Download A. Inselberg: Multidimensional Detective

Mulidimensional Detective
• “Multidimensional” : multivariate, many
parameters
• “Detective” : focus is on the “discovery process”,
finding patterns and trends in datasets
consisting of thousands of points and potentially
hundreds of variables
Displaying datasets in parallel
coordinates
• allows simplification to a 2-D pattern recognition
problem
• makes it easier to find interrelationships and
dependencies among variables
Parallel coordinates
• Cartesian and Parallel representations
of the same line
Properties of parallel coordinate
problems
• complexity is O(N), since number of axes =
number of dimensions (variables)
• conveys information intuitively for N-dimensions,
works for any N
• display can be used with a projective
transformation (e.g. rotation, translation, scaling,
perspective)
• every variable is treated uniformly
Design of queries
• queries should be able to operate in parallel
coordinates
• should be intuitive and well-chosen
• combine “atomic” queries to form complex
queries suitable to cut the dataset of a parallel
coordinate display
Example 1: VLSI chip production
• 473 batches of VLSI chips, measuring 16 process
parameters
• X1 = yield, X2 = quality, X3-X12 = other physical
parameters
• scale is inverted, so 0 appears at top of ||
coordinate display
• objective: raise yield while maintaining high
quality
Obtaining visual cues
• batches having highest X1 and X2 were isolated
• X15 showed separation into two clusters
• some batches low in defect X3 were not in these
batches
• conclusion: some defects may be beneficial to
the high yield, high quality goal
Removing the zero-defect
constraint
• batches with zero defects in 9 out of 10 defect
types were isolated
• result: all of these batches have low yield and low
quality (unexpected)
• when defects are allowed in X6, X3, and X15, the
highest yields and highest quality batches are
obtained
• gap in X15 was obtained by simultaneously
imposing the yield and quality constraints
Example 2: nation’s economy
• trade-off analyses, discovering sensitivities,
understanding impact of constraints
• dataset is outputs of various economic sectors of
a nation (e.g. Agriculture, Mining, etc.)
• parallel coordinates used with “Least Squares”
method to obtain a visual model for the economy
Interpreting the economic model
• hyperplanes are constructed using the interior
point algorithm
– value for 1st variable is chosen
– available range for 2nd variable is reduced by 1st variable
constraint
– continues for all remaining variables
• any hyperplane within the upper and lower
boundaries is a feasible economic policy
• allows us to see impact of decisions
“downstream”
Interpretation continued
• able to see that a low initial values for agriculture
correspond to low values for fishing, and high
values for agriculture correspond to high values
for fishing
• conclusion: it is not possible to have a policy that
favors agriculture without also favoring fishing
Interpretation continued
• high values for fishing correspond to low values
for mining, and vice-versa
• further investigation revealed that the nation had
a large number of migrant workers, who worked
in both fishing and mining
• competition for the same labor pool for these two
industries