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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