Factor analysis graphical representation

It is also beyond the graphical representation capabilities commonly used. Factor analysis is one of the pattern recognition techniques that uses all of the measured variables (features) to examine the interrelationships in the data. It accomplishes dimension reduction by minimizing minor variations so that major variations may be summarized. Thus, the maximum information from the original variables is included in a few derived variables or factors. Once the dimen-... 

Factor analysis techniques and the power of their graphical representation permit rapid Identification of anomalous behavior in multidimensional water quality data. In addition, the techniques permit qualitative class distinctions among waters with different geologic... 

To investigate the influence of wind direction, the factor scores for each fraction were averaged within a sector of 30°. The graphical representation of the scores of both factors (computed from the data set of the first fraction) versus the angle of wind direction is very noisy (Fig. 7-21) and does not enable any conclusions to be drawn on the location of these emission sources. This result is in good agreement with the result from multivariate autocorrelation analysis of the first fraction. 

Among the different linear multivariate methods that can be used to analyze Table 12.2, correspondence factor analysis (CFA) was selected because its yf metrics permits work on data prohles and the natural biplot representation of the variables and objects which greatly facilitates the interpretation of the graphical displays [26], In addition, CFA has been used successfully on similar data matrices for rationalizing (eco)toxicologi-cal information [27-30],... 

The Human Factors analysts needed an approach and a tool to help them in providing a template for the interview process of a Task analysis with the ability to structure the interview phase in order to highlight and examine the deviations from standard practice. These deviations are fundamental to understanding what can and does go wrong in the field and should be an integral part of any safety critical task representation. A graphical representation of the procedure map linked to the template including ... 

Event and causal factors charts are graphic representations that basically produce a picture of an accident—both the sequence of events that led to the accident and the conditions that were causal factors. This tool works very well in conjunction with PET or MORT analysis and is used widely in the Department of Energy. 

The Causal Factors Chart is a formal, and systematic, incident investigation and root cause analysis technique. The technique depicts the events and conditions leading up to an incident. It combines critical thinking, logical analysis, and graphic representations to analyze and depict an incident event scenario. It helps strncture the analysis and data gathering processes to ensure necessary and snfficient information is collected. The CFC also has been applied to Root Cause Analysis. The CFC is sometimes referred to as the Events and Causal Factors (ECF) chart. The ECF chart depicts the necessary and sufficient events and causal factors associated with a specific incident scenario. 

If the empirical model is validated, we can then calculate the response studied at each point of the experimental domain. If the number of factors is big. it is not very easy to extract all of the existing information. There are tools that facilitate this interpretation (canonical analysis, study of optimal de.sign, graphic representations. etc.) (9.12). 

The response surface representing the model can be visualised graphically by means of 2D contour plots and/or 3D response surface plots. In a 2D contour plot, the isoresponse lines are represented as a function of levels of two factors, while in a 3D plot the response is represented on a third dimension, as a function of the factor levels (see Figure 3.24). When more than two factors are examined and modelled, all but two factors need to be fixed at a given level to draw both plots. The optimal or acceptable experimental conditions can be derived from the graphical representation of the model or by mathematical analysis of its equation. 

This indicates that study of the interaction effects of factor combinations is essential to increase the effectiveness of the experimental design by improving the reliability of the observed results. The statistical analysis of interaction effects was performed as demonstrated in the design matrices, and the graphical representation of two-factor interaction effects AB, BC, and AC are shown in Figures 8.15—8.17, respectively. 

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