Relevant bibliographies by topics / Principal Component Analysis (PCA)

Academic literature on the topic 'Principal Component Analysis (PCA)'

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Published: 4 June 2021
Last updated: 7 September 2023

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Journal articles on the topic "Principal Component Analysis (PCA)"

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Gewers, Felipe L., Gustavo R. Ferreira, Henrique F. De Arruda, Filipi N. Silva, Cesar H. Comin, Diego R. Amancio, and Luciano Da F. Costa. "Principal Component Analysis." ACM Computing Surveys 54, no. 4 (May 2021): 1–34. http://dx.doi.org/10.1145/3447755.

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Principal component analysis (PCA) is often applied for analyzing data in the most diverse areas. This work reports, in an accessible and integrated manner, several theoretical and practical aspects of PCA. The basic principles underlying PCA, data standardization, possible visualizations of the PCA results, and outlier detection are subsequently addressed. Next, the potential of using PCA for dimensionality reduction is illustrated on several real-world datasets. Finally, we summarize PCA-related approaches and other dimensionality reduction techniques. All in all, the objective of this work is to assist researchers from the most diverse areas in using and interpreting PCA.
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Jensen, Matt, Trent Stellingwerff, Courtney Pollock, James Wakeling, and Marc Klimstra. "Can Principal Component Analysis Be Used to Explore the Relationship of Rowing Kinematics and Force Production in Elite Rowers during a Step Test? A Pilot Study." Machine Learning and Knowledge Extraction 5, no. 1 (February 17, 2023): 237–51. http://dx.doi.org/10.3390/make5010015.

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Investigating the relationship between the movement patterns of multiple limb segments during the rowing stroke on the resulting force production in elite rowers can provide foundational insight into optimal technique. It can also highlight potential mechanisms of injury and performance improvement. The purpose of this study was to conduct a kinematic analysis of the rowing stroke together with force production during a step test in elite national-team heavyweight men to evaluate the fundamental patterns that contribute to expert performance. Twelve elite heavyweight male rowers performed a step test on a row-perfect sliding ergometer [5 × 1 min with 1 min rest at set stroke rates (20, 24, 28, 32, 36)]. Joint angle displacement and velocity of the hip, knee and elbow were measured with electrogoniometers, and force was measured with a tension/compression force transducer in line with the handle. To explore interactions between kinematic patterns and stroke performance variables, joint angular velocities of the hip, knee and elbow were entered into principal component analysis (PCA) and separate ANCOVAs were run for each performance variable (peak force, impulse, split time) with dependent variables, and the kinematic loading scores (Kpc,ls) as covariates with athlete/stroke rate as fixed factors. The results suggested that rowers’ kinematic patterns respond differently across varying stroke rates. The first seven PCs accounted for 79.5% (PC1 [26.4%], PC2 [14.6%], PC3 [11.3%], PC4 [8.4%], PC5 [7.5%], PC6 [6.5%], PC7 [4.8%]) of the variances in the signal. The PCs contributing significantly (p ≤ 0.05) to performance metrics based on PC loading scores from an ANCOVA were (PC1, PC2, PC6) for split time, (PC3, PC4, PC5, PC6) for impulse, and (PC1, PC6, PC7) for peak force. The significant PCs for each performance measure were used to reconstruct the kinematic patterns for split time, impulse and peak force separately. Overall, PCA was able to differentiate between rowers and stroke rates, and revealed features of the rowing-stroke technique correlated with measures of performance that may highlight meaningful technique-optimization strategies. PCA could be used to provide insight into differences in kinematic strategies that could result in suboptimal performance, potential asymmetries or to determine how well a desired technique change has been accomplished by group and/or individual athletes.
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Adamu, Nuraddeen, Samaila Abdullahi, and Sani Musa. "Online Stochastic Principal Component Analysis." Caliphate Journal of Science and Technology 4, no. 1 (February 10, 2022): 101–8. http://dx.doi.org/10.4314/cajost.v4i1.13.

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This paper studied Principal Component Analysis (PCA) in an online. The problem is posed as a subspace optimization problem and solved using gradient based algorithms. One such algorithm is the Variance-Reduced PCA (VR-PCA). The VR-PCA was designed as an improvement to the classical online PCA algorithm known as the Oja’s method where it only handled one sample at a time. The paper developed Block VR-PCA as an improved version of VR-PCA. Unlike prominent VR-PCA, the Block VR-PCA was designed to handle more than one dimension in subspace optimization at a time and it showed good performance. The Block VR-PCA and Block Oja method were compared experimentally in MATLAB using synthetic and real data sets, their convergence results showed Block VR-PCA method appeared to achieve a minimum steady state error than Block Oja method. Keywords: Online Stochastic; Principal Component Analysis; Block Variance-Reduced; Block Oja
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Tiwari, Priya, and Stuti Sharma. "Principal component analyses in mungbean genotypes under summer season." INTERNATIONAL JOURNAL OF AGRICULTURAL SCIENCES 17, no. 2 (June 15, 2021): 287–92. http://dx.doi.org/10.15740/has/ijas/17.2/287-292.

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Yield is a complex trait subjective to several components and environmental factors. Therefore, it becomes necessary to apply such technique which can identify and prioritize the key traits to lessen the number of traits for valuable selection and genetic gain. Principal component analysis is primarily a renowned data reduction technique which identifies the least number of components and explain maximum variability, it also rank genotypes on the basis of PC scores. PCA was calculated using Ingebriston and Lyon (1985) method. In present study, PCA performed for phenological and yield component traits presented that out of thirteen, only five principal components (PCs) exhibited more than 1.00 eigen value, and showed about 80.28 per cent of total variability among the traits. Scree plot explained the percentage of variance associated with each principal component obtained by illustrating a graph between eigen values and principal component numbers. PC1 showed 26.12 per cent variability with eigen value 3.40. Graph depicted that the maximum variation was observed in PC1 in contrast to other four PCs. The PC1 was further associated with the phenological and yield attributing traits viz., number of nodes per plant, number of pod cluster per plant, number of pod per plant. PC2 exhibited positive effect for harvest index. The PC3 was more related to yield related traits i.e., number of seeds per pod, number of seeds per plant and biological yield per plant, whereas PC4 was more loaded with phenological traits. PC5 was further related to yield and yield contributing traits i.e. number of primary branches per plant, seed yield per plant and 100 seed weight. A high value of PC score of a particular genotype in a particular PC denotes high value for those variables falling under that specific principal component. Pusa Vishal found in PC 2, in PC 3, PC 4 and PC 5, can be considered as an ideal breeding material for selection and for further deployment in defined breeding programme.
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Sando, Keishi, and Hideitsu Hino. "Modal Principal Component Analysis." Neural Computation 32, no. 10 (October 2020): 1901–35. http://dx.doi.org/10.1162/neco_a_01308.

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Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As a theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point, and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over conventional methods.
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Bijarania, Subhash, Anil Pandey, Mainak Barman, Monika Shahani, and Gharsi Ram. "Assesment of divergence among soybean [Glycine max (L.) Merrill] genotypes based on phenological and physiological traits." Environment Conservation Journal 23, no. 1&2 (February 11, 2022): 72–82. http://dx.doi.org/10.36953/ecj.021808-2117.

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A study was conducted to understand genetic divergence in Randomized complete block design accommodating 30 soybean [Glycine max (L.) Merrill] genotypes randomly in three replications. These genotypes were evaluated for twenty-seven traits: five phenological, nine agro-morphological, eight physiological traits (from field-trial) and five physiological traits (from laboratory experiment) recorded and subjected to PCA (Principal Component Analysis) and cluster analysis. Among all the studied cultivars, significant diversity, as well as analysis of dispersion, was recorded for different agro-morphological characters. D2-statistic (Tocher method) framed (generalized distance-based) nine clusters: largest with eight and five were oligo-genotypic. Harvest index>seed yield per plant>germination relative index>seedling dry weight contributed maximum towards total divergence. From the most divergent clusters, 21 crosses involving cluster v genotypes (PS-1347, RKS-18, PS-1092, NRC-142, VLS-94, NRC-136, and Shalimar Soybean-1) with monogenotypic cluster VII (AMS-2014), VIII (RSC-11-15) and III (RSC-10-71) suggested for future hybridization. Out of eighteen, only eight principal components revealed more than 1.00 eigen value and exhibited about 85.03% variability among the traits studied. The highest variability (25.41%) by PC1 followed by PC2 (15.60%), PC3 (12.35%), PC4 (10.13%), PC5 (7.20%), PC6 (5.43%), PC7 (4.80%) and PC8 (4.11%) for characters under study.
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Okoda, Yuki, Yoko Oya, Shotaro Abe, Ayano Komaki, Yoshimasa Watanabe, and Satoshi Yamamoto. "Molecular Distributions of the Disk/Envelope System of L483: Principal Component Analysis for the Image Cube Data." Astrophysical Journal 923, no. 2 (December 1, 2021): 168. http://dx.doi.org/10.3847/1538-4357/ac2c6c.

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Abstract Unbiased understanding of molecular distributions in a disk/envelope system of a low-mass protostellar source is crucial for investigating physical and chemical evolution processes. We have observed 23 molecular lines toward the Class 0 protostellar source L483 with ALMA and have performed principal component analysis (PCA) for their cube data (PCA-3D) to characterize their distributions and velocity structures in the vicinity of the protostar. The sum of the contributions of the first three components is 63.1%. Most oxygen-bearing complex organic molecule lines have a large correlation with the first principal component (PC1), representing the overall structure of the disk/envelope system around the protostar. Contrary, the C18O and SiO emissions show small and negative correlations with PC1. The NH2CHO lines stand out conspicuously at the second principal component (PC2), revealing more compact distribution. The HNCO lines and the high-excitation line of CH3OH have a similar trend for PC2 to NH2CHO. On the other hand, C18O is well correlated with the third principal component (PC3). Thus, PCA-3D enables us to elucidate the similarities and the differences of the distributions and the velocity structures among molecular lines simultaneously, so that the chemical differentiation between the oxygen-bearing complex organic molecules and the nitrogen-bearing ones is revealed in this source. We have also conducted PCA for the moment 0 maps (PCA-2D) and that for the spectral line profiles (PCA-1D). While they can extract part of characteristics of the molecular line data, PCA-3D is essential for comprehensive understandings. Characteristic features of the molecular line distributions are discussed on NH2CHO.
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Kumar, Preeti, Nilanjaya, and Pankaj Shah. "Study of genetic diversity in rice (Oryza sativa L.) genotypes under direct seeded condition by using principal component analysis." Ecology, Environment and Conservation 29 (2023): 211–19. http://dx.doi.org/10.53550/eec.2023.v29i03s.040.

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The present investigation was carried out to assess the genetic diversity by using principal component analysis for yield and yield contributing traits in thirty-two genotypes of rice under direct seeded condition (DSR). The experiment was conducted at Dr. Rajendra Prasad Central Agricultural University, Pusa, Bihar in randomized block design with three replications. The results revealed that first four component axes had eigen values 1.0, representing a cumulative variability of 76.86 %. Principal component analysis (PCA) indicate that four components (PC1 to PC4) accounted for about 76.86% of the total variation present among all the traits. Out of total principal components PC1, PC2, PC3 and PC4 with values 33.781%, 19.02%, 13.859% and 10.206% respectively, contributed more to the total variation. The first principal component had high positive loading for 15 traits out of 17. Similarly, second and third principal component had 7 traits each, fourth component with 6 traits had high positive loadings which contributed more to the diversity. Genotypes in cluster V showed higher mean performance for most of the yield attributing traits. Therefore, selection of parents for different traits would be effective from this cluster. Thus, result of the present study could be exploited in planning and execution of future breeding programme in rice under direct seeded condition.
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Kondi, Ravi, Sonali Kar, and Soumya Surakanti. "Agro-morphological and biochemical characterization and principal component analysis for yield and quality characters in fine-scented rice genotypes." Genetika 54, no. 3 (2022): 1005–21. http://dx.doi.org/10.2298/gensr2203005k.

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Forty-one fine-scented rice genotypes were evaluated for 18 agro-morphological and quality characters for characterization, and 21 quantitative characters were evaluated for principal component analysis in R-studio software. Characterization of agro-morphological traits viz., plant height, days to 50% flowering, panicle length, number of effective tillers per plant, test weight, grain length, grain breadth, grain L: B ratio, kernel length, kernel breadth, kernel dimensions, awns, colour of awns, distribution of awns, and quality traits viz., alkali spreading value, gel consistency, grain aroma, and amylose content showed huge diversity among the genotypes. PCA revealed that PC1 showed the highest amount of variance (32.0%) followed by PC2 (15.7%), PC3 (9.0%), PC4 (8.1%), PC5 (7.8%), PC6 (5.4%) for quantitative characters. Out of 21 principal components, only 6 showed an eigenvalue greater than 1 and contributes about 78.1% total variance Genotypes in PC1 showed higher values for grain L: B ratio and kernel L: B ratio. Similarly, PC2 showed higher variable values for characters like test weight, kernel length, grain length, grain breadth, alkali spreading value, grain yield per plot and amylose content. PC3 for harvest index, panicle length, gel consistency, no. of effective tillers per plant and head rice recovery. PC4 for characters like plant height, kernel breadth and days to 50% flowering. PC5 for characters like kernel elongation ratio, and filled grains per panicle. PC6 for characters like no. of tillers in a square meter and no. of panicles in a square meter. This pre-breeding characterization study may be useful in finding potential genotypes which are having both yield and quality characters which may be useful in breeding for high-yielding varieties with good-quality characters.
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Aini Abdul Wahab, Nurul, and Shamshuritawati Sharif. "Rice Odours’ Readings Investigation Using Principal Component Analysis." International Journal of Engineering & Technology 7, no. 2.29 (May 22, 2018): 488. http://dx.doi.org/10.14419/ijet.v7i2.29.13803.

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The use of electronic nose (e-nose) devices plus principal component analysis can help the process of categorizing the 16 different rice into its type. Generally, the physical feature of an e-nose own more than one hole to capture the odour of rice. For example, the portable e-nose so-called Insniff does have 10 holes (or variables). In this situations, we will have a dataset that consist high-dimension dataset where lead to the presence of interdependencies between all variables under study. Therefore, this study is presented to investigate the odour of rice for identifying the most important variables contributing to the rice odour readings. The principal component analysis (PCA) is implemented to determine the component that best represent the all 10 variables in order to eliminate the interdependency problem, and (2) to identify which variable is considered as important and influential to the newly-formed principle component (PC). The results from PCA suggested that the first two principle components is chosen. It is based on three assessments which are Kaiser’s criterion larger than 1, cumulative proportion of total variance, and scree plot. These two principle components explained 89% of total variance. Results showed that sensor 1 (0.931) and sensor 2 (0.966) are the two important variables that highly contribute to PC1. On the other hand, for PC2, the highest contribution is from sensor 8 (0.828). This study demonstrate that PCA is effective for investigating rice odour readings.
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Dissertations / Theses on the topic "Principal Component Analysis (PCA)"

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Solat, Karo. "Generalized Principal Component Analysis." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/83469.

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The primary objective of this dissertation is to extend the classical Principal Components Analysis (PCA), aiming to reduce the dimensionality of a large number of Normal interrelated variables, in two directions. The first is to go beyond the static (contemporaneous or synchronous) covariance matrix among these interrelated variables to include certain forms of temporal (over time) dependence. The second direction takes the form of extending the PCA model beyond the Normal multivariate distribution to the Elliptically Symmetric family of distributions, which includes the Normal, the Student's t, the Laplace and the Pearson type II distributions as special cases. The result of these extensions is called the Generalized principal component analysis (GPCA). The GPCA is illustrated using both Monte Carlo simulations as well as an empirical study, in an attempt to demonstrate the enhanced reliability of these more general factor models in the context of out-of-sample forecasting. The empirical study examines the predictive capacity of the GPCA method in the context of Exchange Rate Forecasting, showing how the GPCA method dominates forecasts based on existing standard methods, including the random walk models, with or without including macroeconomic fundamentals.
Ph. D.
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Li, Liubo Li. "Trend-Filtered Projection for Principal Component Analysis." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503277234178696.

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Renkjumnong, Wasuta. "SVD and PCA in Image Processing." Digital Archive @ GSU, 2007. http://digitalarchive.gsu.edu/math_theses/31.

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The Singular Value Decomposition is one of the most useful matrix factorizations in applied linear algebra, the Principal Component Analysis has been called one of the most valuable results of applied linear algebra. How and why principal component analysis is intimately related to the technique of singular value decomposition is shown. Their properties and applications are described. Assumptions behind this techniques as well as possible extensions to overcome these limitations are considered. This understanding leads to the real world applications, in particular, image processing of neurons. Noise reduction, and edge detection of neuron images are investigated.
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Allemang, Matthew R. "Comparison of Automotive Structures Using Transmissibility Functions and Principal Component Analysis." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1367944783.

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Bianchi, Marcelo Franceschi de. "Extração de características de imagens de faces humanas através de wavelets, PCA e IMPCA." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-10072006-002119/.

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Reconhecimento de padrões em imagens é uma área de grande interesse no mundo científico. Os chamados métodos de extração de características, possuem as habilidades de extrair características das imagens e também de reduzir a dimensionalidade dos dados gerando assim o chamado vetor de características. Considerando uma imagem de consulta, o foco de um sistema de reconhecimento de imagens de faces humanas é pesquisar em um banco de imagens, a imagem mais similar à imagem de consulta, de acordo com um critério dado. Este trabalho de pesquisa foi direcionado para a geração de vetores de características para um sistema de reconhecimento de imagens, considerando bancos de imagens de faces humanas, para propiciar tal tipo de consulta. Um vetor de características é uma representação numérica de uma imagem ou parte dela, descrevendo seus detalhes mais representativos. O vetor de características é um vetor n-dimensional contendo esses valores. Essa nova representação da imagem propicia vantagens ao processo de reconhecimento de imagens, pela redução da dimensionalidade dos dados. Uma abordagem alternativa para caracterizar imagens para um sistema de reconhecimento de imagens de faces humanas é a transformação do domínio. A principal vantagem de uma transformação é a sua efetiva caracterização das propriedades locais da imagem. As wavelets diferenciam-se das tradicionais técnicas de Fourier pela forma de localizar a informação no plano tempo-freqüência; basicamente, têm a capacidade de mudar de uma resolução para outra, o que as fazem especialmente adequadas para análise, representando o sinal em diferentes bandas de freqüências, cada uma com resoluções distintas correspondentes a cada escala. As wavelets foram aplicadas com sucesso na compressão, melhoria, análise, classificação, caracterização e recuperação de imagens. Uma das áreas beneficiadas onde essas propriedades tem encontrado grande relevância é a área de visão computacional, através da representação e descrição de imagens. Este trabalho descreve uma abordagem para o reconhecimento de imagens de faces humanas com a extração de características baseado na decomposição multiresolução de wavelets utilizando os filtros de Haar, Daubechies, Biorthogonal, Reverse Biorthogonal, Symlet, e Coiflet. Foram testadas em conjunto as técnicas PCA (Principal Component Analysis) e IMPCA (Image Principal Component Analysis), sendo que os melhores resultados foram obtidos utilizando a wavelet Biorthogonal com a técnica IMPCA
Image pattern recognition is an interesting area in the scientific world. The features extraction method refers to the ability to extract features from images, reduce the dimensionality and generates the features vector. Given a query image, the goal of a features extraction system is to search the database and return the most similar to the query image according to a given criteria. Our research addresses the generation of features vectors of a recognition image system for human faces databases. A feature vector is a numeric representation of an image or part of it over its representative aspects. The feature vector is a n-dimensional vector organizing such values. This new image representation can be stored into a database and allow a fast image retrieval. An alternative for image characterization for a human face recognition system is the domain transform. The principal advantage of a transform is its effective characterization for their local image properties. In the past few years researches in applied mathematics and signal processing have developed practical wavelet methods for the multi scale representation and analysis of signals. These new tools differ from the traditional Fourier techniques by the way in which they localize the information in the time-frequency plane; in particular, they are capable of trading on type of resolution for the other, which makes them especially suitable for the analysis of non-stationary signals. The wavelet transform is a set basis function that represents signals in different frequency bands, each one with a resolution matching its scale. They have been successfully applied to image compression, enhancement, analysis, classification, characterization and retrieval. One privileged area of application where these properties have been found to be relevant is computer vision, especially human faces imaging. In this work we describe an approach to image recognition for human face databases focused on feature extraction based on multiresolution wavelets decomposition, taking advantage of Biorthogonal, Reverse Biorthogonal, Symlet, Coiflet, Daubechies and Haar. They were tried in joint the techniques together the PCA (Principal Component Analysis) and IMPCA (Image Principal Component Analysis)
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Anjasmara, Ira Mutiara. "Spatio-temporal analysis of GRACE gravity field variations using the principal component analysis." Thesis, Curtin University, 2008. http://hdl.handle.net/20.500.11937/957.

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Gravity Recovery and Climate Experiment (GRACE) mission has amplified the knowledge of both static and time-variable part of the Earth’s gravity field. Currently, GRACE maps the Earth’s gravity field with a near-global coverage and over a five year period, which makes it possible to apply statistical analysis techniques to the data. The objective of this study is to analyse the most dominant spatial and temporal variability of the Earth’s gravity field observed by GRACE using a combination of analytical and statistical methods such as Harmonic Analysis (HA) and Principal Component Analysis (PCA). The HA is used to gain general information of the variability whereas the PCA is used to find the most dominant spatial and temporal variability components without having to introduce any presetting. The latter is an important property that allows for the detection of anomalous or a-periodic behaviour that will be useful for the study of various geophysical processes such as the effect from earthquakes. The analyses are performed for the whole globe as well as for the regional areas of: Sumatra- Andaman, Australia, Africa, Antarctica, South America, Arctic, Greenland, South Asia, North America and Central Europe. On a global scale the most dominant temporal variation is an annual signal followed by a linear trend. Similar results mostly associated to changing land hydrology and/or snow cover are obtained for most regional areas except over the Arctic and Antarctic where the secular trend is the prevailing temporal variability.Apart from these well-known signals, this contribution also demonstrates that the PCA is able to reveal longer periodic and a-periodic signal. A prominent example for the latter is the gravity signal of the Sumatra-Andaman earthquake in late 2004. In an attempt to isolate these signals, linear trend and annual signal are removed from the original data and the PCA is once again applied to the reduced data. For a complete overview of these results the most dominant PCA modes for the global and regional gravity field solutions are presented and discussed.
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Ragozzine, Brett A. "Modeling the Point Spread Function Using Principal Component Analysis." Ohio University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1224684806.

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Jot, Sapan. "pcaL1: An R Package of Principal Component Analysis using the L1 Norm." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/2488.

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Principal component analysis (PCA) is a dimensionality reduction tool which captures the features of data set in low dimensional subspace. Traditional PCA uses L2-PCA and has much desired orthogonality properties, but is sensitive to outliers. PCA using L1 norm has been proposed as an alternative to counter the effect of outliers. The R environment for statistical computing already provides L2-PCA function prcomp(), but there are not many options for L1 norm PCA methods. The goal of the research was to create one R package with different options of PCA methods using L1 norm. So, we choose three different L1-PCA algorithms: PCA-L1 proposed by Kwak [10], L1-PCA* by Brooks et. al. [1], and L1-PCA by Ke and Kanade [9]; to create a package pcaL1 in R, interfacing with C implementation of these algorithms. An open source software for solving linear problems, CLP, is used to solve the optimization problems for L1-PCA* and L1-PCA. We use this package on human microbiome data to investigate the relationship between people based on colonizing bacteria.
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Yang, Libin. "An Application of Principal Component Analysis to Stock Portfolio Management." Thesis, University of Canterbury. Department of economics and finance, 2015. http://hdl.handle.net/10092/10293.

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This thesis investigates the application of principal component analysis to the Australian stock market using ASX200 index and its constituents from April 2000 to February 2014. The first ten principal components were retained to present the major risk sources in the stock market. We constructed portfolio based on each of the ten principal components and named these “principal portfolios
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Anjasmara, Ira Mutiara. "Spatio-temporal analysis of GRACE gravity field variations using the principal component analysis." Curtin University of Technology, Department of Spatial Sciences, 2008. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=18720.

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Gravity Recovery and Climate Experiment (GRACE) mission has amplified the knowledge of both static and time-variable part of the Earth’s gravity field. Currently, GRACE maps the Earth’s gravity field with a near-global coverage and over a five year period, which makes it possible to apply statistical analysis techniques to the data. The objective of this study is to analyse the most dominant spatial and temporal variability of the Earth’s gravity field observed by GRACE using a combination of analytical and statistical methods such as Harmonic Analysis (HA) and Principal Component Analysis (PCA). The HA is used to gain general information of the variability whereas the PCA is used to find the most dominant spatial and temporal variability components without having to introduce any presetting. The latter is an important property that allows for the detection of anomalous or a-periodic behaviour that will be useful for the study of various geophysical processes such as the effect from earthquakes. The analyses are performed for the whole globe as well as for the regional areas of: Sumatra- Andaman, Australia, Africa, Antarctica, South America, Arctic, Greenland, South Asia, North America and Central Europe. On a global scale the most dominant temporal variation is an annual signal followed by a linear trend. Similar results mostly associated to changing land hydrology and/or snow cover are obtained for most regional areas except over the Arctic and Antarctic where the secular trend is the prevailing temporal variability.
Apart from these well-known signals, this contribution also demonstrates that the PCA is able to reveal longer periodic and a-periodic signal. A prominent example for the latter is the gravity signal of the Sumatra-Andaman earthquake in late 2004. In an attempt to isolate these signals, linear trend and annual signal are removed from the original data and the PCA is once again applied to the reduced data. For a complete overview of these results the most dominant PCA modes for the global and regional gravity field solutions are presented and discussed.
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Books on the topic "Principal Component Analysis (PCA)"

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Jolliffe, I. T. Principal Component Analysis. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8.

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2

Jolliffe, I. T. Principal component analysis. 2nd ed. New York: Springer, 2010.

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Principal component analysis. 2nd ed. New York: Springer, 2002.

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Principal component analysis. New York: Springer-Verlag, 1986.

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Vidal, René, Yi Ma, and S. S. Sastry. Generalized Principal Component Analysis. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-0-387-87811-9.

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Naik, Ganesh R., ed. Advances in Principal Component Analysis. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-6704-4.

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Sanguansat, Parinya. Principal component analysis - multidisciplinary applications. Rijeka: InTech, 2012.

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Hyvarinen, Aapo. Independent component analysis. New York: J. Wiley, 2001.

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Juha, Karhunen, and Oja Erkki, eds. Independent component analysis. New York: J. Wiley, 2001.

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Kong, Xiangyu, Changhua Hu, and Zhansheng Duan. Principal Component Analysis Networks and Algorithms. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-2915-8.

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Book chapters on the topic "Principal Component Analysis (PCA)"

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Guebel, Daniel V., and Néstor V. Torres. "Principal Component Analysis (PCA)." In Encyclopedia of Systems Biology, 1739–43. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_1276.

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Bisong, Ekaba. "Principal Component Analysis (PCA)." In Building Machine Learning and Deep Learning Models on Google Cloud Platform, 319–24. Berkeley, CA: Apress, 2019. http://dx.doi.org/10.1007/978-1-4842-4470-8_26.

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Ruby-Figueroa, René. "Principal Component Analysis (PCA)." In Encyclopedia of Membranes, 1–2. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-642-40872-4_1999-1.

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Kurita, Takio. "Principal Component Analysis (PCA)." In Computer Vision, 1–4. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-03243-2_649-1.

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Kurita, Takio. "Principal Component Analysis (PCA)." In Computer Vision, 636–39. Boston, MA: Springer US, 2014. http://dx.doi.org/10.1007/978-0-387-31439-6_649.

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Tripathy, B. K., S. Anveshrithaa, and Shrusti Ghela. "Principal Component Analysis (PCA)." In Unsupervised Learning Approaches for Dimensionality Reduction and Data Visualization, 5–16. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003190554-2.

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Trendafilov, Nickolay, and Michele Gallo. "Principal component analysis (PCA)." In Multivariate Data Analysis on Matrix Manifolds, 89–139. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76974-1_4.

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Lê Cao, Kim-Anh, and Zoe Marie Welham. "Principal Component Analysis (PCA)." In Multivariate Data Integration Using R, 109–36. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003026860-12.

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Kurita, Takio. "Principal Component Analysis (PCA)." In Computer Vision, 1013–16. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-63416-2_649.

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Oh, Jiyong, and Nojun Kwak. "Robust PCAs and PCA Using Generalized Mean." In Advances in Principal Component Analysis, 71–98. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6704-4_4.

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Conference papers on the topic "Principal Component Analysis (PCA)"

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Wang, Qianqian, Quanxue Gao, Xinbo Gao, and Feiping Nie. "Angle Principal Component Analysis." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/409.

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Recently, many ℓ1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed. Angle PCA employs ℓ2-norm to measure reconstruction error and variance of projected da-ta and maximizes the summation of ratio between variance and reconstruction error of each data. Angle PCA not only is robust to outliers but also retains PCA’s desirable property such as rotational invariance. To solve Angle PCA, we propose an iterative algorithm, which has closed-form solution in each iteration. Extensive experiments on several face image databases illustrate that our method is overall superior to the other robust PCA algorithms, such as PCA, PCA-L1 greedy, PCA-L1 nongreedy and HQ-PCA.
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Schmeelk, Suzanna, and John Schmeelk. "Image authenticity implementing Principal Component Analysis (PCA)." In 2013 10th International Conference & Expo on Emerging Technologies for a Smarter World (CEWIT). IEEE, 2013. http://dx.doi.org/10.1109/cewit.2013.6713751.

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Zhang, Qingqing. "Principal Component Analysis (PCA) in Smart Growth Theory." In Advances in Materials, Machinery, Electrical Engineering (AMMEE 2017). Paris, France: Atlantis Press, 2017. http://dx.doi.org/10.2991/ammee-17.2017.96.

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Qiu, Caihua, and Feng Ding. "Face recognition based on principal component analysis (PCA)." In 2022 4th International Conference on Artificial Intelligence and Advanced Manufacturing (AIAM). IEEE, 2022. http://dx.doi.org/10.1109/aiam57466.2022.00185.

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Li, Liming, and Jing Zhao. "Comprehensive Evaluation of Parallel Mechanism and Robot Performance Based on Principal Component Analysis and Kernel Principal Component Analysis." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47032.

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Revealing the relations among parallel mechanism and robot comprehensive performance, topological structure and dimension is the basis to optimize mechanism. Due to the correlation and diversity of the single performance indexes, statistical principles of linear dimension reduction and nonlinear dimension reduction were introduced into comprehensive performance analysis and evaluation for typical parallel mechanisms and robots. Then the mechanism’s topological structure and dimension with the best comprehensive performance could be selected based on principal component analysis (PCA) and kernel principal component analysis (KPCA) respectively. Through comparing the results, KPCA could reveal the nonlinear relationship among different single performance indexes to provide more comprehensive performance evaluation information than PCA, and indicate the numerical calculation relations among comprehensive performance, topological structure and dimension validly.
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Goldberg, Mitchell D., Lihang Zhou, Walter W. Wolf, Chris Barnet, and Murty G. Divakarla. "Applications of principal component analysis (PCA) on AIRS data." In Multispectral and Hyperspectral Remote Sensing Instruments and Applications II. SPIE, 2005. http://dx.doi.org/10.1117/12.578939.

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Khan, Mohammad Asmatullah, Aurangzeb Khan, Tariq Mahmood, Muzahir Abbas, and Nazir Muhammad. "Fingerprint image enhancement using Principal Component Analysis (PCA) filters." In 2010 International Conference on Information and Emerging Technologies (ICIET). IEEE, 2010. http://dx.doi.org/10.1109/iciet.2010.5625686.

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Tonshal, Basavaraj, Yifan Chen, and Pietro Buttolo. "Determine Mesh Orientation by Voxel-Based Principal Component Analysis." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99380.

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In this paper we propose a new method to determine the part orientation of a 3D mesh based on Principal Component Analysis (PCA). Although the idea and practice of using PCA to determine part orientation is not new, it is not without practical issues. A major drawback of PCA, when it comes to dealing with meshes comprised of nodes and elements, is that the results are tessellation-dependent because of its sensitivity to variability. Two CAE meshes derived from the same CAD model but with different mesh node distribution characteristics, for instance, can yield different principal components. This is an undesirable outcome because the primary concern in model reorientation is shape, not the representational details of the shape. In order to reduce the influence of node characteristics, weight factors were proposed in the past, but the improvement is limited. To overcome this limitation, we must eliminate the influence of mesh node distribution. We achieve this by introducing an intermediate workspace, which is subsequently voxelized. We then find the intersection of the mesh model with the voxelized workspace. We collect the intersecting voxels to form an intermediate, tessellation-independent representation of the mesh. Applying PCA to this “neutralized” representation allows us to achieve mesh-property-independent results. The voxel representation also provides an opportunity of computational efficiency. We implemented an octree data structure to store the voxels and implemented a fast intersection (between a mesh element and a voxel) check procedure utilizing the interval overlap check derived from the separating axis theorem. Practical issues concerning determination of the voxel space resolution is addressed. A two-step trial and correction approach is proposed to enhance the consistency of results. Our voxel-based PCA is robust, fast, and straightforward to implement. Application examples are shown demonstrating the effectiveness and efficiency of this approach.
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Sankar, D. Sandeep Vara, and Lakshi Prosad Roy. "Principal component analysis (PCA) approach to segment primary components from pathological phonocardiogram." In 2014 International Conference on Communications and Signal Processing (ICCSP). IEEE, 2014. http://dx.doi.org/10.1109/iccsp.2014.6949976.

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Wang, Di, and Jinhui Xu. "Principal Component Analysis in the Local Differential Privacy Model." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/666.

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In this paper, we study the Principal Component Analysis (PCA) problem under the (distributed) non-interactive local differential privacy model. For the low dimensional case, we show the optimal rate for the private minimax risk of the k-dimensional PCA using the squared subspace distance as the measurement. For the high dimensional row sparse case, we first give a lower bound on the private minimax risk, . Then we provide an efficient algorithm to achieve a near optimal upper bound. Experiments on both synthetic and real world datasets confirm the theoretical guarantees of our algorithms.
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Reports on the topic "Principal Component Analysis (PCA)"

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Corriveau, Elizabeth, Travis Thornell, Mine Ucak-Astarlioglu, Dane Wedgeworth, Hayden Hanna, Robert Jones, Alison Thurston, and Robyn Barbato. Characterization of pigmented microbial isolates for use in material applications. Engineer Research and Development Center (U.S.), March 2023. http://dx.doi.org/10.21079/11681/46633.

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Organisms (i.e., plants and microorganisms) contain pigments that allow them to adapt and thrive under stressful conditions, such as elevated ultraviolet radiation. The pigments elicit characteristic spectral responses when measured by active and passive sensors. This research study focused on characterizing the spectral response of three organisms and how they compared to background spectral signatures of a complex environment. Specifically, spectra were collected from a fungus, a plant, and two pigmented bacteria, one of which is an extremophile bacterium. The samples were measured using Fourier transform infrared spectroscopy and dis-criminated using chemometric means. A top-down examination of the spectral data revealed that organisms could be discriminated from one an-other through principal component analysis (PCA). Furthermore, there was a strong distinction between the plant and the pigmented microorganisms. Spectral differences resulting in samples with the highest variance from the natural background were identified using PCA loading plots. The outcome of this work is a spectral library of pigmented biological candidates for coatings applications.
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Zhao, George, Grang Mei, Bulent Ayhan, Chiman Kwan, and Venu Varma. DTRS57-04-C-10053 Wave Electromagnetic Acoustic Transducer for ILI of Pipelines. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), March 2005. http://dx.doi.org/10.55274/r0012049.

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In this project, Intelligent Automation, Incorporated (IAI) and Oak Ridge National Lab (ORNL) propose a novel and integrated approach to inspect the mechanical dents and metal loss in pipelines. It combines the state-of-the-art SH wave Electromagnetic Acoustic Transducer (EMAT) technique, through detailed numerical modeling, data collection instrumentation, and advanced signal processing and pattern classifications, to detect and characterize mechanical defects in the underground pipeline transportation infrastructures. The technique has four components: (1) thorough guided wave modal analysis, (2) recently developed three-dimensional (3-D) Boundary Element Method (BEM) for best operational condition selection and defect feature extraction, (3) ultrasonic Shear Horizontal (SH) waves EMAT sensor design and data collection, and (4) advanced signal processing algorithm like a nonlinear split-spectrum filter, Principal Component Analysis (PCA) and Discriminant Analysis (DA) for signal-to-noise-ratio enhancement, crack signature extraction, and pattern classification. This technology not only can effectively address the problems with the existing methods, i.e., to detect the mechanical dents and metal loss in the pipelines consistently and reliably but also it is able to determine the defect shape and size to a certain extent.
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MARTIN, SHAWN B. Kernel Near Principal Component Analysis. Office of Scientific and Technical Information (OSTI), July 2002. http://dx.doi.org/10.2172/810934.

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Aït-Sahalia, Yacine, and Dacheng Xiu. Principal Component Analysis of High Frequency Data. Cambridge, MA: National Bureau of Economic Research, September 2015. http://dx.doi.org/10.3386/w21584.

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Eick, Brian, Zachary Treece, Billie Spencer, Matthew Smith, Steven Sweeney, Quincy Alexander, and Stuart Foltz. Miter gate gap detection using principal component analysis. Engineer Research and Development Center (U.S.), June 2018. http://dx.doi.org/10.21079/11681/27365.

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Federer, W. T., C. E. McCulloch, and J. J. Miles-McDermott. Illustrative Examples of Principal Component Analysis Using SYSTAT/FACTOR. Fort Belvoir, VA: Defense Technical Information Center, May 1987. http://dx.doi.org/10.21236/ada184920.

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Federer, W. T., C. E. McCulloch, and N. J. Miles-McDermott. Illustrative Examples of Principal Component Analysis using BMDP/4M. Fort Belvoir, VA: Defense Technical Information Center, May 1987. http://dx.doi.org/10.21236/ada185179.

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Krishnaiah, P. R., and S. Sarkar. Principal Component Analysis Under Correlated Multivariate Regression Equations Model. Fort Belvoir, VA: Defense Technical Information Center, April 1985. http://dx.doi.org/10.21236/ada160266.

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Thompson, David C., Janine C. Bennett, Diana C. Roe, and Philippe Pierre Pebay. Scalable multi-correlative statistics and principal component analysis with Titan. Office of Scientific and Technical Information (OSTI), February 2009. http://dx.doi.org/10.2172/984172.

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Fujikoshi, Y., P. R. Krishnaiah, and J. Schmidhammer. Effect of Additional Variables in Principal Component Analysis, Discriminant Analysis and Canonical Correlation Analysis. Fort Belvoir, VA: Defense Technical Information Center, August 1985. http://dx.doi.org/10.21236/ada162069.

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