the potential of kernel PCA for dimensionality reduction and feature extraction in multimedia retrieval. By the use of Gaussian kernels, the principal components were computed in the feature space of an image data set and they are used as new dimensions to approximate image features. Extensive experimental results show that kernel PCA performs better than linear PCA with respect to the retrieval quality as well as the retrieval precision in content-based image retrievals.Keywords: Principal component analysis, kernel principal component analysis, multimedia retrieval, dimensionality reduction, image retrieval

Genome Data Exploration Using Correspondence Analysis.

Recent developments of sequencing technologies that allow the production of massive amounts of genomic and genotyping data have highlighted the need for synthetic data representation and pattern recognition methods that can mine and help discovering biologically meaningful knowledge included in such large data sets. Correspondence analysis (CA) is an exploratory descriptive method designed to analyze two-way data tables, including some measure of association between rows and columns. It constructs linear combinations of variables, known as factors. CA has been used for decades to study high-dimensional data, and remarkable inferences from large data tables were obtained by reducing the dimensionality to a few orthogonal factors that correspond to the largest amount of variability in the data. Herein, I review CA and highlight its use by considering examples in handling high-dimensional data that can be constructed from genomic and genetic studies. Examples in amino acid compositions of large sets of species (viruses, phages, yeast, and fungi) as well as an example related to pairwise shared orthologs in a set of yeast and fungal species, as obtained from their proteome comparisons, are considered. For the first time, results show striking segregations between yeasts and fungi as well as between viruses and phages. Distributions obtained from shared orthologs show clusters of yeast and fungal species corresponding to their phylogenetic relationships. A direct comparison with the principal component analysis method is discussed using a recently published example of genotyping data related to newly discovered traces of an ancient hominid that was compared to modern human populations in the search for ancestral similarities. CA offers more detailed results highlighting links between modern humans and the ancient hominid and their characterizations. Compared to the popular principal component analysis method, CA allows easier and more effective interpretation of results, particularly by the ability of relating individual patterns with their corresponding characteristic variables.

Block Principal Component Analysis With Nongreedy $\ell _{1}$ -Norm Maximization

Block principal component analysis with l1 -norm (BPCA-L1) has demonstrated its effectiveness in a lot of visual classification and data mining tasks. However, the greedy strategy for solving the l1 -norm maximization problem is prone to being struck in local solutions. In this paper, we propose a BPCA with nongreedy l1 -norm maximization, which obtains better solutions than BPCA-L1 with all the projection directions optimized simultaneously. Other than BPCA-L1, the new algorithm has been evaluated against some popular principal component analysis (PCA) algorithms including PCA-L1 and 2-D PCA-L1 on a variety of benchmark data sets. The results demonstrate the effectiveness of the proposed method.

Most informative component analysis

In this paper, we extend the popular principal component analysis (PCA) to the investigation of nonlinear dependence among variables, called most informative component analysis (MICA). The most informative components are a few linear combinations of the variables that capture both linear and nonlinear dependence among the variables. Compared with the existing extensions such as the principal curve and the kernel PCA, MICA is more interpretable and thus more meaningful in statistical analysis. Properties of MICA are investigated; estimation method is developed; and asymptotics of the estimators are obtained. Real data sets are analyzed to illustrate the usefulness of MICA.

Practical comparison of multivariate chemometric techniques for pattern recognition used in environmental monitoring

Environmental datasets usually contain multiple and highly correlated variables. The use of multivariate techniques in this case has experienced a significant development. This paper provides a feasible comparison among several methods for pattern recognition: Principal Component Analysis (PCA), Multivariate Curve Resolution (MCR), Parallel Factor Analysis (PARAFAC) and Tucker3. They have been systematically applied on the same dataset, consisting of the concentration of trace elements measured in sediments of the estuary of the Nerbioi-Ibaizabal river (Basque Country). The results obtained have been critically discussed in terms of ease of use, interpretation of the results, and amount of information provided. The most popular PCA is probably enough for a correct and overall interpretation of the results. MCR, however, may lead to slightly different results due to the non-perceptive orthogonality of the principal components. Both PARAFAC and Tucker3 provide simplified graphical outputs that make easier interpretation of the results.

An efficient algorithm for Kernel two-dimensional principal component analysis

Recently, a new approach called two-dimensional principal component analysis (2DPCA) has been proposed for face representation and recognition. The essence of 2DPCA is that it computes the eigenvectors of the so-called image covariance matrix without matrix-to-vector conversion. Kernel principal component analysis (KPCA) is a non-linear generation of the popular principal component analysis via the Kernel trick. Similarly, the Kernelization of 2DPCA can be benefit to develop the non-linear structures in the input data. However, the standard K2DPCA always suffers from the computational problem for using the image matrix directly. In this paper, we propose an efficient algorithm to speed up the training procedure of K2DPCA. The results of experiments on face recognition show that the proposed algorithm can achieve much more computational efficiency and remarkably save the memory-consuming compared to the standard K2DPCA.

Non-Negative Matrix Factorization for Detection and Diagnosis of Plantwide Oscillations

In this paper, we propose the use of non-negative matrix factorization (NMF) of multivariate spectra for plantwide oscillation detection. One of the key features of NMF is that it provides a parts-based representation that allows us to retain the causal basis spectral shapes or parts that constitute the spectra of measurements, unlike the popular principal component analysis (PCA)-based methods. The contributions of this paper are as follows: (i) a novel measure known as the pseudo-singular value (PSV) to assess the order of the basis space (the PSV is also useful in determining the most dominant features of a data set); (ii) a power decomposition plot that contains the total power (defined in this work) and its decomposition by NMF (the power plot is a useful and compact visual tool that provides overall spectral characteristics of the plant and shows the decomposition of these characteristics into well-localized frequency components); and (iii) a novel measure defined as the strength factor (SF) to ass...

An Improved Algorithm for Kernel Principal Component Analysis

Kernel principal component analysis (KPCA), introduced by Scholkopf et al., is a nonlinear generalization of the popular principal component analysis (PCA) via the kernel trick. KPCA has shown to be a very powerful approach of extracting nonlinear features for classification and regression applications. However, the standard KPCA algorithm (Scholkopf et al., 1998, Neural Computation 10, 1299--1319) may suffer from computational problem for large scale data set. To overcome these drawbacks, we propose an efficient training algorithm in this paper, and show that this approach is of much more computational efficiency compared to the previous ones for KPCA.