Factor score determination

Cluster analysis (which is covered extensively in Chapter 30) can be performed on the factor scores of a data table using a reduced number of factors (Section 31.1.4) rather than on the data table itself. This way, one can apply cluster analysis on the structural information only, while disregarding the noise or artefacts in the data. The number of structural factors may be determined by means of internal... 

The goal of Q-mode FA is to determine the absolute abundance of the dominant components (i.e., physical or chemical properties) for environmental contaminants. It provides a description of the multivariate data set in terms of a few end members (associations or factors, usually orthogonal) that account for the variance within the data set. A factor score represents the importance of each variable in each end member. The set of scores for all factors makes up the factor score matrix. The importance of each variable in each end member is represented by a factor score, which is a unit vector in n (number of variables) dimensional space, with each element having a value between -1 and 1 and the... 

Then using these 91 peaks only, the original data set was reexamined by principal components analysis. Eigenvalues greater than one were plotted to determine how many factors should be retained. After variraax rotation, the factor scores were plotted and interpreted. 

Firstly, the weights of each factor were determined using FAHP. Secondly, the expert scoring method can be applied to determine the different annual evaluation in order to establish the evaluation matrix. In addition to, the fuzzy comprehensive evaluation method can be used to calculate the annual risk of the coal and gas outburst, and ultimately arrive at the results of the evaluation. 

B. Factors. These elements [except for (6), Training] are divided into factors, which will also be scored. The score for an element will be determined by the factor scores. The factors are ... 

To classify samples with various pathogens, SIMCA (21) was employed to develop models for milk sample classification regarding NIR spectra. SIMCA develops models for each class based on factor analysis, that is, principal components that describe the variations of the spectral data. Once each class has its own model new samples are classified to one or another class according to their spectra. Samples from the calibration set were used to develop SIMCA models for class 1 and class 2, respectively. The obtained models were evaluated with samples from the test set, and different models were compared. SIMCA identified variations that were quite different from the inherent variance of the training set. First, the training set data matrix was decomposed by principle component analysis (PCA) and the optimum number of factors was determined. Mahalanobis distance calculations were applied to the score matrix, for the primary set of factors, to compare unknowns to the training set. If an unknown sample was not a member of the groups, it was rejected. A spectrum was classified as a member of a respective class if its Mahalanobis distance was less than 3 standard deviations from the cluster s centroid. 

The marine industry is recognising the need for powerful techniques that can be used to perform risk analysis of marine systems. One technique that has been applied in both national and international marine regulations and operations is Failure Mode and Effects Analysis (FMEA). This risk analysis tool assumes that a failure mode occurs in a system/component through some failure mechanism. The effect of this failure is then evaluated. A risk ranking is produced in order to prioritise the attention for each of the failure modes identified. The traditional method utilises the Risk Priority Number (RPN) ranking system. This method determines the RPN by finding the multiplication of factor scores. The three factors considered are probability of failure, severity and detectability. Traditional FMEA has been criticised to have several weaknesses. These weaknesses are addressed in this Chapter. A new approach, which utilises the fuzzy rules base and grey relation theory, is presented. 

An examination of the sample distributions observed in principal components projections using isomer concentration data expressed as fractional composition, as well as the clustering of samples by similar values of their second principal component score term, revealed consistent differences existed in sample profiles. The next step in this data evaluation is to statistically analyze correlations of the PLS components from analyses with the external variables such as percent sand, clay and silt, and total organic matter in samples. These correlations may play an important role in identifying factors resulting in changes in PCB composition and enable one to more clearly understand the forces determining the distribution and fate of PCB in a complex ecosystem. 

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