Multidimensional
Detective
Alfred Inselberg, Multidimensional Graphs Ltd
Tel Aviv University, Israel
Presented by Yimeng Dou
04-24-2002 ydou@ics.uci.edu
1
Parallel Coordinates
• We can use parallel coordinates to model
relations among multiple variables, and turn our
problem into a 2-D pattern recognition problem.
• It’s very useful for Visual Data Mining.
• Two examples: VLSI chip and model of a
country’s economy.
• The model can be used to do trade-off analyses,
discover sensitivities, do approximate
optimizations, monitor and Decision Support.
2
Goals of The Program
• Without any loss of information.
• Low representational complexity O(N) (N is the number
of dimensions).
• Works for any N.
• Treat every variable uniformly.
• Can use transformations to recognize objects (rotation,
translation, scaling, etc.).
• Easily/Intuitively convey information on the properties of
the N-Dimensional object.
• Should be based on rigorous mathematical and
algorithmic results.
3
In order to discover patterns from a
large data set…
• Must use parallel coordinates effectively, with
proper geometrical understanding and queries
(hence the notion of ―Multidimensional Detective‖).
• Instead of mimicking the experience derived
from standard display, a good model should
exploit the special strengths of the methodology,
avoids its weakness.
• This task is similar to accurately cutting
complicated portions of an N-dimensional
watermelon. The cutting tools should be well
chosen and intuitive.
4
The VLSI Chip Problem
• Understand Figure 1—the full real data set. 473
batches, 16 processes (X1—X16).
• X1—Yield (The percentage of useful chips
produced in the batch).
• X2—Quality (Speed performance)
• X3 through X12– 10 different types of defects. 0
defect appears on top.
• X13 through X16—physical parameters.
• The author didn’t specify how to find high yield
or high quality. I think high values appear on top,
with hints from some of his later description. 5
Objective
• Raise the yield (X1), and maintain high
quality (X2). It’s a multiobjective
optimization problem.
• It’s believed that the presence of defects
hindered high yields and qualities.
• So the goal is—to achieve zero defects.
• (But is that really the case? ….let’s see)
6
Observations From Figure 2
• It isolates the batches having the highest X1 and
X2. Also, notice the two clusters of X15.
• It doesn’t include some batches having high X3
value (nearly 0 defects). So it casts doubt on the
goal of ―achieve zero defects‖. Is it the right
aim?
• To answer this question, we construct Figure 3,
which includes batches having 0 defects in at
least 9 categories (they are really close to the aim
of zero defects). Do they have high yields and
quality?
7
Figure 3—Our assumption is
challenged.
• The nine batches have poor yields and low
quality.
• Here’s another visual cue—X6. The
process is much more sensitive to
variations in X6 than the other defects.
• Treat X6 differently—select those batches
with 0 X6 defects—the very best batch is
included. (As shown in Figure 4).
8
Figure 5 and Figure 6—Test The
Assumption
• Figure 5 shows those batches which does not
have zeros for X3 and X6.
• Figure 6 shows the cluster of batches with top
yields (notice there’s a gap in X1 between them
and remaining batches, as seen in Figure 1).
• The finding—small amounts of X3 and X6 type
defects are essential for high yields and quality.
• Besides, back to Fig.2, we can see X15’s
relationship with X1/X2.
9
Our Conclusion For VLSI Chip
Problem
• Small ranges of X3, X6 close to (but not
equal to) zero, together with the lower
range of X15 provide necessary conditions
for high yields and quality.
• Fig.9 shows the result of constraining only
X1 and the resulting gap in X15.
• Fig.10 shows only constraining X2 does
not yield a gap in X15.
10
Other Insights and The Lesson We
Learned From VLSI Example
• Fig.11 shows that except for two batches, the
others all have very high X2. So we isolate these
two batches in Fig.12—and find that the high
yields but lower quality may be due to ranges of
X6, X13, X14, X15.
• So it suggests that we can further partition this
multivariate problem into sub-problems
pertaining to individual objectives.
11
The Economic Model Example
• This example illustrates how to use interior point
algorithm with the model, to do trade-off
analyses, understand the impact of constraints,
and in some cases do optimizations.
• Interior point algorithm—We can use it to find a
point that is interior to a region, and satisfies all
the constraints simultaneously, so in this case, it
represents a feasible economic policy for a
country.
• It is done interactively by sequentially choosing
values of the variables. (Fig 13)
12
Result of Choosing The First
Variable
• Once a value of the first variable is
chosen(Agriculture output), the dimensionality of
the region is reduced by one. We can see the
relationship between Agriculture and Fishing
(Low ranges corresponds to each other).
• So it’s possible to find a policy that favors
Agriculture but not favoring Fishing and vice
versa.
• Mining and Fishing (see from the lower lines of
Fishing in Fig.13). We find the competition
between them.
13
Neighborhood
• In Fig.15, a 20-dimensional model. The
intermediate curves provide useful
insights.
• The steep strips in X13, X14 and X15.
These 3 are critical variables, where the
point is bumping the boundary.
14
Boundary Point and Exterior Point
• Boundary point—If the polygonal line is tangent
to anyone of the intermediate curves then it
represents a boundary point.
• Exterior point—If it crosses any intermediate
curves.
• Exterior point enables us to see the first variable
for which the construction failed and what is
needed to make corrections.
• By changing variables interactively, we can
discover sensitive regions and other patterns.
15
Before We Come To Conclusion
• Is this model merely a model, or is it used (with
the ―intuitive‖ functionalities and high
interactivity) in any software products?
• Is this model accurate enough?
• Is it sufficient to come to any conclusion about a
problem using this technique when data set is
very large?
• How to become a skillful detective? Can any
software substitute people?
16
Conclusion
• Each multivariate dataset and problem has its
own ―personality‖ , so it requires substantial
variations in the discovery scenarios and calls for
considerable ingenuity ( a characteristic of a
detective).
• An effort of automating the exploration process
is under way. It will have a number of new
features, like intelligent agents, which will learn
from gathered experiences.
17