A Set Theoretic Framework for Unsupervised Preprocessing and Power Consumption Optimisation in IoT-Enabled Healthcare Systems for Smart Cities
Abstract
1. Introduction
2. Background
2.1. Related Work
Algorithm 1 Apriori Algorithm for Minimum Support |
procedure Input: : Candidate item set of size k //set of electronic device. Output: : frequent item set of size k //electronic device in candidate item set. Initialise: • ; // initialise set of frequencies items • REPEAT • //generates a new candidate REPEAT • // transaction in T, database subgroups of electronic device • do begin // this function generates candidates in transaction // for all candidates • do begin //determine support • end // new set • end UNTIL , UNTIL , OUTPUT END end procedure |
2.2. Principal Component Analysis for Smart Digital Devices
2.3. Independent Component Analysis
2.4. Pushdown Automaton
2.5. Gauss–Seidel
Algorithm 2 Algorithm for mining the dataset |
procedure Input: : Candidate set items m of size n, and initial guess Output: g: // REPEAT • // transaction in T, database subgroups of electronic device • // transaction in T, database subgroups of electronic device • // transaction in T, database subgroups of electronic device •if then // • endif // new set • endfor • endfor UNTIL , OUTPUT g END end procedure |
3. Methodology
4. Proposed Framework for Power Optimisation in Healthcare Devices
5. Case Study: IoT-Based Power Optimisation in Healthcare
5.1. Proposed Framework for Dataset D0
5.2. Proposed Framework for Dataset D1
5.3. Proposed Framework for Dataset D2
5.4. Proposed Framework for Dataset D3
5.5. Proposed Framework for Dataset D4
6. Result and Discussion
7. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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RID | Devices Sequence | A | L | F | T |
---|---|---|---|---|---|
ALFTAA | 3 | 1 | 1 | 1 | |
AFLLLT | 1 | 3 | 1 | 1 | |
LFFTTL | 0 | 2 | 2 | 2 | |
TALTF | 1 | 1 | 1 | 2 |
Rules | Confidence | Result Status |
---|---|---|
: | 4/4 = 100% | Selected |
: | 4/5 = 80% | Selected |
: | 4/5 = 80% | Selected |
: | 4/5 = 80% | Selected |
: | 4/7 = 57.14% | Rejected |
: | 4/6 = 66.67% | Rejected |
… | … | … |
Iteration | a | l | f | t |
---|---|---|---|---|
1 | 2.00000 | 1.34000 | 1.66000 | 0.00000 |
2 | 1.01000 | 1.11890 | 1.88110 | 0.49500 |
3 | 0.84665 | 0.93649 | 1.56851 | 0.82418 |
4 | 0.90137 | 0.91296 | 1.26286 | 0.96140 |
5 | 0.96472 | 0.94764 | 1.09096 | 0.99834 |
6 | 0.99781 | 0.98125 | 1.02040 | 1.00027 |
7 | 1.00937 | 1.00009 | 0.99965 | 0.99545 |
RID | Devices Sequence | A | L | F | T |
---|---|---|---|---|---|
ALTTA | 2 | 1 | 0 | 2 | |
TALLF | 1 | 2 | 1 | 1 | |
AFLFT | 1 | 1 | 2 | 1 | |
TALTT | 1 | 1 | 0 | 3 |
Rules | Confidence | Result Status |
---|---|---|
: | 4/4 = 100% | Selected |
: | 4/5 = 80% | Selected |
: | 4/4 = 100% | Selected |
: | 4/5 = 80% | Selected |
: | 4/5 = 80% | Selected |
: | 4/7 = 57.14% | Rejected |
… | … | … |
Iteration | A | L | F | T |
---|---|---|---|---|
1 | 2.50000 | 1.25000 | 0.62500 | 0.43250 |
2 | 1.44250 | 1.25000 | 0.93750 | 0.78147 |
3 | 1.09353 | 1.09375 | 1.01563 | 0.94820 |
4 | 1.00493 | 1.01563 | 1.01563 | 1.00322 |
5 | 0.98897 | 0.99609 | 1.00586 | 1.01493 |
6 | 0.98702 | 0.99609 | 1.00098 | 1.01557 |
RID | Devices Sequence | A | L | F | T |
---|---|---|---|---|---|
AALLTA | 3 | 2 | 0 | 1 | |
LAFLFT | 1 | 2 | 2 | 1 | |
LTALAF | 2 | 2 | 1 | 1 | |
LFTTAL | 1 | 2 | 1 | 2 |
Rules | Confidence | Result Status |
---|---|---|
: | 4/6 = 66.67% | Rejected |
: | 4/4 = 100% | Selected |
: | 4/5 = 80% | Selected |
: | 4/7 = 57.14% | Rejected |
: | 4/8 = 50% | Rejected |
: | 4/5 = 80% | Selected |
… | … | … |
Iteration | a | l | f | t |
---|---|---|---|---|
1 | 2.00000 | 1.00000 | 1.00000 | 0.50000 |
2 | 1.16500 | 1.08500 | 1.08250 | 0.79125 |
3 | 1.01194 | 1.05119 | 1.04722 | 0.91923 |
4 | 0.99236 | 1.02442 | 1.01979 | 0.96951 |
5 | 0.99370 | 1.01165 | 1.00675 | 0.98813 |
6 | 0.99611 | 1.00645 | 1.00143 | 0.99478 |
7 | 0.99740 | 1.00449 | 0.99942 | 0.99710 |
8 | 0.99795 | 1.00380 | 0.99868 | 0.99789 |
RID | Devices Sequence | A | L | F | T |
---|---|---|---|---|---|
TLAAFF | 2 | 1 | 2 | 1 | |
LLFTAT | 1 | 2 | 1 | 2 | |
FLFTLA | 1 | 2 | 2 | 1 | |
AFLFTT | 1 | 1 | 2 | 2 |
Rules | Confidence | Result Status |
---|---|---|
: | 4/4 = 100% | Selected |
: | 4/4 = 100% | Selected |
: | 4/4 = 100% | Selected |
: | 4/4 = 100% | Selected |
: | 4/5 = 80% | Selected |
: | 4/7 = 57.14% | Rejected |
: | 4/6 = 66.67% | Rejected |
: | 4/6 = 66.67% | Rejected |
… | … | … |
Iteration | a | l | f | t |
---|---|---|---|---|
1 | 3.00000 | 1.50000 | 0.00000 | 0.75000 |
2 | 1.87500 | 1.31250 | 0.37500 | 1.03125 |
3 | 1.45313 | 1.05469 | 0.70313 | 1.04297 |
4 | 1.24805 | 0.98145 | 0.87305 | 1.01221 |
5 | 1.13013 | 0.98621 | 0.94263 | 0.99921 |
6 | 1.06467 | 0.99715 | 0.97092 | 0.99818 |
7 | 1.03142 | 1.00065 | 0.98455 | 0.99942 |
8 | 1.01542 | 1.00060 | 0.99198 | 1.00001 |
9 | 1.00771 | 1.00014 | 0.99599 | 1.00008 |
RID | Devices Sequence | A | L | F | T |
---|---|---|---|---|---|
AFAFL | 2 | 1 | 2 | 0 | |
ALLLT | 1 | 3 | 0 | 1 | |
AFLFT | 1 | 1 | 2 | 1 | |
LFTAT | 1 | 1 | 1 | 2 |
Rules | Confidence | Result Status |
---|---|---|
: | 4/6 = 66.67% | Rejected |
: | 4/4 = 100% | Selected |
: | 4/5 = 80% | Selected |
: | 4/7 = 57.14% | Rejected |
: | 4/8 = 50% | Rejected |
: | 4/5 = 80% | Selected |
… | … | … |
Iteration | a | l | f | t |
---|---|---|---|---|
1 | 2.50000 | 0.84500 | 0.82750 | 0.41375 |
2 | 1.25000 | 1.12096 | 1.10764 | 0.76070 |
3 | 0.83188 | 1.14445 | 1.13149 | 0.94609 |
4 | 0.79629 | 1.09502 | 1.08130 | 1.01370 |
5 | 0.87119 | 1.04799 | 1.03356 | 1.02363 |
6 | 0.94244 | 1.02120 | 1.00637 | 1.01500 |
7 | 0.98304 | 1.01065 | 0.99566 | 1.00533 |
8 | 0.99902 | 1.00857 | 0.99354 | 0.99944 |
9 | 1.00217 | 1.00947 | 0.99446 | 0.99695 |
Digital Device Size | Time for PCA (ns) | Time for ICA (ns) |
---|---|---|
1000 | 1276 | 734 |
2000 | 1374 | 899 |
3000 | 1654 | 998 |
4000 | 2037 | 1076 |
5000 | 2787 | 1198 |
6000 | 3687 | 1489 |
7000 | 4798 | 1876 |
8000 | 5454 | 2054 |
9000 | 7512 | 2189 |
10,000 | 8765 | 2588 |
11,000 | 10,871 | 2821 |
12,000 | 13,345 | 3972 |
13,000 | 16,643 | 4065 |
14,000 | 17,754 | 4198 |
15,000 | 21,098 | 4778 |
16,000 | 26,654 | 5076 |
17,000 | 29,765 | 9654 |
18,000 | 37,452 | 120,876 |
Digital Device Size | Time for PCA (ns) | Time for ICA (ns) |
---|---|---|
1000 | 598 | 545 |
2000 | 612 | 567 |
3000 | 745 | 643 |
4000 | 1043 | 754 |
5000 | 1409 | 943 |
6000 | 1964 | 1078 |
7000 | 2375 | 1112 |
8000 | 3075 | 1399 |
9000 | 3478 | 1445 |
10,000 | 4375 | 1787 |
11,000 | 5276 | 1967 |
12,000 | 5976 | 2297 |
13,000 | 7182 | 2412 |
14,000 | 8954 | 2587 |
15,000 | 9912 | 2634 |
16,000 | 10,123 | 2876 |
17,000 | 10,654 | 3088 |
18,000 | 10,912 | 3378 |
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Share and Cite
Parvin, S.; Fahd, K. A Set Theoretic Framework for Unsupervised Preprocessing and Power Consumption Optimisation in IoT-Enabled Healthcare Systems for Smart Cities. Appl. Sci. 2025, 15, 9047. https://doi.org/10.3390/app15169047
Parvin S, Fahd K. A Set Theoretic Framework for Unsupervised Preprocessing and Power Consumption Optimisation in IoT-Enabled Healthcare Systems for Smart Cities. Applied Sciences. 2025; 15(16):9047. https://doi.org/10.3390/app15169047
Chicago/Turabian StyleParvin, Sazia, and Kiran Fahd. 2025. "A Set Theoretic Framework for Unsupervised Preprocessing and Power Consumption Optimisation in IoT-Enabled Healthcare Systems for Smart Cities" Applied Sciences 15, no. 16: 9047. https://doi.org/10.3390/app15169047
APA StyleParvin, S., & Fahd, K. (2025). A Set Theoretic Framework for Unsupervised Preprocessing and Power Consumption Optimisation in IoT-Enabled Healthcare Systems for Smart Cities. Applied Sciences, 15(16), 9047. https://doi.org/10.3390/app15169047