Orthogonal Loadings Research Articles

Real-time quantification of fresh and hardened mechanical property for 3D printing material by intellectualization with piezoelectric transducers

This study is a pilot exploration to develop rigorous, green, intellectualized approach for optimal controlling the 3D concrete printing. The mechanical performances of 3D printed samples during super-early age, early age, and hardened state are tested and monitored using piezoelectric zirconate titanate (PZT) patches. EMI sensing technique is applied to quantify stiffness gain of printed concrete to evaluate the structural build-up behaviour by establishing the instant correlation between the stiffness of concrete and the EMI signatures. An optimization method for printing process based on EMI detection is proposed. In this way, the PZT signals can be feedback to the digital control system of printer in real time to adjust the printing setting. Instant intellectualization for the 3D printing technique is then realized and the buildability of the printed concrete is expected to be improved. The different early age properties of both printed and casted composites are elaborated. Thereafter, changes of frequency and amplitude in the conductance spectrum acquired by mounted PZT patches are employed to characterize and quantify the mechanical behaviours of the 3D printed samples exposed to orthogonal loadings, which contribute to the understanding of damage accumulation and failure process of concrete materials.

Distinct Variation Pattern Discovery Using Alternating Nonlinear Principal Component Analysis.

Autoassociative neural networks (ANNs) have been proposed as a nonlinear extension of principal component analysis (PCA), which is commonly used to identify linear variation patterns in high-dimensional data. While principal component scores represent uncorrelated features, standard backpropagation methods for training ANNs provide no guarantee of producing distinct features, which is important for interpretability and for discovering the nature of the variation patterns in the data. Here, we present an alternating nonlinear PCA method, which encourages learning of distinct features in ANNs. A new measure motivated by the condition of orthogonal loadings in PCA is proposed for measuring the extent to which the nonlinear principal components represent distinct variation patterns. We demonstrate the effectiveness of our method using a simulated point cloud data set as well as a subset of the MNIST handwritten digits data. The results show that standard ANNs consistently mix the true variation sources in the low-dimensional representation learned by the model, whereas our alternating method produces solutions where the patterns are better separated in the low-dimensional space.

Application of orthogonal L-shaped PLS to chemogenomics data and its chemical interpretation from predictive and orthogonal regression coefficients

In the orthogonal LPLS (OLPLS) method, the scores and loadings of the latent variables can be transformed to the regression coefficient value of each descriptor. Furthermore, the regression coefficient values are expressed in the atom-coloring method. That is, the fragments and atoms are colored by the signs and values of the regression coefficients. Both computational and medicinal chemists make cooperatively molecular design using the common language of chemical structures and atom colors. In this paper, we examined the possibility of the clear chemical interpretation using the human ATP-binding cassette (ABC) transporters inhibitory data set. The full data set was generated using the pair-wise kernel regression method. The generated score matrix was analyzed by the ECFP_6 fingerprints and the z-scales derived from the chemical structures and the amino acid residues in the active sites of human ABC transporters. The result of atom-coloring for predictive chemical parts of an inhibitor was examined by the human ABCB1 transporter homology model based on the mouse X-ray crystal structure. It was well matched to strong hydrophobic sites within the active site. The originality of this paper has two folds: the regression coefficients in the OLPLS model are expressed by the atom-coloring method and the chemical interpretation for inhibitors is rigorously validated by the human ABC transporter homology model.

Sparse principal component analysis by choice of norm

Recent years have seen the developments of several methods for sparse principal component analysis due to its importance in the analysis of high dimensional data. Despite the demonstration of their usefulness in practical applications, they are limited in terms of lack of orthogonality in the loadings (coefficients) of different principal components, the existence of correlation in the principal components, the expensive computation needed, and the lack of theoretical results such as consistency in high-dimensional situations. In this paper, we propose a new sparse principal component analysis method by introducing a new norm to replace the usual norm in traditional eigenvalue problems, and propose an efficient iterative algorithm to solve the optimization problems. With this method, we can efficiently obtain uncorrelated principal components or orthogonal loadings, and achieve the goal of explaining a high percentage of variations with sparse linear combinations. Due to the strict convexity of the new norm, we can prove the convergence of the iterative method and provide the detailed characterization of the limits. We also prove that the obtained principal component is consistent for a single component model in high dimensional situations. As illustration, we apply this method to real gene expression data with competitive results.

Higher Order Partial Least Squares (HOPLS): A Generalized Multilinear Regression Method

A new generalized multilinear regression model, termed the higher order partial least squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) Y from a tensor X through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low-dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both X and Y. Instead of decomposing X and Y individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.

Coupling hyperspectral image data having different spatial resolutions using Multiple Co-inertia Analysis

Coupling different techniques in spectroscopy is an efficient approach to characterise complex biological material. This work is carried out to characterise maize stem cell wall composition in the context of biofuel production. In this research, we propose to couple infrared, fluorescence and Raman hyperspectral images.Investigations have been attempted in coupling spectral data by means of multiblock methods. Multiblock techniques have been assumed to be equally applicable and effective in the analysis of biological samples with complex chemical composition and structure. The most commonly used methods are based on sequential approaches. In this article, we propose 1) to condition the data to be analysed towards multiblock analysis in term of pre-processing and organising the blocks from the initial hyperspectral images, 2) to apply Multiple Co-inertia Analysis (MCoA) a symmetrical method providing orthogonal loadings for spectral interpretation and score images for spatial analysis, and 3) to interpret and to analyse in one hand the common structure revealed by the three modalities and in the other hand the independent contribution to explain the variability under each block.

Characterization and mapping of carotenoids in the algae Dunaliella and Phaeodactylum using Raman and target orthogonal partial least squares

A method was developed for the characterisation of carotenoid pigments in algal species using Raman spectroscopy in combination with multivariate hyperspectral analysis. Target orthogonal partial least squares (T-OPLS) operates by designating one known reference spectrum as the target. The target spectrum is put as the single y column in an OPLS regression model where the X matrix consists of the unfolded image spectra as variables in its columns. The spectral shape of the OPLS first orthogonal target score enabled us to verify the peak positions of the standard, and detect new peaks, not present in the reference standard. It was shown that the mixture of carotenoids present in the algae did not fully match the reference spectrum, however, the method provided enough information to make an analysis possible also in this case. The image results were constructed from the OPLS loading vectors that were showing a correlation map for the reference spectrum from the predictive loadings and maps of the occurrence of deviations from the orthogonal loadings.

A Chi-Squared Statistic for Comparing the Independence of Out-of-Sample Factor Returns

We present a simple asymptotic statistic to evaluated the independence of factor return series when computed from orthogonal loadings used out-of-sample.

Factor Analytic Modeling of Within Person Variation in Score Profiles

A profile is a vector of scores for one examinee. The mean score in the vector can be interpreted as a measure of overall profile height, the variance can be interpreted as a measure of within person variation, and the ipsatized vector of score deviations about the mean can be said to describe the pattern in the score profile. A within person pattern interpretation of orthogonal factor loadings is developed. A statistic is proposed to index the amount of within person variation accounted for by an orthogonal factor. The statistic can be used to determine whether a factor warrants a within person pattern interpretation. A factor model with a random coefficient intercept is proposed for the study of within person score patterns accounting for within person variation. Two examples, one involving items from the Life Orientation Test and the other involving subscales of the Strong Vocational Interest Inventory, illustrate application of the factor model with an intercept, the within person variation statistic, and the profile pattern interpretation of factor loadings. With empirical support from the examples, it is conjectured that theoretically important traits often manifest themselves through within person score patterns.

Plastic Deformation of Thin Plates Subjected to Quasi-Static and Dynamic Loadings

Deformation and failure of thin plates of mild steel were studied under quasi-static and dynamic impact loadings. Particular emphasis was placed on responses of simply supported circular plates subjected to centric orthogonal loadings. The latter comprised loadings due to relatively massive rigid cylindrical strikers with a hemispherical-end as well as a flat-end. The projectile motions featured variable and low impact velocities. Generally, good agreement was found between experimental results and those predicted by finite-element techniques for displacement-time curves and for force histories of the striker. It was concluded that the ABAQUS-based study (both the implicit and the explicit versions) revealed beneficial insights into the impact mechanics of plates by rigid projectiles.

STATISTICAL ANALYSIS OF THE 2001 TOUR DE FRANCE

The 2001 Tour de France consisted of 21 daily stages over 23 days over flat and mountain terrain. Purpose: The study defined the statistical performance structure of the 2001 Tour finishers. Methods: The official race times for the Prologue and each of the 20 stages were downloaded from the Tour web site. These data were processed to obtain each cyclist's elapsed time for each stage. Exploratory factor analysis (Alpha) identified the performance structure. Results: The analysis identified two orthogonal factors that accounted for 33% of total race variance. Stages 10 to 14 were the primary variables that defined factor 1 and accounted for 28% of total race variance. These stages consisted of the 4 most-difficult climbs and the 32 km time trial that include a 21 km uphill climb. The orthogonal loadings for this climbing factor were: 0.78 for the time trial; and 0.81 to 0.84 for the four climbing stages. The 61-km individual time trial loaded moderately (0.38) on the climbing factor. Factor 2 accounted for just 5% of performance variance and included: four flat stages (0.38 to 0.57); 8 km Prologue time trial (0.44); and 67 km team time trial (0.51). The correlation between time for stages 10–14 and total race time was 0.94. The lowest times for these climbing stages (10–14) defined the final top four finishers (Armstrong, Ullrich, Beloki & Kivilev) Conclusion: The climbing performance was nearly 6 times more important than the speed factor and support Armstrong's stated view that the Tour starts in the mountains, but also suggests that it ended at Luz-Ardiden, the last major climbing stage.

Construct Validation of a 10-Item Eating Attitudes Screening Test for College Students

The 26-item Eating Attitudes Test (EAT-26) is used to identify eating disturbances in non-clinical populations. The present study examined the construct validity of a screening version of EAT-26. The EAT-26 was administered to 2104 college students and their data were factor analyzed. The initial Alpha solution was rotated with orthogonal and oblique solutions. The analysis produced 5 factors that accounted for 57.4% of the total variance. The first principle component accounted for 61.3% of the total factor variance. The other 4 factors accounted for the remaining 38.7%. The factor 1 items with orthogonal loadings > 0.6 were retained resulting in a 10-item EAT (EAT-10). The Chronbach alpha reliability estimates of EAT-26 and EAT-10 were 0.897 and 0.952. The correlation between EAT-10 and EAT-26 was 0.92. The EAT-10 was directly correlated with age (i=0.14), BMI (r=0.19), percent body fat (r=0.19), and inversely correlated with VO 2max (r=−0.16). The EAT-10 was re-administered to a new sample of college students (n = 1776). These data, combined with the data from the original sample, were used to establish population norms (n = 3880). These data show the EAT-10 is a highly internal consistent measure of the principal EAT construct and has promise of being a valid eating disorder screening test. Additional calibration research is underway to develop probability models for estimating the risk of the presence of eating disorders in a non-clinical population.

A fast method to compute orthogonal loadings partial least squares

\Ve give a computationally fast method for the orthogonal loadings partial least squares. Our algorithm avoids the multiple regression computations at each step and yields identical scores and loadings to the usual method. We give a proof of the equivalence to the standard algorithm. Ve discuss briefiy the computational advantages over both orthogonal scores and orthogonal loadings partial least squares.

Resolution of infrared spectra of mixtures of potential organic workplace pollutants by factor analysis

A new approach for factor analysis of MIR spectra is proposed and applied to 15 mixtures of three potential workplace pollutants. PCA is performed on small regions of the overall experimental data matrix consisting of ω spectral frequencies and 15 spectra. The window is moved across the spectral data set, and the number of significant components in each window is computed. Regions where only one component absorbs (‘composition one’) are then identified. Correlations between the abstract concentration profiles for these points are used to sort the composition one regions into three groups. Each group represents a single component. Elimination of one of these groups permits new orthogonal spectra to be computed consisting of two components. The process is further repeated to yield one pure spectrum. Choosing and eliminating different groups allows the other pure spectra to be revealed. For correct choice of window size, the recovery of the pure spectra is good. It is shown that combination of orthogonal loadings spectra is mathematically equivalent to rotation as used in evolutionary factor analysis in HPLC.

A statistical approach towards a regionalization of daily rainfall in Sri Lanka

AbstractRegionalization of daily rainfall in Sri Lanka was examined using orthogonal factor analysis (OFA) based on daily rainfall data of 42 stations for a 15‐year period (1971–1985). The number of potential rainy days was computed from the original data matrix and subjected to S‐mode OFA. The first 10 orthogonal factors were shown as highly significant, explaining 65.1 per cent of the total variance of the whole data matrix, where the level of eigenvalues represented was > 1.0. Noticeably, the 10 orthogonal factors clearly revealed the different homogeneous daily rainfall regions in Sri Lanka (labelled as A to J), according to the orthogonal factor high loadings matrix. Delimitation of the daily rainfall regions was carried out in accordance with the ‘variance boundaries’ resulting from the rotated factor loadings matrix. The number of potential rainy days has been identified for each region, showing an increasing trend with elevation. The probability of rainy days, wet spells and their mean length have been computed separately on a monthly and yearly basis in order to analyse the nature of the daily rainfall reliability in each region. The main factors for the daily rainfall fluctuation patterns in Sri Lanka are the typical monsoon rainfall, the dominant influence of the Inter Tropical Convergence Zone and topography.

Utilizing Rating Instruments for Evaluating Behavioral Characteristics Differentiating Elderly Patients Selected for Skilled Nursing, Intermediate, and Psychiatric Care

This study examined behavioral characteristics distinguishing psychiatric geriatric patients requiring alternative levels of care. Multiple behavior rating scales were administered to 389 elderly patients, concurrent with, but independent from, placement decisions of a clinical team. A discriminant function analysis revealed loadings on care needed, activities of daily living, and disorientation as factors discriminating skilled nursing from intermediate care patients. Orthogonal function loadings characterized psychiatric patients as having poorer communication skills, being less cooperative, manifesting greater psychopathology, and showing more seclusiveness. Further analysis provided by a cross-validation study support the utility of behavior rating scales for simulating outcome actions of decision makers.

Method of orthogonal loadings - A fresh look

The present work reviews Graham's (1952) use of orthogonal loadings as a method for obtaining minimum-drag wing shapes and shows how this method could be adopted for automatic calculations. It is shown that the orthogonalization process amounts to diagonalizing a certain matrix. The Lagrange multiplier method is then used to solve the problem of obtaining minimum drag subject to given lift and pitching constraints.