Image Processing Reference
In-Depth Information
The construction of a
probabilistic model
begins with a set of
training instances
for
a given domain. Each instance consists of a vector of attribute values (for a fixed set
of attributes that are associated with that particular domain) and a class label (which
may be a binary “yes/no” label, or may be one of a set of categorical values). We
are currently using the Weka machine learning toolkit [
6
] to construct models. The
model maps from an unlabeled instance (attribute vector) to a probability distribution
over class values (i.e., an assignment of a real-valued probability in the range
]
to each class value, such that the sum of the probabilities is one). Once the model has
been built, it can be used to generate predictions for both the training data and a set of
previously unseen
test instances.
The test instances also have associated class labels,
so they can be used to understand prediction errors on previously unseen instances.
To begin the visualization process, a
dimension reduction
method is applied to
a set of instances. This process results in a mapping from the high-dimensional
attribute space to a two-dimensional display space. Ideally, the dimension reduction
process will preserve important properties of the instance distribution, so that similar
instances appear near each other in the display space. Finally, a set of instances (which
could be the training instances, the test instances, both of these sets, or a new set
of sample data generated using the model) is displayed in the display space, using
glyph-based representations to show the probabilistic class predictions associated
with each instance. We have developed and are currently evaluating two alternative
glyph representations: pie charts and a “speckled” texturing.
[
0
,
1
6.3.1 Dimension Reduction
The first step in developing a model visualization is to project the high-dimensional
instance space into a two-dimensional display space. The most effective dimen-
sion reduction methods for continuous spaces, such as the ones we are interested
in, produce clusters or projections in two-dimensional space that are based on the
distribution and similarity of data instances in the higher dimensions. These meth-
ods include principal components analysis, multi-dimensional scaling [
3
], relevance
maps [
1
], and self-organizing maps [
10
,
13
].
The figures in this paper show visualizations that use two dimension reduction
methods: feature selection (orthogonal projection using two selected attributes as
axes) and principal components analysis (a statistical method for computing an
orthogonal projection using linear combinations of the original attributes). We are
also implementingmultidimensional scaling (a similarity-preserving iterative dimen-
sion reduction technique) and self-organizing maps (an iterative method based on
neural network learning).
Figure
6.1
shows two projections of an income prediction model in the census
domain. Test instances are shown with circular glyphs. In both images, individuals
who are predicted to make a high income are colored white, while those predicted to
make a low income are colored green. In the left image, the model is projected using
feature selection, with education level on the
x
axis and hours worked per week on
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