Multivariate Data Analysis

Data are easy to collect; what we really need in complex problem solving is information. We may view a data base as a domain that requires probes and tools to extract relevant information. As in the measurement process itself, appropriate instruments of reasoning must be applied to the data interpretation task. Effective tools serve in two capacities: to summarize the data and to assist in interpretation. The objectives of interpretive aids are to reveal the data at several levels of detail.

Exploring the fuzzy data picture sometimes requires a wide-angle lens to view its totality. At other times it requires a closeup lens to focus on fine detail. The graphically based tools that we use provide this flexibility. Most chemical systems are complex because they involve many variables and there are many interactions among the variables. Therefore, chemometric techniques rely upon multivariate statistical and mathematical tools to uncover interactions and reduce the dimensionality of the data.

Principal component analysis used for exploring data. Two closely related techniques, principal component analysis and factor analysis, are used to reduce the dimensionality of multivariate data. In these techniques correlations and interactions among the variables are summarized in terms of a small number of underlying factors. The methods rapidly identify key variables or groups of variables that control the system under study. The resulting dimension reduction also permits graphical representation of the data so that significant relationships among observations or samples can be identified.

Other techniques include Multidimensional Scaling, Cluster Analysis, and Correspondence Analysis.

Multivariate analysis is a branch of statistics involving the consideration of objects on each of which are observed the values of a number of variables. A wide range of methods is used for the analysis of multivariate data, and this course will give a view of the variety of methods available, as well as going into some of them in detail. Multivariate techniques are used across the whole range of fields of statistical application: in medicine, physical and biological sciences, economics and social science, and of course in many industrial and commercial applications.

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