Mulidimensional Detective

1. 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

2. Displaying datasets in parallel coordinates • allows simplification to a 2-D pattern recognition problem • makes it easier to find interrelationships and dependencies among variables

3. Parallel coordinates • Cartesian and Parallel representations of the same line

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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”

11. 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

12. 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