Dynamic Parallel Mining Algorithm of Association Rules Based on Interval Concept Lattice
Abstract
:1. Introduction
2. Concepts and Methods
2.1. Interval Concept Lattice
- , i.e.,is the mapping betweenand its attributes;
- , i.e.,is the mapping betweenand its objects.
2.2. Interval Association Rules
- (1)
- The number of frequent nodes generated does not increase;
- (2)
- The node with the largest intent in frequent nodes does not increase in intent cardinality.
- (3)
- The number of candidate binary arrays generated does not increase;
- (4)
- The number of generated association rules does not increase.
3. Algorithm and Results
3.1. Vertical Union Principle of Interval Association Rules
3.2. Dynamic Mining Algorithms for Interval Association Rules
3.2.1. Algorithm Design
Algorithm 1. DMA (Dynamic Mining Algorithm) |
Input: Association rule sets Output: Association rule set Step1 ; Step2 The interval association rules in the rule set is stored in the form of arrays. Set and initialize. Comparing the of rule set and , we unit interval association rules vertically according to Theorems 4 and 5. For the rules that have been united in and , let and put the united rule number in . According to Theorems 6–8, calculate the frequency,, , , and of and in . =1, = + 1. Delete the rules of in and , and renumbering. Let rules number in add the renumbering number in . Putting the remain rules of into ; then renumbering in , and putting the remain rules of into . Rule Vertical Union ()
|
3.2.2. Algorithm Analysis
3.3. Example Study
4. Discussion
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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a | b | c | d | e | |
---|---|---|---|---|---|
1 | 1 | 1 | 1 | 0 | 0 |
2 | 0 | 0 | 0 | 1 | 0 |
3 | 1 | 1 | 0 | 1 | 0 |
4 | 1 | 0 | 1 | 0 | 1 |
a | b | c | d | e | |
---|---|---|---|---|---|
(1) | 1 | 0 | 1 | 1 | 0 |
(2) | 1 | 1 | 0 | 1 | 0 |
(3) | 0 | 1 | 0 | 1 | 1 |
Frequent Node | Frequent Degree | Frequent Node | Frequent Degree |
---|---|---|---|
a | 75% | acd | 100% |
b | 50% | ace | 50% |
c | 75% | ade | 50% |
d | 50% | bcd | 75% |
ab | 50% | bce | 50% |
ac | 50% | cde | 50% |
abc | 75% | abcd | 50% |
abd | 50% | abce | 50% |
abe | 75% | abcde | 75% |
Frequent Node | Frequent Degree | Frequent Node | Frequent Degree |
---|---|---|---|
a | 67% | acd | 67% |
b | 67% | ade | 100% |
d | 100% | bcd | 100% |
ad | 67% | bde | 67% |
bd | 67% | cde | 67% |
abc | 67% | abcd | 67% |
abd | 100% | abde | 67% |
abe | 67% | abcde | 100% |
Rule | Support | Confidence | Accuracy | Uncertainty | Frequent Number |
---|---|---|---|---|---|
75% | 100% | 60% | 40% | 1 | |
75% | 100% | 60% | 40% | 1 | |
75% | 100% | 60% | 40% | 1 | |
75% | 75% | 60% | 40% | 1 | |
50% | 67% | 75% | 25% | 1 | |
50% | 67% | 75% | 25% | 1 | |
50% | 100% | 75% | 25% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 100% | 67% | 33% | 1 | |
50% | 67% | 75% | 25% | 1 | |
50% | 100% | 75% | 25% | 1 | |
50% | 100% | 75% | 25% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 100% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 100% | 67% | 33% | 1 | |
75% | 100% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
50% | 100% | 67% | 33% | 1 | |
50% | 100% | 67% | 33% | 1 | |
75% | 100% | 67% | 33% | 1 | |
50% | 67% | 100% | 0% | 1 | |
50% | 67% | 100% | 0% | 1 | |
50% | 67% | 100% | 0% | 1 | |
50% | 100% | 100% | 0% | 1 |
Rule | Support | Confidence | Accuracy | Uncertainty | Frequent Number |
---|---|---|---|---|---|
100% | 100% | 60% | 40% | 1 | |
100% | 100% | 60% | 40% | 1 | |
100% | 100% | 60% | 40% | 1 | |
100% | 100% | 60% | 40% | 1 | |
67% | 100% | 75% | 25% | 1 | |
67% | 67% | 75% | 25% | 1 | |
67% | 100% | 75% | 25% | 1 | |
67% | 67% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 | |
67% | 67% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 | |
67% | 100% | 75% | 25% | 1 | |
67% | 67% | 75% | 25% | 1 | |
67% | 100% | 75% | 25% | 1 | |
67% | 100% | 67% | 33% | 1 | |
67% | 67% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 | |
67% | 67% | 67% | 33% | 1 | |
50% | 67% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 | |
67% | 67% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 | |
100% | 100% | 67% | 33% | 1 | |
100% | 100% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 | |
67% | 67% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 | |
100% | 100% | 67% | 33% | 1 | |
67% | 100% | 67% | 33% | 1 |
Rule | Support | Confidence | Accuracy | Uncertainty | Frequent Number |
---|---|---|---|---|---|
57% | 80% | 75% | 25% | 2 | |
57% | 80% | 67% | 33% | 2 | |
57% | 80% | 67% | 33% | 2 | |
57% | 67% | 67% | 33% | 2 | |
71% | 100% | 67% | 33% | 2 |
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Yang, Y.; Zhang, R.; Liu, B. Dynamic Parallel Mining Algorithm of Association Rules Based on Interval Concept Lattice. Mathematics 2019, 7, 647. https://doi.org/10.3390/math7070647
Yang Y, Zhang R, Liu B. Dynamic Parallel Mining Algorithm of Association Rules Based on Interval Concept Lattice. Mathematics. 2019; 7(7):647. https://doi.org/10.3390/math7070647
Chicago/Turabian StyleYang, Yafeng, Ru Zhang, and Baoxiang Liu. 2019. "Dynamic Parallel Mining Algorithm of Association Rules Based on Interval Concept Lattice" Mathematics 7, no. 7: 647. https://doi.org/10.3390/math7070647