Factor and principal component analyses as alternatives to index selection

Summary Selections from factor and principal component analyses were compared with those from the Smith-Hazel index when selecting for several switchgrass (Panicum virgatum L.) traits. The objective of this study was to examine several alternatives to index selection. Such procedures would potentially eliminate problems of selection associated with Smith-Hazel indices, including errors in genetic parameter estimates and difficulty in assigning relative economic weights to traits. Selection was performed on 1,280 plants that were evaluated over 2 years at 1 location, in a randomized complete block design with 4 replicates. The plants were evaluated for forage yield and several forage quality traits. The comparisons of index selection with principal factor analysis, maximum-likelihood factor analysis and principal component analysis were made for three sets of traits (five traits per set) to estimate repeatability for the comparisons. Multivariate analyses were performed on both simple and genotypic correlation matrices. Comparisons were made by computing Spearman's rank correlations between selection index plant scores and scores computed from multivariate analysis and by determining the number of plants selected in common for the selection methods. Among the three multivariate analysis methods evaluated in this study, principal component analysis had the highest correlation with index selection. The high correlation for principal component analysis of simple correlation matrices indicates the potential for using this statistical method for selection purposes. This would permit the breeder to reduce field costs (e.g., time, labor, equipment) required to obtain the genetic parameter estimates necessary to construct selection indices.     

On the resolving power of principal component analysis in plant community ordination

Summary A comparison between centered and non-centered principal component analysis is made on the basis of the resolving power of the methods. The results indicate the appropriateness of using a centered PCA when the aim is an ordination of plant communities, and the noncentered PCA when the aim is to elicit the taxonomic structure of a collection.Contribution from the Working Group for Data-Processing in Phytosociology, International Society for Vegetation Science.This work was supported by the Italian C.N.R. and the Centro di Calcolo dell'Università di Trieste within the framework of a broader project entitled I metodi statistici e le loro applicazioni mediante l'uso dell'elaboratore.     

Application of projection pursuit based robust principal component analysis to ECG enhancement

The paper presents an application of principal component analysis (PCA) to ECG processing. For this purpose the ECG beats are time-aligned and stored in the columns of an auxiliary matrix. The matrix, considered as a set of multidimensional variables, undergoes PCA. Reconstruction of the respective columns on the basis of a low dimensional principal subspace leads to the enhancement of the stored ECG beats. A few modifications of this classical approach to ECG signal filtering by means of a multivariate analysis are introduced. The first one is based on replacing the classical PCA by its robust extension. The second consists in replacing the analysis of the whole synchronized beats by the analysis of shorter signal segments. This creates the background for the third modification, which introduces the concept of variable dimensions of the subspaces corresponding to different parts of ECG beats. The experiments performed show that introduction of the respective modifications significantly improves the classical approach to ECG processing by application of principal component analysis.     

Data reduction prior to inference: Are there consequences of comparing groups using a t-test based on principal component scores?

Researchers often use a two-step process to analyze multivariate data. First, dimensionality is reduced using a technique such as principal component analysis, followed by a group comparison using a $t$-test or analysis of variance. Although this practice is often discouraged, the statistical properties of this procedure are not well understood, starting with the hypothesis being tested. We suggest that this approach might be considering two distinct hypotheses, one of which is a global test of no differences in the mean vectors, and the other being a focused test of a specific linear combination where the coefficients have been estimated from the data. We study the asymptotic properties of the two-sample $t$-statistic for these two scenarios, assuming a nonsparse setting. We show that the size of the global test agrees with the presumed level but that the test has poor power. In contrast, the size of the focused test can be arbitrarily distorted with certain mean and covariance structures. A simple method is provided to correct the size of the focused test. Data analyses and simulations are used to illustrate the results. Recommendations on the use of this two-step method and the related use of principal components for prediction are provided.     

Using principal component analysis to find correlations between loop-related and thermodynamic variables for G-quadruplex-forming sequences

The application of Principal Component Analysis (PCA) is proposed here as a simple means of revealing correlations between thermodynamic variables corresponding to folding equilibria of intramolecular G-quadruplexes and Watson–Crick duplexes, and the length of loops in the corresponding guanine-rich DNA sequences. To this end, two previously studied data sets were analyzed (Arora and Maiti, J. Phys. Chem. B. 2009 and Kumar and Maiti, Nucleic Acids. Res. 2008). All of the sequences considered shared the common structure 5’- GGG - loop1 - GGG - loop2 - GGG - loop3 - GGG -3’. PCA of these data sets supported a series of correlations between the variables studied. First, the association of loop length with thermodynamic stability and quadruplex structure was corroborated. Secondly, it is proposed that the addition of ethylene glycol produces a stronger stabilization on those sequences showing long loop1 and/or loop3. Thirdly, it is proposed that a low content of adenine in loop1 and/or loop3 will produce an increase in the stability of G-quadruplex and its related Watson–Crick duplex.     

A combined FT-IR microscopy and principal component analysis on softwood cell walls

A combined FT-IR microscopy and principle component analysis was used to investigate chemical variations between softwood species as well as types of wood cell walls; latewood tracheids, earlywood tracheids and earlywood ray parenchyma cells. The method allowed us to detect small spectral differences between cell types rather than species and to predict characteristic chemical components of each cell type. The method enabled information to be obtained which allowed a evaluation of the polysaccharide composition even in lignified woody plant cell walls.     

Interpreting principal components in biomechanics: Representative extremes and single component reconstruction

Principal component analysis is a powerful tool in biomechanics for reducing complex multivariate datasets to a subset of important parameters. However, interpreting the biomechanical meaning of these parameters can be a subjective process. Biomechanical interpretations that are based on visual inspection of extreme 5th and 95th percentile waveforms may be confounded when extreme waveforms express more than one biomechanical feature. This study compares interpretation of principal components using representative extremes with a recently developed method, called single component reconstruction, which provides an uncontaminated visualization of each individual biomechanical feature. Example datasets from knee joint moments, lateral gastrocnemius EMG, and lumbar spine kinematics are used to demonstrate that the representative extremes method and single component reconstruction can yield equivalent interpretations of principal components. However, single component reconstruction interpretation cannot be contaminated by other components, which may enhance the use and understanding of principal component analysis within the biomechanics community.     

EMG-based muscle fatigue assessment during dynamic contractions using principal component analysis

A novel approach to fatigue assessment during dynamic contractions was proposed which projected multiple surface myoelectric parameters onto the vector connecting the temporal start and end points in feature-space in order to extract the long-term trend information. The proposed end to end (ETE) projection was compared to traditional principal component analysis (PCA) as well as neural-network implementations of linear (LPCA) and non-linear PCA (NLPCA). Nine healthy participants completed two repetitions of fatigue tests during isometric, cyclic and random fatiguing contractions of the biceps brachii. The fatigue assessments were evaluated in terms of a modified sensitivity to variability ratio (SVR) and each method used a set of time-domain and frequency-domain features which maximized the SVR. It was shown that there was no statistical difference among ETE, PCA and LPCA (p > 0.99) and that all three outperformed NLPCA (p < 0.0022). Future work will include a broader comparison of these methods to other new and established fatigue indices.     

高维蛋白质波谱癌症数据特征提取

高维蛋白质波谱癌症数据分析,一直面临着高维数据的困扰。针对高维蛋白质波谱癌症数据在降维过程中的问题,提出基于小波分析技术和主成分分析技术的高维蛋白质波谱癌症数据特征提取的方法,并在特征提取之后,使用支持向量机进行分类。对8-7-02数据集进行2层小波分解时,分别使用db1、db3、db4、db6、db8、db10、haar小波基,并使用支持向量机进行分类,正确率分别达到98.18%、98.35%、98.04%、98.36%、97.89%、97.96%、98.20%。在进一步提高分类识别正确率的同时,提高了时间率。     

An application of principal component analysis for lower body kinematics between loaded and unloaded walking

Load carriage is a very common daily activity at home and in the workplace. Generally, the load is in the form of an external load carried by an individual, it could also be the excessive body mass carried by an overweight individual. To quantify the effects of carrying extra weight, whether in the form of an external load or excess body mass, motion capture data were generated for a diverse subject set. This consisted of twenty-three subjects generating one hundred fifteen trials for each loading condition. This study applied principal component analysis (PCA) to motion capture data in order to analyze the lower body gait patterns for four loading conditions: normal weight unloaded, normal weight loaded, overweight unloaded and overweight loaded.PCA has been shown to be a powerful tool for analyzing complex gait data. In this analysis, it is shown that in order to quantify the effects of external loads and/or for both normal weight and overweight subjects, the first principal component (PC1) is needed. For the work in this paper, PCs were generated from lower body joint angle data. The PC1 of the hip angle and PC1 of the ankle angle are shown to be an indicator of external load and BMI effects on temporal gait data.     

南充雉鸡的巢址选择和春夏季栖息地选择

2006年3-6月,采用野外直接观察法和样方法,在四川省南充市太和白鹭自然保护区对雉鸡(Phasianus colchicus)的巢址选择和春夏季栖息地选择进行了研究。通过主成分分析和对比分析,巢址选择研究结果表明:雉鸡的巢都是选择在乔木盖度小、距水距离较近、草本高度和盖度都较大的白茅(Imperata cylindri-cal)干草丛中;影响雉鸡巢址选择的主要因子依次为:坡度、总盖度、乔木平均胸径、乔木盖度、郁闭度、距水距离、距路距离、灌木平均高度、巢周围干草比例、裸地面积、巢上方覆盖物厚、灌木盖度和巢所在草丛宽度等13个因子。春夏季栖息地选择研究结果表明:雉鸡在春夏季倾向于在植被总盖度大、坡度适中、乔木盖度适中、草本盖度和高度较大、灌木盖度较小、灌木高度较大、隐蔽度较大、距路距离较远和郁闭度较大等的生境栖息。     

Scapulothoracic kinematic pattern in the shoulder pain and scapular dyskinesis: A principal component analysis approach

The relationship between shoulder pain and scapular dyskinesis (SDK) is unclear. Differences between groups with and without SDK have been demonstrated, focusing on the amount of scapular motion at specific degrees of humeral elevation. However, this approach does not consider the temporal information and shape of the scapular motion temporal series. Principal Component Analysis (PCA) may clarify this variability and advance current understanding of ‘abnormal’ movement patterns. This study aimed to evaluate the scapular kinematics in patients with shoulder pain and in asymptomatic participants with and without SDK using PCA. Data were collected in 98 participants separated in four groups: Pain + SDK (n = 24), Pain (n = 25), No Pain + SDK (n = 24), and No Pain (n = 25). Scapulothoracic kinematic data were measured with an electromagnetic tracking device during arm elevation and lowering phases. PCA and analysis of variance were used to compare the groups. The No Pain + SDK group had a progressive increasing in anterior tilt over the elevation phase compared to the Pain (effect size = 0.79) and No Pain (effect size = 0.80) groups. During the arm-lowering, the Pain + SDK group had a progressive increasing in anterior tilt over this phase in comparison to the No Pain + SDK group (effect size = 0.68). Therefore, PCA demonstrated differences in the scapular anterior tilt related to SDK and shoulder pain. The presence of SDK revealed a scapular pattern with progressive increasing in anterior tilt over the elevation phase. However, during the arm-lowering phase, asymptomatic participants with SDK changed their motion pattern, unlike the symptomatic group, reinforcing the suggested association between scapular modifications and shoulder symptoms.     

Key joint kinematic characteristics of the gait of fallers identified by principal component analysis

It has been reported that fallers have a higher risk of subsequent falls than non-fallers. Therefore, if the differences between the movements of recent fallers and non-fallers can be identified, such could be regarded as the basis of the high risk of falling of the former. The objective of the present study was the identification of the key joint kinematic characteristics of human gait related to the risk of falling while walking on level ground. For this purpose, joint kinematics data obtained from 18 recent fallers and 19 non-fallers were analyzed using principal component analysis (PCA). The PCA was conducted using an input matrix constructed from the time-normalized average and standard deviation of the lower limb joint angles on three planes (101 data×2 parameters×3 angles×3 planes). The PCA revealed that only the 5th principal component vector (PCV 5) among the 23 generated PCVs was related to the risk of falling (p<0.05, ES=0.71). These findings as well as those of previous studies suggest that the joint kinematics of PCV 5 is the key characteristic that affects the risk of falling while walking. We therefore recombined the joint kinematics corresponding to PCV 5 and concluded that the variability of the joint kinematics for fallers was larger than that for non-fallers regardless of the joint. These observations as well as the findings of previous studies suggest that the risk of falling can be reduced by reducing the variability of the joint kinematics using an intervention such as external cues or a special garment.     

Multivariate denoising methods combining wavelets and principal component analysis for mass spectrometry data

The identification of new diagnostic or prognostic biomarkers is one of the main aims of clinical cancer research. In recent years, there has been a growing interest in using mass spectrometry for the detection of such biomarkers. The MS signal resulting from MALDI‐TOF measurements is contaminated by different sources of technical variations that can be removed by a prior pre‐processing step. In particular, denoising makes it possible to remove the random noise contained in the signal. Wavelet methodology associated with thresholding is usually used for this purpose. In this study, we adapted two multivariate denoising methods that combine wavelets and PCA to MS data. The objective was to obtain better denoising of the data so as to extract the meaningful proteomic biological information from the raw spectra and reach meaningful clinical conclusions. The proposed methods were evaluated and compared with the classical soft thresholding denoising method using both real and simulated data sets. It was shown that taking into account common structures of the signals by adding a dimension reduction step on approximation coefficients through PCA provided more effective denoising when combined with soft thresholding on detail coefficients.     

普通菜豆种质资源芽期抗旱性鉴定

摘要：干旱是影响我国普通菜豆生产的主要因素之一,筛选芽期抗旱性种质资源,培育抗旱品种,有利于提高普通菜豆品种的出苗率和幼苗长势,对发展我国普通菜豆生产具有重要意义。本研究首先以4份普通菜豆种质为材料,检测了不同渗透势PEG6000溶液模拟旱胁迫下的发芽率和发芽势,确定了PEG6000溶液的最适渗透势为-0.7MPa（浓度为19.6%）;以-0.7MPa的PEG6000溶液对121份普通菜豆种质进行芽期模拟旱胁迫,测定发芽率、发芽势、下胚轴长、胚根长、干重和鲜重等10项指标;通过主成分分析筛选出相对发芽率、相对发芽势、相对鲜重、相对干重、相对胚根长,相对总芽长,相对胚根/下胚轴指数、相对发芽指数、相对活力指数等9项指标可以有效评价普通菜豆的芽期抗旱性;利用隶属函数分析法对121份种质的芽期抗旱性进行综合评价,筛选出跃进豆（F0000156）、白扁豆（F0000613）等芽期抗旱性种质,为普通菜豆抗旱生理与机制研究、抗旱育种奠定了基础。