PRINCIPAL COMPONENT ANALYSIS OF KNEE ANGLE WAVEFORMS DURING RACE WALKING

This study aimed at understanding whether principal component analysis (PCA) may be useful to characterize race-walkers abilities at different performance levels. Seven young race-walkers of national and international rank were recruited. PCA was applied for classifying and detecting the structure of knee sagittal angle. This statistical technique allowed extracting multidimensional features that capture the greatest variation in race walking data. The scores, i.e. the projections of the original data on the components, revealed to be good discriminative factors for performance level detection. Finally, the underlying linear structure of the principal components provided a biomechanical interpretation of motor skill. The best athletes were able to correctly lock the knee during the mid-stance; the worst ones tended to bend the knee prematurely

Evaluating Local Garlic (Allium sativum L ) Accessions using Multivariate Analysis Based on agro-morphological Characters in Southern Tigray, Ethiopia

To assess the diversity and trait association of eight local garlic accessions, a study was conducted in southern Tigray, Ethiopia using Randomized Complete Block Design with three replications during 2014 cropping season. Cluster analysis using Ward's method classified the eight accessions into three clusters. Cluster I and III were equally with three number of accessions while, cluster II contains two accessions. The three principal component analysis with Eigen value greater than one explained 81% of the variability in the data set. Using the first principal component and the second principal component indirect selection could be effective using all accessions except accessions three and eight. The accessions by trait biplot showed that traits under study have positive association signifying narrow angle between them. Key words: cluster analysis, principal component, garlic accessions

Data processing method applying Principal Component Analysis and Spectral Angle Mapper for imaging spectroscopic sensors

A data processing method for hyperspectral images is presented. Each image contains the whole diffuse reflectance spectra of the analyzed material for all the spatial positions along a specific line of vision. This data processing method is composed of two blocks: data compression and classification unit. Data compression is performed by means of Principal Component Analysis (PCA) and the spectral interpretation algorithm for classification is the Spectral Angle Mapper (SAM). This strategy of classification applying PCA and SAM has been successfully tested on the raw material on-line characterization in the tobacco industry. In this application case the desired raw material (tobacco leaves) should be discriminated from other unwanted spurious materials, such as plastic, cardboard, leather, candy paper, etc. Hyperspectral images are recorded by a spectroscopic sensor consisting of a monochromatic camera and a passive Prism- Grating-Prism device. Performance results are compared with a spectral interpretation algorithm based on Artificial Neural Networks (ANN)

Formation of machine groups and part families in cellular manufacturing systems using a correlation analysis approach

The important step in the design of a cellular manufacturing (CM) system is to identify the part families and machine groups and consequently to form manufacturing cells. The scope of this article is to formulate a multivariate approach based on a correlation analysis for solving cell formation problem. The proposed approach is carried out in three phases. In the first phase, the correlation matrix is used as similarity coefficient matrix. In the second phase, Principal Component Analysis (PCA) is applied to find the eigenvalues and eigenvectors on the correlation similarity matrix. A scatter plot analysis as a cluster analysis is applied to make simultaneously machine groups and part families while maximizing correlation between elements. In the third stage, an algorithm is improved to assign exceptional machines and exceptional parts using respectively angle measure and Euclidian distance. The proposed approach is also applied to the general Group Technology (GT) problem in which exceptional machines and part are considered. Furthermore, the proposed approach has the flexibility to consider the number of cells as a dependent or independent variable. Two numerical examples for the design of cell structures are provided in order to illustrate the three phases of proposed approach. The results of a comparative study based on multiple performance criteria show that the present approach is very effective, efficient and practical.cellular manufacturing; cell formation; correlation matrix; Principal Component Analysis; exceptional machines and parts

Statistical shape modelling of the first carpometacarpal joint reveals high variation in morphology

The first carpometacarpal (CMC) joint, located at the base of the thumb and formed by the junction between the first metacarpal and trapezium, is a common site for osteoarthritis of the hand. The shape of both the first metacarpal and trapezium contributes to the intrinsic bony stability of the jointandvariability in the morphology of both these bones can affect the joint’s function. The objectivesof this study wereto quantify the morphological variation of the complete metacarpal and trapeziumand determine anycorrelation between anatomical features ofthese two components of the first CMC joint. A multi-object statistical shape modelling pipeline, consisting of scaling, hierarchical rigid registration, non-rigid registration and projection pursuit principal component analysis, was implemented. Four anatomical measureswere quantified from the shape model, namely the first metacarpal articular tilt and torsion angles and the trapeziumlength and width.Variationsin the first metacarpal articulartilt angle (-6.3°<θ<12.3°) and trapezium width (10.28mm <<11.13mm)wereidentified in the firstprincipal component. In the second principal component, variationsin the first metacarpal14torsion angle (0.2°<α<14.2°), first metacarpal articular tilt angle (1.0°<θ<6.4°) and trapezium length (12.25mm <ℓ<17.33mm)weredetermined. Due to their implications for joint stability, the first metacarpal articular tilt angle and trapezium width maybe important anatomical features which couldbe used toadvance early detectionand treatment offirst CMC joint osteoarthritis

Orthogonal rotation in PCAMIX

Kiers (1991) considered the orthogonal rotation in PCAMIX, a principal component method for a mixture of qualitative and quantitative variables. PCAMIX includes the ordinary principal component analysis (PCA) and multiple correspondence analysis (MCA) as special cases. In this paper, we give a new presentation of PCAMIX where the principal components and the squared loadings are obtained from a Singular Value Decomposition. The loadings of the quantitative variables and the principal coordinates of the categories of the qualitative variables are also obtained directly. In this context, we propose a computationaly efficient procedure for varimax rotation in PCAMIX and a direct solution for the optimal angle of rotation. A simulation study shows the good computational behavior of the proposed algorithm. An application on a real data set illustrates the interest of using rotation in MCA. All source codes are available in the R package "PCAmixdata"

Tangent space estimation for smooth embeddings of Riemannian manifolds

Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a point from locally available data samples. Local sampling conditions such as (i) the size of the neighborhood (sampling width) and (ii) the number of samples in the neighborhood (sampling density) affect the performance of learning algorithms. In this work, we propose a theoretical analysis of local sampling conditions for the estimation of the tangent space at a point P lying on a m-dimensional Riemannian manifold S in R^n. Assuming a smooth embedding of S in R^n, we estimate the tangent space T_P S by performing a Principal Component Analysis (PCA) on points sampled from the neighborhood of P on S. Our analysis explicitly takes into account the second order properties of the manifold at P, namely the principal curvatures as well as the higher order terms. We consider a random sampling framework and leverage recent results from random matrix theory to derive conditions on the sampling width and the local sampling density for an accurate estimation of tangent subspaces. We measure the estimation accuracy by the angle between the estimated tangent space and the true tangent space T_P S and we give conditions for this angle to be bounded with high probability. In particular, we observe that the local sampling conditions are highly dependent on the correlation between the components in the second-order local approximation of the manifold. We finally provide numerical simulations to validate our theoretical findings