Interactive Visual Exploration and Analysis - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 158

A very powerful extension of the IVA methodology as described up to here is
adding the capability to interactively derive new, user-defined data attributes, based
on computational data analysis procedures. While in principle there are no limits to
the set of potentially useful data derivation mechanisms, it is the authors' opinion
that it is worthwhile to emphasize a few more general examples:
Interactive Spatiotemporal Data Derivation: Interactive estimation of gradients
with respect to the usually spatiotemporal domain is a generally useful data
derivation mechanisms. Spatial and temporal derivatives, including higher order
derivatives obtained by repeated application of an interactive derivation operator,
are often useful for defining features definition since features are often based on
some notion of change. Using temporal derivatives, for example, supports a more
advanced analysis of time-dependent aspects of such datasets, where the con-
sideration of first- and second-order derivatives (wrt. time) leads to a massively
parallel data analysis similar to how curve sketching is performed for individual
time series.
Interactive and Targeted Data Normalization: Data analysis commonly adopts
two types of perspective: an absolute perspective that considers absolute data
values (or derived attribute values), and a relative perspective that examines rela-
tive values. One mechanism that enables a relative perspective in IVA is to support
interactive data normalization. A powerful aspect of performing this normaliza-
tion as part of IVA is that it not only allows for global normalization procedures,
which usually do not add too much in terms of opportunities to understand data
aspects that otherwise would not be accessible, but to also enables more localized
normalization operations. Examples are normalization per time step, normaliza-
tion per height-level, etc. Useful normalization operators include the scaling to the
unit interval, z -standardization, or the normalization against other data statistics
like the median and the MAD.
Interactive Derivation of Data Statistics: Statistics are powerful means to sum-
marize and characterize data. Having data statistics, in particular localized data
statistics, available for subsequent computations and interactive feature specifi-
cations, enriches the spectrum of possibilities in IVA substantially. A very good
starting point are the standard descriptive statistics mean , standard deviation ,
skewness , and kurtosis . Interesting complements include more robust estimates
such as the median , MAD , etc., as well as ranking-based statistics (e.g., based on
quartiles or octiles). Interesting applications for IVA have been demonstrated, for
example, in the context of multi-run data analysis for climatology [ 14 ].
Considering correlation information, data clustering, etc.: Data analysis techniqu
es from statistics, data mining, machine learning, etc., are very rich in terms of
history and available related work, and the potential set of useful mechanisms
that are promising candidates for integration into IVA is almost unlimited. Partic-
ularly interesting candidates for extending the power of IVA are: the interactive
derivation of correlation information between data attributes (e.g., based on the
standard Pearson correlation, or Spearman's correlation measure), techniques for
attribute selection or dimension reduction (such as PCA or LDA, for example),