PMC:2667511 / 30946-50756 JSONTXT

{"target":"http://pubannotation.org/docs/sourcedb/PMC/sourceid/2667511","sourcedb":"PMC","sourceid":"2667511","source_url":"https://www.ncbi.nlm.nih.gov/pmc/2667511","text":"Interpretation of Discovered Association Rules\n\nDetermination of Important Rules\nTo 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.\nTable 6 Representative examples of association rules for each type\n#a Ob Rule descriptionc Typed Confe Suppf Cg Gh Ki Uj Sk Il\n1 3 If 77.31 ≤ Loop \u003c 80.56 ENZ 0.811 0.032 1 0.214 1 1 1 0.722\n2 8 If 17.57 ≤ Helix \u003c 20.87 ENZ 0.545 0.032 1 0.102 1 1 1 0.668\n3 9 If SCOPClass = 7 ENZ 0.725 0.053 1 0.184 1 1 - 0.660\n4 26 If 67.59 ≤ Loop \u003c 70.83 ENZ 0.526 0.032 - 0.048 1 1 1 0.601\n5 28 If 461.83 ≤ df-ASA \u003c 681.42 AND 2.3 ≤ LCS \u003c 2.73 ENZ 0.625 0.032 - 0.120 1 1 - 0.555\n6 37 If 57.87 ≤ Loop \u003c 61.11 ENZ 0.467 0.037 - 0.045 - 1 1 0.510\n7 2 If SCOPClass = 1 AND 12.25 ≤ nFrag \u003c 16 AND NoStrand nonENZ 0.882 0.032 1 0.250 1 1 1 0.738\n8 11 If .66 ≤ inPro \u003c .87 nonENZ 0.597 0.042 1 0.129 1 1 - 0.628\n9 15 If 26.74 ≤ nAA \u003c 35.32 AND 901.01 ≤ df-ASA \u003c 1120.6 nonENZ 0.556 0.032 1 0.133 1 1 - 0.620\n10 18 If SCOPClass = 1 AND 1.87 \u003c= LCS \u003c 2.3 9 nonENZ 0.545 0.032 1 0.137 1 1 - 0.619\n11 20 If 1.43 ≤ LCS \u003c 1.87 nonENZ 0.556 0.042 1 0.074 1 1 - 0.612\n12 21 If NoStrand AND 1.87 ≤ LCS \u003c 2.3 nonENZ 0.515 0.037 - 0.113 1 1 1 0.611\n13 36 If 58.11 ≤ ASAPR \u003c 59.52 nonENZ 0.476 0.032 1 0.065 - 1 - 0.515\n14 38 If 41.67 ≤ Loop \u003c 44.91 nonENZ 0.423 0.032 - 0.046 - 1 1 0.500\n15 40 If SCOPClass = 1 AND NoStrand nonENZ 0.484 0.064 - 0.074 - 1 0.406\n16 46 If 125.14 ≤ nAtom \u003c 165.52 AND 901.01 ≤ df-ASA \u003c 1120.6 nonENZ 0.412 0.037 - 0.050 - 1 - 0.375\n17 64 If .42 ≤ HH \u003c .44 nonENZ 0.347 0.037 - 0.009 - 1 - 0.348\n18 5 If 7.78 ≤ Strand \u003c 10.27 HET 0.660 0.037 1 0.141 1 1 1 0.691\n19 7 If 2.8 ≤ Strand \u003c 5.29 HET 0.565 0.037 1 0.089 1 1 1 0.670\n20 12 If 205.9 ≤ nAtom \u003c 246.28 HET 0.574 0.037 1 0.143 1 1 - 0.626\n21 25 If 44.91 ≤ Loop \u003c 48.15 HET 0.479 0.037 1 0.110 - 1 1 0.604\n22 32 If 3.6 ≤ LCS \u003c 4.03 HET 0.461 0.037 1 0.100 - 1 - 0.520\n23 33 If .44 ≤ HH \u003c .46 HET 0.467 0.045 1 0.070 - 1 - 0.516\n24 63 If SCOPClass = 1 AND NoStrand HET 0.282 0.037 - 0.074 - - 1 0.348\n25 31 If SCOPClass = 3 AND 2.3 ≤ LCS \u003c 2.73 HOM 0.470 0.033 1 0.100 - 1 - 0.521\n26 98 If 3.17 ≤ LCS \u003c 3.6 HOM 0.337 0.035 - 0.034 - - - 0.135\n27 133 If 26.74 ≤ nAA \u003c 35.32 HOM 0.237 0.039 - 0.041 - - - 0.106\nRepresentative 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.\na#: Rule identifier;\nbO: Order of a rule ranking by importance factor;\ncRule description: The body of a rule;\ndType: The head of a rule representing a PPI type;\neConf: Confidence of a rule;\nf Supp: Support of a rule;\ngC: Rules selected from correlation-based feature subset selection [32];\nhG: The worth of a rule by measuring the gain ratio [33]with respect to PPI types;\niK: Top K rules ranked within top 30%;\njU: Unique rules;\nkS: SSE content rules;\nlI: 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.\nTable 7 Representative examples of ENZ type presenting different structural features\n# O Rule description Subtype Conf Supp C G K U S I\n28 24 If NoHelix ENZ_A, ENZ_B, ENZ_C 0.508 0.069 - 0.058 1 1 1 0.606\n29 1 If SCOPClass = 7 AND NoHelix ENZ_A, ENZ_B 1.000 0.032 1 0.315 1 1 1 0.764\n30 17 If 461.83 ≤ df-ASA \u003c 681.42 AND NoHelix ENZ_A, ENZ_B 0.593 0.037 - 0.085 1 1 1 0.619\n31 39 If 461.83 ≤ df-ASA \u003c 681.42 ENZ_A, ENZ_B 0.477 0.111 1 0.076 - - - 0.416\n32 16 If NoHelix AND nFrag \u003c 4.75 ENZ_A 0.612 0.032 - 0.076 1 1 1 0.620\n33 19 If 4.75 ≤ nSSE \u003c 6.62 AND NoHelix ENZ_A 0.588 0.032 - 0.072 1 1 1 0.538\n34 51 If 461.83 ≤ df-ASA \u003c 681.42 AND 4.75 ≤ nSSE \u003c 6.62 ENZ_A 0.417 0.032 - 0.018 - 1 - 0.367\n35 77 If 44.38 ≤ nAtom \u003c 84.76 AND 461.83 ≤ df-ASA \u003c 681.42 ENZ_A 0.396 0.058 - 0.023 - - - 0.159\n36 34 If 9.58 ≤ nAA \u003c 18.16 AND 44.38 ≤ nAtom \u003c 84.76 AND 461.83 ≤ df-ASA \u003c 681.42 ENZ_A 0.500 0.032 - 0.045 1 1 - 0.515\n37 60 If 18.16 ≤ nAA \u003c 26.74 AND 44.38 ≤ nAtom \u003c 84.76 ENZ_A 0.357 0.032 - 0.015 - 1 - 0.351\n38 10 If 84.76 ≤ nAtom \u003c 125.14 AND 461.83 ≤ df-ASA \u003c681.42 ENZ_B 0.617 0.053 1 0.145 1 1 - 0.636\n39 13 If 12.66 ≤ sRatio \u003c 15.06 AND 461.83 ≤ df-ASA \u003c 681.42 ENZ_B 0.600 0.032 1 0.113 1 1 - 0.624\n40 14 If 461.83 ≤ df-ASA \u003c 681.42 AND 10.38 ≤ nSSE \u003c 12.25 AND SCOPClass = 2 ENZ_B 0.857 0.032 - 0.230 1 1 - 0.624\n41 27 If SCOPClass = 2 AND 461.83 ≤ df-ASA \u003c 681.42 AND 84.76 ≤ nAtom \u003c 125.14 ENZ_B 0.789 0.032 - 0.176 1 1 - 0.599\n42 35 If 10.38 ≤ nSSE \u003c 12.25 AND 12.25 ≤ nFrag \u003c 16 ENZ_B 0.500 0.032 - 0.043 1 1 - 0.515\n43 73 If 84.76 ≤ nAtom \u003c 125.14 AND SCOPClass = 2 ENZ_B 0.408 0.042 - 0.043 - - - 0.164\n44 114 If 84.76 ≤ nAtom \u003c 125.14 AND 26.74 ≤ nAA \u003c 35.32 ENZ_B 0.307 0.037 - 0.024 - - - 0.123\n45 109 If 681.42 ≤ df-ASA \u003c 901.01 ENZ_C 0.317 0.048 - 0.013 - - - 0.126\n46 137 If 84.76 ≤ nAtom \u003c 125.14 AND 681.42 ≤ df-ASA \u003c 901.01 ENZ_C 0.252 0.032 - 0.009 - - - 0.098\n47 146 If SCOPClass = 4 ENZ_C 0.221 0.042 - 0.011 - - - 0.091\n48 101 If 35.32 901.01 nAA \u003c 43.9 AND 125.14 ≤ nAtom \u003c 165.52 ENZ_D 0.323 0.032 - 0.041 - - - 0.132\n49 130 If SCOPClass = 3 ENZ_D 0.238 0.069 - 0.016 - - - 0.108\n50 141 If 901.01 ≤ df-ASA \u003c 1120.6 ENZ_D 0.207 0.032 - 0.050 - - - 0.096\n51 54 If 1120.6 ≤ df-ASA \u003c 1340.19 ENZ_E 0.392 0.042 - 0.018 - 1 - 0.363\nAbbreviation of column names is the same as that of Table 6.\nThe 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.\nFigure 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.\nFigure 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.\n\nInference of Subtypes\nSome rules which share the same sets of properties but differ in their value ranges or have other properties can be effective in order to compare features of different interaction types or to identify subtypes in a PPI type. For example, among the top 30% rules, Rules 38 (Table 7) and 16 (Table 6) describe types ENZ and nonENZ respectively, using the same set of properties such as number of atoms and df-ASA. However, their values imply that the interaction sites of nonENZ (Rule 16) are larger than those of ENZ (Rule 38). The ranges of size scales of interaction sites in ENZ are presented in Rules 35, 38 and 46 (Table 7) that share the same set of properties but differ in their values. The overall size of interaction sites in ENZ are described by Rule 38 with the highest confidence among those rules encoding the size of interaction sites. These are interesting cases where the structural difference between types can be directly inferred and subtypes of a PPI type can be derived by grouping different features of interaction sites. We deduced five subtypes of ENZ and a hierarchical tree (Figure 4) to account for those subtypes. We compiled a list of representative association rules (Table 7) to show structural features different among these subtypes.\nFigure 4 A hierarchical tree for supporting inference of subtypes. A hierarchical tree drawn from association rules (Table 7) represents different structural groups in ENZ. Enzyme-inhibitor interactions are characterized with size scales of interaction sites (number of atoms and df-ASA) and SSE content information (helix content). These differences of structural groups result in subtypes of PPIs. Letters in red are identifiers of rules (Tables 6 and 7) to split branches of a tree. Dashed lines show interaction between enzymes and inhibitors in different subtypes. We note that interaction sites of enzymes are distinguished from those of inhibitors in enzyme-inhibitor complexes. Interaction sites for inhibitors are relatively small, i.e., mainly \u003c 1000 Å^2 (Rules 34, 35, 37, 38 and 46), and are made up of strands (Rule 41) and mostly non-regular regions (Rules 1, 4 and 6) without helix content (Rule 3, 28, 29, 30, 32, and 33) which is very informative in order to characterize inhibitors. Remarkably Rules 30 and 28 generalize common features of inhibitors with respect to the size of interaction sites and SSE content. As Rule 29 was considered to be very discriminative to differentiate ENZ from other types, it can depict characteristics of a small group of inhibitors with indicating that inhibitors in SCOP class 7 do not contain helix in interaction sites (Figure 3(a), (b) and 3(c)).\nIn contrast, enzymes have larger interaction sites than their inhibitors and form mixtures of helices and strands in interaction sites (Rules 40, 48, 49, 50 and 51). Both Rules 33 and 40 show that enzymes (Rule 40) have SSEs twice as many as inhibitors (Rule 33). This indicates that both enzymes and inhibitors may contain mainly strands as regular SSEs in interaction sites since enzymes are included in SCOP class 2 (mainly β) and inhibitors do not contain helices in interaction sites. This suggests that non regular regions and beta strands are mainly involved in the interfaces of enzyme-inhibitor interactions. Such extracted information can be useful for the prediction of interaction sites for enzyme-inhibitor complexes. This observation is demonstrated by some small inhibitors in Type ENZ_A (1tabi_, 2ptci_, and 4sgbi_) and Type ENZ_B (1mcti_). Those inhibitors interact with enzymes in Type ENZ_B. The enzymes described by Rules 40, 41 and 43 are included in SCOP superfamily trypsin-like serine proteases (2.47.1) and the inhibitors are mainly in SCOP class 7 which is composed of small proteins dominated by metal ligand, heme, and disulfide bridges.\nIt is possible in a similar way to infer subtypes of other PPI types. Among PPI types, ENZ has plenty of rules (a total of 65) to derive subtypes. Hence, the comparative analysis of association rules was presented for ENZ.\n\nComparison of Association Rules to PART Rules\nTo 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.\nTable 8 PART rules generated by decision trees using C4.5a\n#b Rules discovered by C4.5 Decision Tree Type Conf Supp Corresponding rulesc\n5 AVGASA \u003e 68.73025 AND nAtom \u003e 60 AND LCS \u003e 2.61 AND Strand ≤ 32.857 AND SCOPClass = 7 ENZ 1 0.03 35, 5, 3, 36\n38 sRatio ≤ 29.411765 AND HH \u003e 0.277096 AND SCOPClass = 2 AND Strand \u003e 16.949 AND Strand \u003e 21.324 AND nSSE \u003e 10 ENZ 1 0.02 40, 39\n4 Loop \u003e 50.299 AND nAtom \u003e 60 AND Helix ≤ 33.636 AND AVGASA ≤ 41.137133 ENZ 0.99 0.07 35, 6\n27 inPro ≤ 2.016077 AND Helix \u003e 48.485 AND LCS \u003e 1.727 AND Strand ≤ 8.571 AND SCOPClass = 1 AND AVGASA ≤ 53.133 nonENZ 1 0.02 8, 10\n40 SCOPClass = 1 AND Strand ≤ 2.26 nonENZ 1 0.01 15\n1 nAtom \u003e 189 AND Loop ≤ 66.316 AND nSSE \u003e 13 AND Helix ≤ 19.481 AND sRatio ≤ 80.833 AND inPro \u003e -1.570 AND LCS \u003e 3.714 AND Loop ≤ 46.7 HET 1 0.05 20, 21\n3 nAtom \u003e 212 AND Strand ≤ 10.738 AND nSSE \u003e 13 AND inPro \u003e -1.476973 AND nAtom \u003e 384 HET 1 0.05 20, 18, 19\n34 SCOPClass = 3 AND Helix \u003e 18.421 HOM 1 0.02 25\n15 HH \u003e 0.433 AND AVGASA \u003e 55.984 AND nAA ≤ 34 HOM 1 0.01 27\na: A total of 44 rules produced by a decision tree using C4.5 algorithm in WEKA machine learning library;\nb#: PART rule identifier;\ncCorresponding 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.\nTable 9 Representative examples of overlapping association rules\n#a #b Rule descriptionc Typesd Confe Suppf Confg Supph\n52 43 If 84.76 ≤ nAtom \u003c 125.14 AND SCOPClass = 2 ENZ1 OR nonENZ2 0.408 0.042 0.306 0.032\n53 35 If 44.38 ≤ nAtom \u003c 84.76 AND 461.83 ≤ df-ASA \u003c 681.42 ENZ1 OR nonENZ2 0.396 0.058 0.252 0.037\n54 48 If 35.32 ≤ nAA \u003c 43.9 AND 125.14 ≤ nAtom \u003c 165.52 ENZ1 OR nonENZ2 0.323 0.032 0.376 0.037\n55 46 If 84.76 ≤ nAtom \u003c 125.14 AND 681.42 ≤ df-ASA \u003c 901.01 ENZ1 OR nonENZ2 0.252 0.032 0.336 0.042\n56 26 If 3.17 ≤ LCS \u003c 3.6 HET1 OR HOM2 0.357 0.037 0.337 0.035\nExamples of overlapping rule are selected from Tables 6 and 7.\na# Rule identifier;\nb#: Rule identifier in Tables 6 and 7;\nRule descriptionc: The body of overlapping rules between the two types;\ndTypes: PPI Type1 and Type2 having overlapping rules in common;\ne, gCon f: Confidences of overlapping rules for Type1 and Type2 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