Principal Component Model Research Articles

Using unsupervised learning techniques to assess interactions among complex traits in soybeans

Soybean yield components and agronomic traits are connected through physiological pathways that impose tradeoffs through genetic and environmental constraints. Our primary aim is to assess the interdependence of soybean traits by using unsupervised machine learning techniques to divide phenotypic associations into environmental and genetic associations. This study was performed on large scale, jointly analyzing 14 quantitative traits in a large multi-parental population designed for genetic studies. We collected phenotypes from 2012 to 2015 from a soybean nested association panel with 40 families of approximately 140 individuals each. Pearson and Spearman correlations measured phenotypic associations. A multivariate mixed linear model provided genotypic and environmental correlations. To evaluate relationships among traits, the study used principal component and undirected graphical models from phenotypic, genotypic, and environmental correlation matrices. Results indicate that high phenotypic correlation occurs when traits display both genetic and environmental correlations. In genetic terms, length of reproductive period, node number, and canopy coverage play important roles in determining yield potential. Optimal grain yield production occurs when the growing environment favors faster canopy closure and extended reproductive length. Environmental associations found among yield components give insight into the nature of yield component compensation. The use of unsupervised learning methods provides a good framework for investigating interactions among various quantitative traits and defining target traits for breeding.

Gait analysis of young male patients diagnosed with primary bladder neck obstruction

Primary bladder neck obstruction (PBNO) represents an inappropriate or inadequate relaxation of the bladder neck during micturition. Based on the observation of an increased rate of postural imbalances in male patients with PBNO, we hypothesized a possible role of an unbalanced biomechanics of the pelvis on urethral sphincters activity. Our aim was to identify kinematic imbalances, usually disregarded in PBNO patients, and which could eventually be involved in the etiopathogenesis of the disease.Seven male adult patients (39.6±7.1years) were recruited; in all patients, PBNO was suspected at bladder diary and uroflowmetry, and was endoscopically confirmed with urethroscopy. Participants gait was recorded with a motion capture system (BTS Spa, Italy) to obtain three-dimensional joint angles and gait parameters. Multivariate statistics based on a Principal Component model allowed to assess the similarity of patients’ gait patterns with respect to control subjects.The main finding is that patients with PBNO showed significant discordance in the observations at the ankle and pelvis level. Additionally, 6/7 patients demonstrated altered trunk positions compared to normal curves. We suggest that the identified postural imbalances could represent the cause for an anomalous activation of pelvic floor muscles (hypertonia). The consequent urinary sphincters hypercontraction may be responsible for the development of voiding dysfunction in male patients with no significant morphological alterations.Results reinforced the hypothesis of an etiopathogenetic role of postural imbalances on primary bladder neck obstruction in male patients.

Bridging drought and climate aridity

Drought is a complex phenomenon, and tracing its periodicity is often a puzzle. In time and space, the frequency of drought events inspires suspicion of connections with local climate features including aridity gradients. The present study analyzes the connection between drought patterns and regional aridity gradients. Specially, the study addresses environmental water stresses in the Great Plains of the United States over the two time periods: 1951 to 1982 and 1983 to 2014. The regional aridity gradients were estimated then analyzed along with the time series of the standardized precipitation index. Employing a multivariate regression on principal components model, the study evaluates the connection between drought patterns and regional aridity gradients. The results indicate significant relationships between drought patterns and climate aridity over the time. The comparison of the aridity gradients of the Great Plains region over the two time periods indicates a wetter period from 1983 to 2014. Meanwhile, there is a shift of drought intensity, as the tendency for exceptional drought events increased significantly across the Great Plains during the period 1983 to 2014. The contrast observed with the wetting trend and the increased drought severity implies that exceptional droughts are not necessarily the cause of a drying climate. A consideration of this paradigm may help to better implement drought monitoring strategies at regional levels.

Evaluation and selection of sealants and fillers using principal component analysis for cracks in asphalt concrete pavements

The objective of this paper was to develop a comprehensive evaluation method and index to evaluate the performance of sealants and fillers for cracks in asphalt concrete pavements using the method of principal component analysis. The performance experiments including cone penetration, softening point, flow, resilience and tension at low temperature respectively were conducted by reference of ASTM D5329 for eight sealants and fillers often used in China. There by a principal component model was developed and weight of every index was calculated. The experimental results show that there are significantly different performances for sealants and fillers often used in China. Principal component analysis is an objective method that evaluates and selects the performance of sealants and fillers for cracks in asphalt concrete pavements.

Robust Graph Regularized Nonnegative Matrix Factorization for Clustering

Matrix factorization is often used for data representation in many data mining and machine-learning problems. In particular, for a dataset without any negative entries, nonnegative matrix factorization (NMF) is often used to find a low-rank approximation by the product of two nonnegative matrices. With reduced dimensions, these matrices can be effectively used for many applications such as clustering. The existing methods of NMF are often afflicted with their sensitivity to outliers and noise in the data. To mitigate this drawback, in this paper, we consider integrating NMF into a robust principal component model, and design a robust formulation that effectively captures noise and outliers in the approximation while incorporating essential nonlinear structures. A set of comprehensive empirical evaluations in clustering applications demonstrates that the proposed method has strong robustness to gross errors and superior performance to current state-of-the-art methods.

Sufficient dimension reduction constrained through sub-populations

Most methodologies for sufficient dimension reduction (SDR) in regression are limited to continuous predictors, although many data sets do contain both continuous and categorical variables. Application of these methods to regressions that include qualitative predictors such as gender or species may be inappropriate. Regressions that include a set of qualitative predictors W in addition to a vector X of many-valued predictors and a response Y are considered. Using principal fitted components (PFC) models, a likelihood-based SDR method, a sufficient dimension reduction of X that is constrained through the sub-populations established by W is sought. An estimator of the sufficient reduction subspace is provided and its use is demonstrated through applications.

Discriminant analysis under the common principal components model

ABSTRACTFor two or more populations of which the covariance matrices have a common set of eigenvectors, but different sets of eigenvalues, the common principal components (CPC) model is appropriate. Pepler et al. (2015) proposed a regularized CPC covariance matrix estimator and showed that this estimator outperforms the unbiased and pooled estimators in situations, where the CPC model is applicable. This article extends their work to the context of discriminant analysis for two groups, by plugging the regularized CPC estimator into the ordinary quadratic discriminant function. Monte Carlo simulation results show that CPC discriminant analysis offers significant improvements in misclassification error rates in certain situations, and at worst performs similar to ordinary quadratic and linear discriminant analysis. Based on these results, CPC discriminant analysis is recommended for situations, where the sample size is small compared to the number of variables, in particular for cases where there is uncertainty about the population covariance matrix structures.

Rapid cultivar identification of barley seeds through disjoint principal component modeling.

Classification of barley varieties is a crucial part of the control and assessment of barley seeds especially for the malting and brewing industry. The correct classification of barley is essential in that a majority of decisions made regarding process specifications, economic considerations, and the type of product produced with the cereal are made based on the barley variety itself. This fact combined with the need to promptly assess the cereal as it is delivered to a malt house or production facility creates the need for a technique to quickly identify a barley variety based on a sample. This work explores the feasibility of differentiating between barley varieties based on the protein spectrum of barley seeds. In order to produce a rapid analysis of the protein composition of the barley seeds, lab-on-a-chip micro fluid technology is used to analyze the protein composition. Classification of the barley variety is then made using disjoint principle component models. This work included 19 different barley varieties. The varieties consisted of both winter and summer barley types. In this work, it is demonstrated that this system can identify the most likely barley variety with an accuracy of 95.9% based on cross validation and can screen summer barley with an accuracy of 95.2% and a false positive rate of 0.0% based on cross validation. This demonstrates the feasibility of the method to provide a rapid and relatively inexpensive method to verify the heritage of barley seeds.

Considering Horn’s Parallel Analysis from a Random Matrix Theory Point of View

Horn's parallel analysis is a widely used method for assessing the number of principal components and common factors. We discuss the theoretical foundations of parallel analysis for principal components based on a covariance matrix by making use of arguments from random matrix theory. In particular, we show that (i) for the first component, parallel analysis is an inferential method equivalent to the Tracy-Widom test, (ii) its use to test high-order eigenvalues is equivalent to the use of the joint distribution of the eigenvalues, and thus should be discouraged, and (iii) a formal test for higher-order components can be obtained based on a Tracy-Widom approximation. We illustrate the performance of the two testing procedures using simulated data generated under both a principal component model and a common factors model. For the principal component model, the Tracy-Widom test performs consistently in all conditions, while parallel analysis shows unpredictable behavior for higher-order components. For the common factor model, including major and minor factors, both procedures are heuristic approaches, with variable performance. We conclude that the Tracy-Widom procedure is preferred over parallel analysis for statistically testing the number of principal components based on a covariance matrix.

Robust estimators under a functional common principal components model

When dealing with several populations of functional data, equality of the covariance operators is often assumed even when seeking for a lower-dimensional approximation to the data. Usually, if this assumption does not hold, one estimates the covariance operator of each group separately, which leads to a large number of parameters. As in the multivariate setting, this is not satisfactory since the covariance operators may exhibit some common structure, as is, for instance, the assumption of common principal directions. The existing procedures to estimate the common directions are sensitive to atypical observations. For that reason, robust projection-pursuit estimators for the common directions under a common principal component model are considered. A numerical method to compute the first directions is also provided. Under mild conditions, consistency results are obtained. A Monte Carlo study is performed to compare the finite sample behaviour of the estimators based on robust scales and on the standard deviation. The usefulness of the proposed approach is illustrated on a real data set.

Covariance Matrix Estimation for Interest-Rate Risk Modeling via Smooth and Monotone Regularization

Estimating covariance matrices in high-dimensional settings is a challenging problem central to modern finance. The sample covariance matrix is well-known to give poor estimates in high dimensions with insufficient samples, and may cause severe risk underestimates of optimized portfolios in the Markowitz framework. In order to provide useful estimates in this regime, a variety of improved covariance matrix estimates have been developed that exploit additional structure in the data. Popular approaches include low-rank (principal component and factor analysis) models, banded structure, sparse inverse covariances, and parametric models. We investigate a novel nonparametric prior for random vectors which have a spatial ordering: we assume that the covariance is monotone and smooth with respect to this ordering. This applies naturally to problems such as interest-rate risk modeling, where correlations decay for contracts that are further apart in terms of expiration dates. We propose a convex optimization (semi-definite programming) formulation for this estimation problem, and develop efficient algorithms. We apply our framework for risk measurement and forecasting with Eurodollar futures, investigate limited, missing and asynchronous data, and show that it provides valid (positive-definite) covariance estimates more accurate than existing methods.

Analysis and Modeling for Short- to Medium-Term Load Forecasting Using a Hybrid Manifold Learning Principal Component Model and Comparison with Classical Statistical Models (SARIMAX, Exponential Smoothing) and Artificial Intelligence Models (ANN, SVM): The Case of Greek Electricity Market

In this work we propose a new hybrid model, a combination of the manifold learning Principal Components (PC) technique and the traditional multiple regression (PC-regression), for short and medium-term forecasting of daily, aggregated, day-ahead, electricity system-wide load in the Greek Electricity Market for the period 2004–2014. PC-regression is shown to effectively capture the intraday, intraweek and annual patterns of load. We compare our model with a number of classical statistical approaches (Holt-Winters exponential smoothing of its generalizations Error-Trend-Seasonal, ETS models, the Seasonal Autoregressive Moving Average with exogenous variables, Seasonal Autoregressive Integrated Moving Average with eXogenous (SARIMAX) model as well as with the more sophisticated artificial intelligence models, Artificial Neural Networks (ANN) and Support Vector Machines (SVM). Using a number of criteria for measuring the quality of the generated in-and out-of-sample forecasts, we have concluded that the forecasts of our hybrid model outperforms the ones generated by the other model, with the SARMAX model being the next best performing approach, giving comparable results. Our approach contributes to studies aimed at providing more accurate and reliable load forecasting, prerequisites for an efficient management of modern power systems.

Genetic variation and association mapping of waterlogging tolerance in chrysanthemum.

Forty-five molecular markers were detected significantly associated with chrysanthemum' waterlogging tolerance, and four favorable parental lines were identified as potential donors for improving waterlogging tolerance in chrysanthemum. The productivity of chrysanthemum is downgraded by waterlogging soils, which has driven a search for germplasm showing an enhanced level of waterlogging tolerance (WT). As yet little is known regarding the mode of inheritance of WT in chrysanthemum. The study set out to characterize the extent of genetic variation for WT represented in a collection of one hundred chrysanthemum accessions by testing them under both greenhouse and field conditions. A membership function value of waterlogging (MFVW), which integrated a wilting index, a chlorosis score and the proportion of dead leaf in waterlogged plants, was used as a measure of WT. The variation for MFVW among plants grown in the greenhouse (two experiments) was generally higher than that generated in field-grown (one experiment) plants. The MFVW broad sense heritability was 0.82, and the phenotypic coefficient of variation (31.8%) was larger than the genetic one (28.8%). Association mapping (AM) identified 45 markers related to WT: 25 by applying the general linear model (GLM)+principal component (PC) model, 16 by applying the mixed linear model (MLM), 31 by applying the MLM+Q matrix model and 12 by applying the MLM+PC model. Of the associated markers, eight and two were predictive in two and three experiments within all models, respectively; the proportion of the phenotypic variance explained by the eight associations ranged from 6.3 to 16.4%. On the basis of their harboring all four of the leading markers E2M16-2, SSR150-6, E19M16-1 and E10M10-12, the varieties 'Nannong Xuefeng', 'Qx097', 'Nannong Xunzhang' and 'Finch' were identified as potential donors for future improvement of WT in chrysanthemum.

Analysis of Correlation Matrices Using Scale-Invariant Common Principal Component Models and a Hierarchy of Relationships Between Correlation Matrices

In this article, we demonstrate that the scale-invariant common principal component (CPC) model previously developed in the literature is in fact not scale invariant and cannot be used to analyze correlation matrices. To fill this gap, the correct formulation of the scale-invariant CPC model is provided, and an offspring scale-invariant CPC model is defined. Based on a series of scale-invariant CPC models, a hierarchy of relationships between correlation matrices is established. We illustrate the proposed scale-invariant CPC models with two numeric examples, and spend efforts on the interpretation of the common PCs in the second example. Some suggestions are given at the end regarding the software implementation of the scale-invariant CPC models.

Raw Data Maximum Likelihood Estimation for Common Principal Component Models: A State Space Approach.

The specifications of state space model for some principal component-related models are described, including the independent-group common principal component (CPC) model, the dependent-group CPC model, and principal component-based multivariate analysis of variance. Some derivations are provided to show the equivalence of the state space approach and the existing Wishart-likelihood approach. For each model, a numeric example is used to illustrate the state space approach. In addition, a simulation study is conducted to evaluate the standard error estimates under the normality and nonnormality conditions. In order to cope with the nonnormality conditions, the robust standard errors are also computed. Finally, other possible applications of the state space approach are discussed at the end.

Selection index for meat and milk traits of buffaloes in Colombia

Genetic parameters and breeding values from unitrait, multitrait, and reduced principal component models for weaning weight, yearling weight, weight at 18 months, weight at two years, age at first calving, milk yield, and maternal genetic effects for weaning weight and yearling weight were estimated for dual purpose buffaloes in Colombia. With those values we constructed selection indices (SI) and estimated genetic progress obtained through mating-modeling under various selection criteria and weighted values for each trait. Comparison of SI was performed using duality diagrams in principal components of breeding values obtained by pseudo-simulation of mating with animals selected with the constructed SIs. The index constructed with the first principal component of the reduced range model led to improved meat, milk yield, and age at first calving.

Statistical Assessment of Sustainability of Finger Millet Yield through Rainfall and Soil Fertility Variables using Regression and Principal Component Models in Rainfed Semi-Arid Alfisol

ABSTRACTField experiments were conducted in farmyard manure (FYM) and maize-residue (MR) blocks during 1984–2011 with the objective of identifying a superior treatment for attaining maximum finger millet yield and soil fertility at Bangalore. The treatments tested in the FYM block were Control; FYM@10tha−1; FYM@10tha−1 + 50% nitrogen, phosphorus, and potassium (NPK); FYM@10tha−1 + 100%NPK; 100%NPK; and in the MR block, Control; MR@5tha−1; MR@5t ha−1 + 50%NPK; MR@5tha−1 + 100%NPK; 100%NPK. FYM@10t/ha + 100%NPK gave a maximum mean yield of 3207 kg/ha in the FYM block, while MR@5t/ha + 100%NPK gave 2548 kg/ha in the MR block. Regression and principal component (PC) models of yield were developed through soil fertility and rainfall variables to assess the treatments. Maximum yield predictability of 60% and 65% under regression, and 76% and 75% under the PC model were observed for the FYM and MR blocks, respectively. FYM@10t/ha + 50%NPK was superior, with maximum gross returns of Rs.41286/ha and benefit–cost ratio (BCR) of 2.27 in the FYM block compared to MR@5t/ha + 100%NPK (gross returns of Rs.34530/ha and BCR of 2.09) in the MR block with maximum soil fertility, and are recommended for adoption under semi-arid Alfisols.

Asymmetric ground reaction forces and knee kinematics during squat after anterior cruciate ligament (ACL) reconstruction

BackgroundThis bilateral squat study tests whether people with anterior cruciate ligament (ACL) reconstruction have symmetric three-dimensional ground reaction forces (GRFs) and symmetric anterior–posterior (AP) translation rates of the femur with respect to the tibia when compared with healthy control subjects. We hypothesized that there would be no long-term asymmetry in knee kinematics and kinetics in ACL reconstructed subjects following surgery and rehabilitation. MethodsPosition and GRF data were collected on eight ACL reconstructed and eight control subjects during bilateral squat. The rate of relative AP translation was determined for each subject. Principal component models were developed for each of the three GRF waveforms. Principal component scores were used to assess symmetry within the ACL reconstructed group and within the control group. ResultsACL reconstructed knees analyzed in early flexion during squat descent displayed a four-fold greater rate of change in anterior translation in the reconstructed knee relative to the contralateral side than did a similar comparison of normal knees. Differences were found between the ACL reconstructed subjects' injured and uninjured limbs for all GRFs. ConclusionsSubjects following ACL reconstruction had asymmetric GRFs and relative rates of AP translation at an average of seven years after ACL reconstructive surgery when compared with control subjects. Clinical RelevanceThese alterations in loading may lead to altered load distributions across the knee joint and may put some subjects at risk for future complications such as osteoarthritis.

Principal component models with stochastic mean‐reverting levels. Pricing and covariance surface improvements

In this work, we create a family of simple stochastic covariance models, which display stochastic mean‐reverting levels of covariance as an additional level of stochastic behavior beyond well‐known stochastic volatility and correlation. The one‐dimensional version of our model is inspired by Heston model, while the multidimensional model generalizes the principal component stochastic volatility model. Their main contribution is that they capture stochastic mean‐reversion levels on the volatility and on the eigenvalues of the instantaneous covariance matrix of the vector of stock prices, with direct implications on the correlations as well. Our focus is on the multidimensional model; we investigate its properties and derive a closed‐form expression for the characteristic function. This allows us to study the pricing of financial derivatives, such as correlation and spread options. Those prices are compared with simulated Monte Carlo prices for correctness. A sensitivity analysis is performed on the parameters of the stochastic mean‐reverting level of volatilities to study their impact on the price. Finally, implied volatility curves and correlation surfaces are built to reveal the additional flexibility gained within the new model. Copyright © 2016 John Wiley & Sons, Ltd.

Simulation of Indexes Influencing Import and Export Trade Based On the Principal Component Model

Simulation of Indexes Influencing Import and Export Trade Based On the Principal Component Model