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In prior work [
Rankability paper [
Citation: |
Figure 2. Cityplots of $ n = 8 $ college football data matrices with the original ordering (left) and the optimal hillside reordering (right). The top row is the 2008 season, a less rankable season with hillside $ \delta = 155 $ and $ \rho = 6 $. The bottom row is the 2005 season, a more rankable season with hillside $ \delta = 92 $ and $ \rho = 4 $
Table 1. Sample Input/Output economic data based on Japan 2005 [22] (A) and its graphical representation in (B)
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Table 2. Sample of movie rating data based on MovieLens [19] (A) and graphical representation of user rating data transformed into pairwise comparisons (B)
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Table 3.
Sample of NCAA Men's Basketball games is shown in (A) and the graphical representation of the aggregate dominance information, i.e.,
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Table 4. 5 fold cross-validation results for predicting the upset measure for NCAA Men's March Madness 2002-2018
Dominance Method | Parameters | Method | MAE | |
1 | Direct+Indirect | dt=0, st=1, wi=1 | Hillside | 3.148221 |
2 | Direct+Indirect | dt=0, st=0, wi=1 | Hillside | 3.148221 |
3 | Direct+Indirect | dt=1, st=0, wi=1 | LOP | 3.172793 |
4 | Direct+Indirect | dt=1, st=1, wi=1 | LOP | 3.172793 |
5 | Direct+Indirect | dt=0, st=0, wi=0.25 | Hillside | 3.213978 |
6 | Direct+Indirect | dt=0, st=1, wi=0.25 | Hillside | 3.213978 |
7 | Direct | dt=2 | Hillside | 3.309455 |
8 | Direct+Indirect | dt=2, st=1, wi=1 | LOP | 3.311588 |
9 | Direct+Indirect | dt=2, st=0, wi=1 | LOP | 3.311588 |
10 | Direct+Indirect | dt=2, st=2, wi=0.5 | Hillside | 3.331698 |
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Cityplot of
Cityplots of
Approximate fractional matrix
Spaghetti plots and summary of diversity of
Two maximally discordant optimal solutions for Examples 1 and 2