Determination of Important Rules
To select a set of informative and discriminative rules for the extraction of knowledge, most of the existing approaches rank the association rules based on the confidence value of a individual rule. A strong rule which is highly confident and represents general knowledge, may not be a good discriminative rule for the classification. Instead, a better measure of the importance of a rule should include the following factors considered together: correlation between a property and a class, the degree of classification power, confidence and support, top K coverage and uniqueness of a rule. As noted in the previous section, the inclusion of the SSE content information in our ARBC approach has a positive effect on the classification accuracy (Table 4). The importance of a rule can be quantified by integrating the various factors including the SSE content information. We defined a importance factor (I in Tables 6 and 7) by an average value of all the factors. In order to illustrate the informativeness of the rules in understanding interface features, some representative rules within the top 30% (ranked higher than 48) of I are listed in Table 6. The list was complemented by some other rules ranked below 48 in order to explain overlapping rules and compare association rules to rules generated from a decision tree. Similarly, rules describing the ENZ type with varying different structural features are listed in Table 7. Rules in Tables 6 and 7 are sorted by Type and I.
Table 6  Representative examples of association rules for each type
#a  Ob  Rule descriptionc  Typed  Confe  Suppf  Cg  Gh  Ki  Uj  Sk  Il
1  3  If 77.31 ≤ Loop < 80.56  ENZ  0.811  0.032  1  0.214  1  1  1  0.722
2  8  If 17.57 ≤ Helix < 20.87  ENZ  0.545  0.032  1  0.102  1  1  1  0.668
3  9  If SCOPClass = 7  ENZ  0.725  0.053  1  0.184  1  1  -  0.660
4  26  If 67.59 ≤ Loop < 70.83  ENZ  0.526  0.032  -  0.048  1  1  1  0.601
5  28  If 461.83 ≤ df-ASA < 681.42 AND 2.3 ≤ LCS < 2.73  ENZ  0.625  0.032  -  0.120  1  1  -  0.555
6  37  If 57.87 ≤ Loop < 61.11  ENZ  0.467  0.037  -  0.045  -  1  1  0.510
7  2  If SCOPClass = 1 AND 12.25 ≤ nFrag < 16 AND NoStrand  nonENZ  0.882  0.032  1  0.250  1  1  1  0.738
8  11  If .66 ≤ inPro < .87  nonENZ  0.597  0.042  1  0.129  1  1  -  0.628
9  15  If 26.74 ≤ nAA < 35.32 AND 901.01 ≤ df-ASA < 1120.6  nonENZ  0.556  0.032  1  0.133  1  1  -  0.620
10  18  If SCOPClass = 1 AND 1.87 <= LCS < 2.3 9  nonENZ  0.545  0.032  1  0.137  1  1  -  0.619
11  20  If 1.43 ≤ LCS < 1.87  nonENZ  0.556  0.042  1  0.074  1  1  -  0.612
12  21  If NoStrand AND 1.87 ≤ LCS < 2.3  nonENZ  0.515  0.037  -  0.113  1  1  1  0.611
13  36  If 58.11 ≤ ASAPR < 59.52  nonENZ  0.476  0.032  1  0.065  -  1  -  0.515
14  38  If 41.67 ≤ Loop < 44.91  nonENZ  0.423  0.032  -  0.046  -  1  1  0.500
15  40  If SCOPClass = 1 AND NoStrand  nonENZ  0.484  0.064  -  0.074  -   1  0.406
16  46  If 125.14 ≤ nAtom < 165.52 AND 901.01 ≤ df-ASA < 1120.6  nonENZ  0.412  0.037  -  0.050  -  1  -  0.375
17  64  If .42 ≤ HH < .44  nonENZ  0.347  0.037  -  0.009  -  1  -  0.348
18  5  If 7.78 ≤ Strand < 10.27  HET  0.660  0.037  1  0.141  1  1  1  0.691
19  7  If 2.8 ≤ Strand < 5.29  HET  0.565  0.037  1  0.089  1  1  1  0.670
20  12  If 205.9 ≤ nAtom < 246.28  HET  0.574  0.037  1  0.143  1  1  -  0.626
21  25  If 44.91 ≤ Loop < 48.15  HET  0.479  0.037  1  0.110  -  1  1  0.604
22  32  If 3.6 ≤ LCS < 4.03  HET  0.461  0.037  1  0.100  -  1  -  0.520
23  33  If .44 ≤ HH < .46  HET  0.467  0.045  1  0.070  -  1  -  0.516
24  63  If SCOPClass = 1 AND NoStrand  HET  0.282  0.037  -  0.074  -  -  1  0.348
25  31  If SCOPClass = 3 AND 2.3 ≤ LCS < 2.73  HOM  0.470  0.033  1  0.100  -  1  -  0.521
26  98  If 3.17 ≤ LCS < 3.6  HOM  0.337  0.035  -  0.034  -  -  -  0.135
27  133  If 26.74 ≤ nAA < 35.32  HOM  0.237  0.039  -  0.041  -  -  -  0.106
Representative examples of 27 rules within top 30% are listed by sorting Columns Type and I. Rules of which order is below 48 are added for explaining overlapping rules and the comparison to rules produced from a decision tree.
a#: Rule identifier;
bO: Order of a rule ranking by importance factor;
cRule description: The body of a rule;
dType: The head of a rule representing a PPI type;
eConf: Confidence of a rule;
f Supp: Support of a rule;
gC: Rules selected from correlation-based feature subset selection [32];
hG: The worth of a rule by measuring the gain ratio [33]with respect to PPI types;
iK: Top K rules ranked within top 30%;
jU: Unique rules;
kS: SSE content rules;
lI: Importance factor of a rule calculated by an average of all factors such as Conf, Supp, C, G, K, U and S; "-" is replaced with value 0 when the importance factor was calculated.
Table 7  Representative examples of ENZ type presenting different structural features
#  O  Rule description  Subtype  Conf  Supp  C  G  K  U  S  I
28  24  If NoHelix  ENZ_A, ENZ_B, ENZ_C  0.508  0.069  -  0.058  1  1  1  0.606
29  1  If SCOPClass = 7 AND NoHelix  ENZ_A, ENZ_B  1.000  0.032  1  0.315  1  1  1  0.764
30  17  If 461.83 ≤ df-ASA < 681.42 AND NoHelix  ENZ_A, ENZ_B  0.593  0.037  -  0.085  1  1  1  0.619
31  39  If 461.83 ≤ df-ASA < 681.42  ENZ_A, ENZ_B  0.477  0.111  1  0.076  -  -  -  0.416
32  16  If NoHelix AND nFrag < 4.75  ENZ_A  0.612  0.032  -  0.076  1  1  1  0.620
33  19  If 4.75 ≤ nSSE < 6.62 AND NoHelix  ENZ_A  0.588  0.032  -  0.072  1  1  1  0.538
34  51  If 461.83 ≤ df-ASA < 681.42 AND 4.75 ≤ nSSE < 6.62  ENZ_A  0.417  0.032  -  0.018  -  1  -  0.367
35  77  If 44.38 ≤ nAtom < 84.76 AND 461.83 ≤ df-ASA < 681.42  ENZ_A  0.396  0.058  -  0.023  -  -  -  0.159
36  34  If 9.58 ≤ nAA < 18.16 AND 44.38 ≤ nAtom < 84.76 AND 461.83 ≤ df-ASA < 681.42  ENZ_A  0.500  0.032  -  0.045  1  1  -  0.515
37  60  If 18.16 ≤ nAA < 26.74 AND 44.38 ≤ nAtom < 84.76  ENZ_A  0.357  0.032  -  0.015  -  1  -  0.351
38  10  If 84.76 ≤ nAtom < 125.14 AND 461.83 ≤ df-ASA <681.42  ENZ_B  0.617  0.053  1  0.145  1  1  -  0.636
39  13  If 12.66 ≤ sRatio < 15.06 AND 461.83 ≤ df-ASA < 681.42  ENZ_B  0.600  0.032  1  0.113  1  1  -  0.624
40  14  If 461.83 ≤ df-ASA < 681.42 AND 10.38 ≤ nSSE < 12.25 AND SCOPClass = 2  ENZ_B  0.857  0.032  -  0.230  1  1  -  0.624
41  27  If SCOPClass = 2 AND 461.83 ≤ df-ASA < 681.42 AND 84.76 ≤ nAtom < 125.14  ENZ_B  0.789  0.032  -  0.176  1  1  -  0.599
42  35  If 10.38 ≤ nSSE < 12.25 AND 12.25 ≤ nFrag < 16  ENZ_B  0.500  0.032  -  0.043  1  1  -  0.515
43  73  If 84.76 ≤ nAtom < 125.14 AND SCOPClass = 2  ENZ_B  0.408  0.042  -  0.043  -  -  -  0.164
44  114  If 84.76 ≤ nAtom < 125.14 AND 26.74 ≤ nAA < 35.32  ENZ_B  0.307  0.037  -  0.024  -  -  -  0.123
45  109  If 681.42 ≤ df-ASA < 901.01  ENZ_C  0.317  0.048  -  0.013  -  -  -  0.126
46  137  If 84.76 ≤ nAtom < 125.14 AND 681.42 ≤ df-ASA < 901.01  ENZ_C  0.252  0.032  -  0.009  -  -  -  0.098
47  146  If SCOPClass = 4  ENZ_C  0.221  0.042  -  0.011  -  -  -  0.091
48  101  If 35.32 901.01 nAA < 43.9 AND 125.14 ≤ nAtom < 165.52  ENZ_D  0.323  0.032  -  0.041  -  -  -  0.132
49  130  If SCOPClass = 3  ENZ_D  0.238  0.069  -  0.016  -  -  -  0.108
50  141  If 901.01 ≤ df-ASA < 1120.6  ENZ_D  0.207  0.032  -  0.050  -  -  -  0.096
51  54  If 1120.6 ≤ df-ASA < 1340.19  ENZ_E  0.392  0.042  -  0.018  -  1  -  0.363
Abbreviation of column names is the same as that of Table 6.
The ENZ subtypes are defined in Figure 4. Note that ENZ_B includes both inhibitors and enzymes while the others are exclusively formed by inhibitors (e.g. ENZ_A, ENZ_C and ENZ_E) or enzymes (e.g. ENZ_D). We have shown that the interaction sites were dominated by non-regular region: especially for ENZ interactions, almost 23 of the sites in average were composed of non-helix and non-beta strand regions (Figure 1). This is manifested in rules 29 (Table 7), 1, 4 and 6, all of which require 50 – 80% content of non-regular regions to be classified as ENZ. Some of the rules containing negation predicates are strong indicators of certain interaction types. For example, "Nohelix " and "Nostrand " in the interaction sites imply ENZ (Rule 29) and nonENZ (Rules 7, 12 and 15), respectively. HET is characterized by relatively small portions of strands (Rules 18, and 19) and "Nostrand " (Rule 24). It is also observed that rules containing such SSE content information conjuncted with other properties (Rules 29, 7, 12, 15 and 24 in Figure 2) or combined with other rules (Figure 3(a), (b) and 3(c)) become stronger discriminators for classifying PPI types than rules containing only SSE content information (Rules 1, 2, 4, 6, 14, 18, 19 and 21 in Figure 2). We note that some rules (Rules 29 and 7 in Figure 2) containing SSE information with SCOP classes are the most discriminative and informative in order to characterize ENZ and nonENZ.
Figure 2  A scatter Plot matrix for PPI types and association rules. This scatter plot matrix shows clusters as collection of points separated by association rules encoding SSE content information or a SCOP class. Different colors of the left in each plot (a cell) correspond to four PPI types. The right of a plot area presents the distribution of points met with a rule on the head of a cell. Rules 29, 40, 1, and 3 separate ENZ and nonENZ from other types remarkably with few errors. The Rule 29 is a strong discriminator to classify ENZ from other types completely.
Figure 3  2D plots for pairs of association rules. These plot data points by pairs of association rules. X and Y axes are a pair of rules and each of them have two boolean values. 0 represents negative data points not meeting with a rule of each axis and 1 represents for positive data points meeting with the rule. The data points on the upper left corner meet a rule used for Y axis and the data points on the down right corner meet a rule used for X axis. The points on the upper right corner meet with both rules used for X and Y axes. Plots in Figure 3(a), (b), and (c) characterize distribution of inhibitors in enzyme-inhibitors interactions. Rule 28 is used for X axis in plots (a), (b) and (c). Rules 1, 3 and 38 are used for the Y axis in those plots. (a) represents an example for a pair of rules both including SSE information (e.g. helix and loop content). (b) and (c) show examples for combination of SSE content information (Rule 28: "Nohelix ") with other properties (e.g. SCOPClass, number of atoms and etc.). Plot (b) (Rule 3 versus Rule 28) is identical to the plot generated by Rule 29. Enzymes interacting with a group of inhibitors characterized by (a), (b), and (c) are featured by in Figure 3(e), and (f). Enzymes and inhibitors described by Rules 40 and 29 respectively are plotted in (d) where there is no point matching with both rules. Plot (d) reflects proper interpretation of association rules regarding interactions between enzymes and inhibitors.