Principal Component Analysis Of Three -Way Data

1994 ◽  
Author(s):  
Michael Edward Hohn
Keyword(s):  
Principal Component Analysis ◽  
Three Dimensional ◽  
Principal Component ◽  
Component Analysis ◽  
Quality Data ◽  
Mode Analysis ◽  
Core Matrix ◽  
Eigenvector Analysis ◽  
Different Depths ◽  
Principal Component Model

Extension of conventional eigenvector analysis to three-way sets of data is possible through three-mode principal component analysis. First introduced in the 1960's, this method gives three sets of loadings corresponding to the three ways in the data, e.g., variable, location, and time. A core matrix relates loadings across modes. Data must be centered and scaled before analysis, and as in conventional two-way analysis, preprocessing options affect the reduction in dimensionality and the appearance of the results. An example using water quality data illustrates the method and preprocessing effects. Although three-way tables can be studied through conventional analysis of a two-way table created by combining two modes of the data, three-mode analysis treats each mode separately and with the same weight. In addition, a restricted three-mode principal component model avoids problems in rotational indeterminacy, and results in a particularly simple model. Factor analysis or principal component analysis begins with a two-way table with samples along one margin and variables along the other. For instance, samples may be arranged as rows and variables as columns. R-mode analysis of the columns displays interdependencies among variables and Q-mode analysis displays similarities among samples. The analysis increases in complexity if a set of variables is repeatedly observed on the same samples; each set of measurements might represent a different experimental condition, chemical or sedimentological fraction, or simply geologic time. The resulting table of data can be visualized as a three-dimensional block: horizontal slices represent samples, vertical slices parallel with the front represent variables, and vertical slices parallel with the ends represent different conditions, times, or fractions. For example, Oudin (1970) performed elemental analyses of organic extracts from Jurassic shales in the Paris basin. Samples represented very different depths of maximum burial. Each was fractionated into several extracts according to solubility in organic solvents. Data published by Oudin (1970) have the three ways: locality, fraction, and element. Multivariate analysis of these data was presented by Hohn (1979). Hohn and Friberg (1979) applied principal component analysis to petrographic data in which the three modes were sample, mineral phase, and chemical component.

scholarly journals Principal Component Analysis of Munich Functional Developmental Diagnosis

2021 ◽  
Vol 13 (2) ◽  
pp. 227-233
Author(s):  
Grażyna Pazera ◽  
Marta Młodawska ◽  
Jakub Młodawski ◽  
Kamila Klimowska
Keyword(s):  
Principal Component Analysis ◽  
Social Skills ◽  
Motor Development ◽  
Three Dimensional ◽  
Principal Component ◽  
Component Analysis ◽  
Three Dimensions ◽  
Matrix Analysis ◽  
Psychomotor Development ◽  
First Year Of Life

Objectives: Munich Functional Developmental Diagnosis (MFDD) is a scale for assessing the psychomotor development of children in the first months or years of life. The tool is based on standardized tables of physical development and is used to detect developmental deficits. It consists of eight axes on which the following skills are assessed: crawling, sitting, walking, grasping, perception, speaking, speech understanding, social skills. Methods: The study included 110 children in the first year of life examined with the MFDD by the same physician. The score obtained on a given axis was coded as a negative value (defined in months) below the child’s age-specific developmental level. Next, we examined the dimensionality of the scale and the intercorrelation of its axes using polychoric correlation and principal component analysis. Results: Correlation matrix analysis showed high correlation of MFDD axes 1–4, and MFDD 6–8. The PCA identified three principal components consisting of children’s development in the areas of large and small motor skills (axis 1–4), perception (axis 5), active speech, passive speech and social skills (axis 6–8). The three dimensions obtained together account for 80.27% of the total variance. Conclusions: MFDD is a three-dimensional scale that includes motor development, perception, and social skills and speech. There is potential space for reduction in the number of variables in the scale.

scholarly journals Competitive and Recreational Running Kinematics Examined Using Principal Components Analysis

Healthcare ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1321
Author(s):  
Wenjing Quan ◽  
Huiyu Zhou ◽  
Datao Xu ◽  
Shudong Li ◽  
Julien S. Baker ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Principal Components ◽  
Sagittal Plane ◽  
Three Dimensional ◽  
Frontal Plane ◽  
Principal Component ◽  
Component Analysis ◽  
Ankle Inversion ◽  
Motion System ◽  
Recreational Runners

Kinematics data are primary biomechanical parameters. A principal component analysis (PCA) of waveforms is a statistical approach used to explore patterns of variability in biomechanical curve datasets. Differences in experienced and recreational runners’ kinematic variables are still unclear. The purpose of the present study was to compare any differences in kinematics parameters for competitive runners and recreational runners using principal component analysis in the sagittal plane, frontal plane and transverse plane. Forty male runners were divided into two groups: twenty competitive runners and twenty recreational runners. A Vicon Motion System (Vicon Metrics Ltd., Oxford, UK) captured three-dimensional kinematics data during running at 3.3 m/s. The principal component analysis was used to determine the dominating variation in this model. Then, the principal component scores retained the first three principal components and were analyzed using independent t-tests. The recreational runners were found to have a smaller dorsiflexion angle, initial dorsiflexion contact angle, ankle inversion, knee adduction, range motion in the frontal knee plane and hip frontal plane. The running kinematics data were influenced by running experience. The findings from the study provide a better understanding of the kinematics variables for competitive and recreational runners. Thus, these findings might have implications for reducing running injury and improving running performance.

scholarly journals Improving three‐dimensional mechanical imaging of breast lesions with principal component analysis

2017 ◽  
Vol 44 (8) ◽  
pp. 4194-4203 ◽  
Author(s):  
Mohit Tyagi ◽  
Yuqi Wang ◽  
Timothy J. Hall ◽  
Paul E. Barbone ◽  
Assad A. Oberai
Keyword(s):  
Principal Component Analysis ◽  
Three Dimensional ◽  
Principal Component ◽  
Component Analysis ◽  
Breast Lesions ◽  
Mechanical Imaging

scholarly journals Evaluation of water pollution and source identification in Merbok River Kedah, Northwest Malaysia

2020 ◽  
Vol 16 (4) ◽  
pp. 458-463
Author(s):  
Ateshan Msahir Haidr ◽  
Misnan Rosmilah ◽  
Sinang Som Cit ◽  
Koki Baba Isa
Keyword(s):  
Water Quality ◽  
Principal Component Analysis ◽  
Anthropogenic Activities ◽  
Human Health Risk ◽  
Principal Component ◽  
Component Analysis ◽  
Quality Data ◽  
Toxic Heavy Metals ◽  
Water Quality Data ◽  
Fish And Shellfish

This study investigates the temporal water quality variations and pollution sources identification in Merbok River using principal component analysis. The variables analyzed include As, Cd, Pb, Fe, Cr, Mn, Zn, Ni, Ca, Mg, Na, K, NH4, F, Cl, Br, NO2, NO3, SO4, PO4, pH, BOD, DO, COD, turbidity, and salinity. These variables were analyzed using inductively coupled plasma mass spectrometry, ion chromatography, and YSI multiprobe. Principal component analysis (PCA) was utilized to evaluate the variations of the most significant water quality parameters and identify the probable source of the pollutants. From the results of PCA, 86% of the total variations were observed in the water quality data with strong dominance of toxic heavy metals (As, Pb, and Cr), parameters associated with industrial discharge, domestic inputs, overland runoff (NH4, pH, BOD, DO, COD), agrochemicals (NO2, NO3, SO4, PO4), and weathering of basement rocks (Ca, Mg, Cl, F, K, and Na). Most of these parameters were present in concentrations exceeded the reference standards limits used in this study, indicating pollution of the river water. Together with the presence of microbial contamination, the results suggest potential human health risk due to water uses, fish and shellfish consumption. Moreover, the results revealed that anthropogenic activities and weathering were the main sources of pollutants in Merbok River. 

scholarly journals Multivariate Analysis of Water Quality Measurements on the Danube River

Water ◽  
2021 ◽  
Vol 13 (24) ◽  
pp. 3634
Author(s):  
Zoltan Horvat ◽  
Mirjana Horvat ◽  
Kristian Pastor ◽  
Vojislava Bursić ◽  
Nikola Puvača
Keyword(s):  
Water Quality ◽  
Principal Component Analysis ◽  
Multivariate Analysis ◽  
Cross Sections ◽  
Principal Component ◽  
Component Analysis ◽  
Danube River ◽  
Quality Data ◽  
Water Quality Data ◽  
The Danube River

This study investigates the potential of using principal component analysis and other multivariate analysis techniques to evaluate water quality data gathered from natural watercourses. With this goal in mind, a comprehensive water quality data set was used for the analysis, gathered on a reach of the Danube River in 2011. The considered measurements included physical, chemical, and biological parameters. The data were collected within seven data ranges (cross-sections) of the Danube River. Each cross-section had five verticals, each of which had five sampling points distributed over the water column. The gathered water quality data was then subjected to several multivariate analysis techniques. However, the most attention was attributed to the principal component analysis since it can provide an insight into possible grouping tendencies within verticals, cross-sections, or the entire considered reach. It has been concluded that there is no stratification in any of the analyzed water columns. However, there was an unambiguous clustering of sampling points with respect to their cross-sections. Even though one can attribute these phenomena to the unsteady flow in rivers, additional considerations suggest that the position of a cross-section can have a significant impact on the measured water quality parameters. Furthermore, the presented results indicate that these measurements, combined with several multivariate analysis methods, especially the principal component analysis, may be a promising approach for investigating the water quality tendencies of alluvial rivers.

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