Extension Of Principal Component Analysis Research Articles

Rozpoznawanie obiekt�w morskich na podstawie obraz�w FLIR metod� analizy obraz�w w�asnych (eigenimages)

This paper presents a method of recognition of maritime objects based on FLIR (forward looking infra-red) sensor images using eigenimages analysis method. The method is an extension of Principal Component Analysis (PCA) method. In last part of the paper are presented preliminary test results of the classification method for a set of FLIR images registered in the Baltic Sea. (Recognition of maritime objects based on FLIR images using eigenimages analysis method. A method of recognition of maritime objects based on FLIR (forward looking infra-red) sensor images Slowa kluczowe: rozpoznawanie obrazow FLIR, segmentacja, metoda analizy glownych skladowych PCA, metoda obrazow wlasnych.

Early pregnancy maternal urinary metabolomic profile and later insulin resistance and fetal adiposity

Objective: Our objective was to determine if early pregnancy urinary metabolomic profiles could predict fetal adiposity and macrosomia.Methods: This is a prospective study of 50 healthy women in their second pregnancy. Fasting urine samples taken during early pregnancy were analyzed using NMR spectroscopy. Maternal glucose and insulin were measured in early pregnancy and at 28 weeks and the HOMA index for insulin resistance calculated. At 34 weeks ultrasound assessed fetal anthropometry including fetal anterior abdominal wall width (AAW). At delivery birth weight was recorded. Probabilistic principal component with covariates analysis (PPCCA), a novel extension of principal component analysis, which facilitates joint modeling of metabolomic data and additional covariate information, was employed to analyze the data.Results: This analysis revealed that maternal HOMA and AAW significantly covaried with the 1H NMR derived metabolomic profile of the urine. As such, in this cohort of healthy, non-diabetic women, early pregnancy urinary metabolomic profile differed significantly according to both maternal insulin resistance and fetal fat deposition in utero.Conclusion: These findings hold potential for early pregnancy identification of those at risk of fetal macrosomia.

Principal Skewness Analysis: Algorithm and Its Application for Multispectral/Hyperspectral Images Indexing

In this letter, we present a new feature extraction approach based on third-order statistics (coskewness tensor) called principal skewness analysis (PSA). PSA is the natural extension of principal components analysis from second-order statistics to third-order statistics. The result of PSA is equivalent to that of FastICA when skewness is considered as a non-Gaussian index. Similar to FastICA, PSA also applies the fixed-point method to search the skewness extreme directions. However, when calculating the new projected direction in each iteration, PSA only requires a coskewness tensor, whereas FastICA requires all the pixels to be involved. Therefore, PSA has an advantage over FastICA in speed.

HYPERPARAMETER SELECTION IN KERNEL PRINCIPAL COMPONENT ANALYSIS

In kernel methods, choosing a suitable kernel is in dispensable for favorable results. No well-founded methods, however, have been established in general for unsupervised learning. We focus on kernel Princ ipal Component Analysis (kernel PCA), which is a nonlinear extension of principal component analysis and ha s been used electively for extracting nonlinear featu res and reducing dimensionality. As a kernel method , kernel PCA also suffers from the problem of kernel choice. Although cross-validation is a popular meth od for choosing hyperparameters, it is not applicable straightforwardly to choose a kernel in kernel PCA because of the incomparable norms given by differen t kernels. It is important, thus, to develop a well founded method for choosing a kernel in kernel PCA. This study proposes a method for choosing hyperparameters in kernel PCA (kernel and the number of components) based on cross-validation for the comparable reconstruction errors of pre-images in t he original space. The experimental results on synthesized and real-world datasets demonstrate tha t the proposed method successfully selects an appropriate kernel and the number of components in kernel PCA in terms of visualization and classification errors on the principal components. The results imply that the proposed method enables automatic design of hyperparameters in kernel PCA.

Entropy principal component analysis and its application to nonlinear chemical process fault diagnosis

ABSTRACTMost chemical processes generally exhibit the characteristics of nonlinear variation. In this paper, an improved principal component analysis method using information entropy theory, called entropy principal component analysis (EPCA), is proposed for nonlinear chemical process fault diagnosis. This approach applies information entropy theory to build an explicit nonlinear transformation, which provides a convenient way for nonlinear extension of principal component analysis. The information entropy can capture the Gaussian and non‐Gaussian information in the measured variables via probability density function estimation. With the entropy of original measured variables, the entropy principal components are calculated using a simple eigenvalue decomposition procedure, and two monitoring statistics are built for fault detection. Once a fault is detected, EPCA similarity factors between the occurred fault dataset and historical fault pattern datasets are computed for fault recognition. Simulations on a continuous stirred tank reactor system show that EPCA performs well in terms of fault detection and recognition. © 2014 Curtin University of Technology and John Wiley & Sons, Ltd.

Subfield management class delineation using cluster analysis from spatial principal components of soil variables

Understanding spatial variation within a field is essential for site-specific crop management, which requires the delineation of management areas. Several soil and terrain variables are used to classify the field points into classes. Fuzzy k-means cluster analysis is a widely used tool to delineate management classes in the multivariate context. However, this clustering method does not consider the presence of spatial correlations in the data. The MULTISPATI-PCA algorithm is an extension of principal component analysis that considers spatial autocorrelation in the original variables to produce synthetic variables. We propose and illustrate the implementation of a new method (KM-sPC) for subfield management class delineation based on the joint use of MULTISPATI-PCA and fuzzy k-means cluster. To assess the performance of KM-sPC, we performed clustering of the original soil variables and of both spatial and classical principal components on three field data sets. KM-sPC algorithm improved the non-spatial clustering in the formation of within-field management classes. Mapping of KM-sPC classification shows a more contiguous zoning. KM-sPC showed the highest yield differences between delineated classes and the smallest within-class yield variance.

Defining the structure of DPCA models and its impact on process monitoring and prediction activities

Dynamic Principal Component Analysis (DPCA) is an extension of Principal Component Analysis (PCA), developed in order to add the ability to capture the autocorrelative behavior of processes, to the existent and well-known PCA capability for modeling cross-correlation between variables. The simultaneous modeling of the dependencies along the “variable” and “time” modes, allows for a more compact and rigorous description of the normal behavior of processes, laying the ground for the development of, for instance, improved Statistical Process Monitoring (SPM) methodologies, able to robustly detect finer deviations from normal operation conditions. A key point in the application of DPCA is the definition of its structure, namely the selection of the number of time-shifted replicates for each variable to include, and the number of components to retain in the final model. In order to address the first of these two fundamental design aspects of DPCA, and arguably the most complex one, we propose two new lag selection methods.The first method estimates a single lag structure for all variables, whereas the second one refines this procedure, providing the specific number of lags to be used for each individual variable. The application of these two proposed methodologies to several case studies led to a more rigorous estimation of the number of lags really involved in the dynamical mechanisms of the processes under analysis. This feature can be explored for implementing improved system identification, process monitoring and process control tasks that rely upon a DPCA modeling framework.

Functional principal components analysis of workload capacity functions

Workload capacity, an important concept in many areas of psychology, describes processing efficiency across changes in workload. The capacity coefficient is a function across time that provides a useful measure of this construct. Until now, most analyses of the capacity coefficient have focused on the magnitude of this function, and often only in terms of a qualitative comparison (greater than or less than one). This work explains how a functional extension of principal components analysis can capture the time-extended information of these functional data, using a small number of scalar values chosen to emphasize the variance between participants and conditions. This approach provides many possibilities for a more fine-grained study of differences in workload capacity across tasks and individuals.

JOINT AND INDIVIDUAL VARIATION EXPLAINED (JIVE) FOR INTEGRATED ANALYSIS OF MULTIPLE DATA TYPES.

Research in several fields now requires the analysis of datasets in which multiple high-dimensional types of data are available for a common set of objects. In particular, The Cancer Genome Atlas (TCGA) includes data from several diverse genomic technologies on the same cancerous tumor samples. In this paper we introduce Joint and Individual Variation Explained (JIVE), a general decomposition of variation for the integrated analysis of such datasets. The decomposition consists of three terms: a low-rank approximation capturing joint variation across data types, low-rank approximations for structured variation individual to each data type, and residual noise. JIVE quantifies the amount of joint variation between data types, reduces the dimensionality of the data, and provides new directions for the visual exploration of joint and individual structure. The proposed method represents an extension of Principal Component Analysis and has clear advantages over popular two-block methods such as Canonical Correlation Analysis and Partial Least Squares. A JIVE analysis of gene expression and miRNA data on Glioblastoma Multiforme tumor samples reveals gene-miRNA associations and provides better characterization of tumor types.

Multiple factor analysis: principal component analysis for multitable and multiblock data sets

AbstractMultiple factor analysis (MFA, also called multiple factorial analysis) is an extension of principal component analysis (PCA) tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, (in dual‐MFA) multiple data tables where the same variables are measured on different sets of observations. MFA proceeds in two steps: First it computes a PCA of each data table and ‘normalizes’ each data table by dividing all its elements by the first singular value obtained from its PCA. Second, all the normalized data tables are aggregated into a grand data table that is analyzed via a (non‐normalized) PCA that gives a set of factor scores for the observations and loadings for the variables. In addition, MFA provides for each data table a set of partial factor scores for the observations that reflects the specific ‘view‐point’ of this data table. Interestingly, the common factor scores could be obtained by replacing the original normalized data tables by the normalized factor scores obtained from the PCA of each of these tables. In this article, we present MFA, review recent extensions, and illustrate it with a detailed example. WIREs Comput Stat 2013, 5:149–179. doi: 10.1002/wics.1246This article is categorized under: Data: Types and Structure > Categorical Data Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

Spatiotemporal dimensionality and Time-Space characterization of multitemporal imagery

Spatiotemporal dimensionality refers to the continuum of spatial and temporal patterns in an image time series. Time-Space characterization refers to a way of representing this continuum of patterns as combinations of spatial and temporal constituents — with a minimum of assumptions about the forms of the patterns. Patterns can be related to processes through modeling. By combining characterization and modeling, two complementary analytical tools can be used together so that each resolves a key limitation of the other. This study describes a straightforward extension of Principal Component Analysis and Spectral Mixture Analysis to multitemporal imagery and illustrates how characterization of the dimensionality and eigenstructure of the data can inform modeling of the processes represented in the data. The relationships among spatiotemporal processes can be represented as combinations of temporal endmembers in a temporal feature space where the dimensions represent different components of the temporal patterns present in the data. The topology of the feature space and the processes being modeled together inform the selection of temporal endmembers and the structure of the model chosen to represent the processes. The dimensionality revealed by the characterization can also provide a partial solution to the problem of endmember variability. The characterization and modeling process is illustrated with the vegetation phenology of the Ganges–Brahmaputra delta using a MODIS vegetation index time series. Additional applications and limitations of Time-Space characterization and mixture modeling are further illustrated by comparing the eigenstructures and temporal feature spaces of Landsat vegetation fraction and DMSP-OLS night light time series.

Expression of Saccharomyces cerevisiae Sdh3p and Sdh4p Paralogs Results in Catalytically Active Succinate Dehydrogenase Isoenzymes

Succinate dehydrogenase (SDH), also known as complex II, is required for respiratory growth; it couples the oxidation of succinate to the reduction of ubiquinone. The enzyme is composed of two domains. A membrane-extrinsic catalytic domain composed of the Sdh1p and Sdh2p subunits harbors the flavin and iron-sulfur cluster cofactors. A membrane-intrinsic domain composed of the Sdh3p and Sdh4p subunits interacts with ubiquinone and may coordinate a b-type heme. In many organisms, including Saccharomyces cerevisiae, possible alternative SDH subunits have been identified in the genome. S. cerevisiae contains one paralog of the Sdh3p subunit, Shh3p (YMR118c), and two paralogs of the Sdh4p subunit, Shh4p (YLR164w) and Tim18p (YOR297c). We cloned and expressed these alternative subunits. Shh3p and Shh4p were able to complement Δsdh3 and Δsdh4 deletion mutants, respectively, and support respiratory growth. Tim18p was unable to do so. Microarray and proteomics data indicate that the paralogs are expressed under respiratory and other more restrictive growth conditions. Strains expressing hybrid SDH enzymes have distinct metabolic profiles that we distinguished by (1)H NMR analysis of metabolites. Surprisingly, the Sdh3p subunit can form SDH isoenzymes with Sdh4p or with Shh4p as well as be a subunit of the TIM22 mitochondrial protein import complex.

A missing data approach to validate nonlinear PCA

Many biological processes behave in a nonlinear way. Observations over time usually show a curved trajectory in the data space. To understand the dynamics of biological processes we have to identify and analyze the time trajectory. This can be done by using a nonlinear extension of principal component analysis (PCA) which provides a noise-reduced description of the curved data structure. To avoid over-fitting a careful control of the model complexity is required for which we need a strategy to validate unsupervised nonlinear methods [1].

STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling

AbstractSTATIS is an extension of principal component analysis (PCA) tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, as in a variant called dual‐STATIS, multiple data tables where the same variables are measured on different sets of observations. STATIS proceeds in two steps: First it analyzes the between data table similarity structure and derives from this analysis an optimal set of weights that are used to compute a linear combination of the data tables called the compromise that best represents the information common to the different data tables; Second, the PCA of this compromise gives an optimal map of the observations. Each of the data tables also provides a map of the observations that is in the same space as the optimum compromise map. In this article, we present STATIS, explain the criteria that it optimizes, review the recent inferential extensions to STATIS and illustrate it with a detailed example.We also review, and present in a common framework, the main developments of STATIS such as (1) X‐STATIS or partial triadic analysis (PTA) which is used when all data tables collect the same variables measured on the same observations (e.g., at different times or locations), (2) COVSTATIS, which handles multiple covariance matrices collected on the same observations, (3) DISTATIS, which handles multiple distance matrices collected on the same observations and generalizes metric multidimensional scaling to three way distance matrices, (4) Canonical‐STATIS (CANOSTATIS), which generalizes discriminant analysis and combines it with DISTATIS to analyze multitable discriminant analysis problems, (5) power‐STATIS, which uses alternative criteria to find STATIS optimal weights, (6) ANISOSTATIS, which extends STATIS to give specific weights to each variable rather than to each whole table, (7) (K + 1)‐STATIS (or external‐STATIS), which extends STATIS (and PLS‐methods and Tucker inter battery analysis) to the analysis of the relationships of several data sets and one external data set, and (8) double‐STATIS (or DO‐ACT), which generalizes (K + 1)‐STATIS and analyzes two sets of data tables, and STATIS‐4, which generalizes double‐STATIS to more than two sets of data.These recent developments are illustrated by small examples. WIREs Comput Stat 2012, 4:124–167. doi: 10.1002/wics.198This article is categorized under: Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data

Latent Semantic Analysis: five methodological recommendations

The recent influx in generation, storage, and availability of textual data presents researchers with the challenge of developing suitable methods for their analysis. Latent Semantic Analysis (LSA), a member of a family of methodological approaches that offers an opportunity to address this gap by describing the semantic content in textual data as a set of vectors, was pioneered by researchers in psychology, information retrieval, and bibliometrics. LSA involves a matrix operation called singular value decomposition, an extension of principal component analysis. LSA generates latent semantic dimensions that are either interpreted, if the researcher's primary interest lies with the understanding of the thematic structure in the textual data, or used for purposes of clustering, categorization, and predictive modeling, if the interest lies with the conversion of raw text into numerical data, as a precursor to subsequent analysis. This paper reviews five methodological issues that need to be addressed by the researcher who will embark on LSA. We examine the dilemmas, present the choices, and discuss the considerations under which good methodological decisions are made. We illustrate these issues with the help of four small studies, involving the analysis of abstracts for papers published in the European Journal of Information Systems.

Comparison of prenatal and postnatal ontogeny: cranial allometry in the African striped mouse (Rhabdomys pumilio)

The relationship between prenatal and postnatal ontogenetic allometry is poorly known, and empirical studies documenting prenatal allometry are few, precluding an understanding of changes in growth patterns during life history and their relation to proximal, physiological, and ultimate evolutionary variables. In this study I compare prenatal and postnatal ontogenetic allometry of the cranium in a cleared and stained developmental series of the African striped mouse (Rhabdomys pumilio). Eighteen cranial measurements, reflecting the dimensions of individual elements, were analyzed using bivariate and multivariate estimates of allometry and methods of matrix comparison. Prenatal allometry is characterized in R. pumilio by a relative rapid lengthening of cranial elements, particularly the frontal, parietal, basisphenoid, premaxilla, and palatine, as evidenced by larger bivariate allometric coefficients (>30% increase) and, across all variables measured, a greater proportion of cranial elements growing with a positive allometry than in the postnatal period. Growth dynamics are found to shift for measurements of several elements including the parietal, frontal, and palatine, indicating a nonlinearity of ontogenetic allometry with respect to birth; similar shifts have been found between prenatal and postnatal growth for some regions of the human cranium. Application of common principal component analyses, a generalized extension of principal component analysis, revealed that the prenatal and postnatal matrices shared a highly similar structure, further quantified by high correlations (>0.78) using the random skewers method of matrix comparison. These results indicate a close correspondence between morphology-based variance structures over the course of ontogeny in R. pumilio.

Statistical Analysis of Multi-Cell Recordings: Linking Population Coding Models to Experimental Data

Statistical Analysis of Multi-Cell Recordings: Linking Population Coding Models to Experimental Data

Three-way analysis of imprecise data

Data are often affected by uncertainty. Uncertainty is usually referred to as randomness. Nonetheless, other sources of uncertainty may occur. In particular, the empirical information may also be affected by imprecision. Also in these cases it can be fruitful to analyze the underlying structure of the data. In this paper we address the problem of summarizing a sample of three-way imprecise data. In order to manage the different sources of uncertainty a twofold strategy is adopted. On the one hand, imprecise data are transformed into fuzzy sets by means of the so-called fuzzification process. The so-obtained fuzzy data are then analyzed by suitable generalizations of the Tucker3 and CANDECOMP/PARAFAC models, which are the two most popular three-way extensions of Principal Component Analysis. On the other hand, the statistical validity of the obtained underlying structure is evaluated by (nonparametric) bootstrapping. A simulation experiment is performed for assessing whether the use of fuzzy data is helpful in order to summarize three-way uncertain data. Finally, to show how our models work in practice, an application to real data is discussed.

Tests of Association for Quantitative Traits in Nuclear Families Using Principal Components to Correct for Population Stratification

Traditional transmission disequilibrium test (TDT) based methods for genetic association analyses are robust to population stratification at the cost of a substantial loss of power. We here describe a novel method for family-based association studies that corrects for population stratification with the use of an extension of principal component analysis (PCA). Specifically, we adopt PCA on unrelated parents in each family. We then infer principal components for children from those for their parents through a TDT-like strategy. Two test statistics within the variance-components model are proposed for association tests. Simulation results show that the proposed tests have correct type I error rates regardless of population stratification, and have greatly improved power over two popular TDT-based methods: QTDT and FBAT. The application to the Genetic Analysis Workshop 16 (GAW16) data sets attests to the feasibility of the proposed method.

Regional differences in world human body dimensions: the multi-way analysis approach

In the global market, it is vital to design products and work environments to satisfactorily meet the regional variations of human body dimensions. Few studies to date have, however, attempted to examine regional differences due to unavailability of data. Jürgens, H.W., Aune, I.A. and Peiper, U., 1990, International Data on Anthropometry, Occupational Safety and Health Series Report #65 (Geneva: International Labor Office) employed various sources to assemble anthropometric data for 20 world regions. The data provided estimates for the 5th, 50th and 95th percentiles of 19 body dimensions for both genders. In this paper, the method parallel factor analysis (PARAFAC), a natural extension of principal component analysis (PCA) to so-called multi-way array, is performed and favourably compared with the results from PCA. Several comparative studies are performed to justify the use of percentiles rather than individual subject body dimensions. It is found that the outcomes using either are comparable, especially if the body dimensions are mean-centred. Body dimensions related to height (such as stature, buttock–heel length, sitting height and forward reach) are the most critical in describing the international variations; hip breadth showing gender difference is the second most important. People in European regions as well as Australia are the tallest and largest, whereas people in South Indian and Latin American (Indian) regions are the shortest and smallest. The 20 world regions are grouped into four groups that are relatively homogeneous in body dimensions. Potential application of PARAFAC is discussed for the areas in which the data are three-dimensional in nature (such as body dimensions × gender/percentile × age).