Comparison of Association Rules to PART Rules
To improve our understanding of the association rules discovered, we compared PART rules produced from a decision tree built using C4.5 over our properties with the association rules. There were a total of 44 PART rules generated and their average confidence and support were 0.99 and 0.02 respectively. We have collected a representative list of PART rules in Table 8. In the comparison of the association rules with PART rules, PART rules are more complicated with the composition of more predicates in rule bodies than those in association rules. Typically, one PART rule corresponds to more than 2 ~3 association rules (Table 8). Both rules provided quantitative descriptions. However, property values in PART rules represent split points for classification and are not represented by intervals of quantitative values. Some PART rules (Rules 1, 3 and 38 in Table 8) including identical properties with different split points in the same rule bodies were not clear enough to determine decision boundaries of properties. These limit the readability and understandability of PART rules whilst the association rules were simple enough to be interpreted by users. It was also possible with association rules to support the comparative analysis of rules between different PPI types as we inferred the possibility of subtypes and relative information by comparison of size scales of interaction sites in ENZ. A set of association rules discovered by ARM comprises mostly weak rules together with a small number of strong rules. On the contrary, most PART rules consist of a number of very strong rules which have the highest confidences and low supports.
Table 8  PART rules generated by decision trees using C4.5a
#b  Rules discovered by C4.5 Decision Tree  Type  Conf  Supp  Corresponding rulesc
5  AVGASA > 68.73025 AND nAtom > 60 AND LCS > 2.61 AND Strand ≤ 32.857 AND SCOPClass = 7  ENZ  1  0.03  35, 5, 3, 36
38  sRatio ≤ 29.411765 AND HH > 0.277096 AND SCOPClass = 2 AND Strand > 16.949 AND Strand > 21.324 AND nSSE > 10  ENZ  1  0.02  40, 39
4  Loop > 50.299 AND nAtom > 60 AND Helix ≤ 33.636 AND AVGASA ≤ 41.137133  ENZ  0.99  0.07  35, 6
27  inPro ≤ 2.016077 AND Helix > 48.485 AND LCS > 1.727 AND Strand ≤ 8.571 AND SCOPClass = 1 AND AVGASA ≤ 53.133  nonENZ  1  0.02  8, 10
40  SCOPClass = 1 AND Strand ≤ 2.26  nonENZ  1  0.01  15
1  nAtom > 189 AND Loop ≤ 66.316 AND nSSE > 13 AND Helix ≤ 19.481 AND sRatio ≤ 80.833 AND inPro > -1.570 AND LCS > 3.714 AND Loop ≤ 46.7  HET  1  0.05  20, 21
3  nAtom > 212 AND Strand ≤ 10.738 AND nSSE > 13 AND inPro > -1.476973 AND nAtom > 384  HET  1  0.05  20, 18, 19
34  SCOPClass = 3 AND Helix > 18.421  HOM  1  0.02  25
15  HH > 0.433 AND AVGASA > 55.984 AND nAA ≤ 34  HOM  1  0.01  27
a: A total of 44 rules produced by a decision tree using C4.5 algorithm in WEKA machine learning library;
b#: PART rule identifier;
cCorresponding rules: Association rule identifiers (Tables 6, 7 and 8) corresponding to a PART rule. One of the most notable differences between association rules and PART rules is in how to handle overlapping rules between different types. If two different interaction types are predicted from the identical head of a rule, these are called overlapping rules. There were 99 such cases out of a total of 157 rules (Table 3). Their distribution is illustrated in Supplementary Figure Nine [see Additional file 2]. Table 9 shows representative examples of overlapping rules. Examination of the overlapping rules shared by ENZ and nonENZ indicated that these types are similar in terms of df-ASA, nAtom, and nAA (Table 9) differentiated by combination with the rest of properties such as SSE content, average length of consecutive residues, size ratio, and hydrophobicity. PART rules are unique cross PPI types.
Table 9  Representative examples of overlapping association rules
#a  #b  Rule descriptionc  Typesd  Confe  Suppf  Confg  Supph
52  43  If 84.76 ≤ nAtom < 125.14 AND SCOPClass = 2  ENZ1 OR nonENZ2  0.408  0.042  0.306  0.032
53  35  If 44.38 ≤ nAtom < 84.76 AND 461.83 ≤ df-ASA < 681.42  ENZ1 OR nonENZ2  0.396  0.058  0.252  0.037
54  48  If 35.32 ≤ nAA < 43.9 AND 125.14 ≤ nAtom < 165.52  ENZ1 OR nonENZ2  0.323  0.032  0.376  0.037
55  46  If 84.76 ≤ nAtom < 125.14 AND 681.42 ≤ df-ASA < 901.01  ENZ1 OR nonENZ2  0.252  0.032  0.336  0.042
56  26  If 3.17 ≤ LCS < 3.6  HET1 OR HOM2  0.357  0.037  0.337  0.035
Examples of overlapping rule are selected from Tables 6 and 7.
a# Rule identifier;
b#: Rule identifier in Tables 6 and 7;
Rule descriptionc: The body of overlapping rules between the two types;
dTypes: PPI Type1 and Type2 having overlapping rules in common;
e, gCon f: Confidences of overlapping rules for Type1 and Type2 respectively;
f, hSupp: Supports of overlapping rules for Type1 and Type2 respectively.