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Table 1 Part (a) Comparing weighting functions for combining the contributions of multiple eigenspaces.

From: Hubs of knowledge: using the functional link structure in Biozon to mine for biologically significant entities

  Weighting Function Max Rank Min Rank Average Rank Max Ratio Min Ratio Average Ratio
Part (a) Principal Eigenspace 1 4 2.14 1 0.20 0.90
  Weighted Sum 1 4 2.64 1 0.30 0.86
  Weighted Max 2 4 2.84 1 0.34 0.85
  Max 1 4 2.37 1 0.32 0.84
Part (b) Principal Eigenspace 1 4 1.37 1 0.96 0.99
  Weighted Sum 1 4 2.12 1 0.69 0.88
  Weighted Max 3 4 3.37 0.99 0.56 0.84
  Max 2 4 3.12 0.99 0.53 0.85
Part (c) Principal Eigenspace 1 4 2.8 1 0.20 0.81
  Weighted Sum 2 4 2.9 1 0.37 0.83
  Weighted Max 2 3 2.3 1 0.37 0.84
  Max 1 4 2 1 0.49 0.83
  1. To evaluate each weighting function f we ran a total of 44 queries. Each query is a distinct combination of (search term, search type, ranking method), for example (ubiquitin, protein, PageRank). For each query we analyzed the focused subgraph and computed the top 20 eigenvectors. The contributions of their derived prominence vectors were weighted using the function f by assigning a total score f(d) to each document d. The documents were sorted based on their total score, and the quality of top fifty documents was assessed in terms of the UROC measure (see text). The different weighting functions were then ranked based on their performance on each query. The minimum, maximum and average rankings for each weighting function over these queries are listed. Furthermore, the ratio of the given function's quality to the maximum quality achieved in that query is also computed and the minimum, maximum and average of this value are computed over the 44 queries. Part (b) Comparison of weighting functions with the PageRank model. Results are reported based on 8 distinct queries in focused subgraph mode. With this model, the Principal Eigenspace clearly dominates performance. Part (c) Comparison of weighting functions with the Hubs & Authorities model. Results are reported based on 10 distinct queries in focused subgraph mode. Unlike PageRank, this model performs better when information from non-principal eigenspaces is included. The best weighting function is Max (see Section).