Recommendation Algorithm Based on Survival Action Rules
Abstract
:1. Introduction
- it is based on a global action model represented by survival action rules,
- recommendations for a specific instance are generated based on the fusion of information contained in the action model,
- the method can be applied to datasets containing numerical as well as categorical attributes,
- the algorithm uses a computationally efficient hill climbing strategy to search recommendations.
2. Related Work
3. Methods
3.1. Basic Notions
3.2. Survival Action Rule Induction
Algorithm 1 An action rule set induction algorithm for censored data. |
Require: —a dataset described by attributes A, observation time T, and survival status P—a set of input parameters —a set of stable attributes from the set A Ensure: R—a set of survival action rules
|
Algorithm 2 Specialization of the action rule in the survival analysis. |
Require: D—a dataset —a collection of examples that are not yet covered —the minimum number of examples that the new rule must cover — the maximum rule coverage —the maximum percentage of examples that can be covered by both the left and right rules —a set of stable attributes from the set A Ensure: r—the action rule
|
Illustrative Example
- The initial step involves searching for the best elementary condition to add to the left side of the rule (line 5 in Algorithm 2). In the first iteration, the condition achieves the highest score. This condition is considered the best because it has the largest log-rank test value when comparing the survival curve where with the curve where (panel A in Figure 2).
- The identified elementary condition is then added to the set of previously tested conditions (line 6 in Algorithm 2).
- The best counter-condition is searched for (line 9 in Algorithm 2). In the first iteration, condition achieves the highest score. This condition is considered the best because it has the largest log-rank test value when comparing the survival curve where with the curve where (panels A and C in Figure 2).
- An action , where denotes the Kaplan–Meier estimate for examples that fulfill the condition , is created from the condition and the counter-condition (line 10 in Algorithm 2). This action is then added to the premise of the rule (line 11 in Algorithm 2).
- The initial step involves searching for the best elementary condition to add to the left side of the rule (line 5 in Algorithm 2). In the second iteration, the condition achieves the highest score. This condition is considered the best because it has the largest log-rank test value when comparing the survival curve where with the curve where (panel B in Figure 3).
- The identified elementary condition is then added to the set of conditions previously considered (line 6 in Algorithm 2).
- The best counter-condition is searched for (line 9 in Algorithm 2). In the second iteration, the condition achieves the highest score. This condition is considered the best because it has the largest log-rank test value when comparing the survival curve where with the curve where (panel B in Figure 4).
- An action is created from the condition and counter-condition (line 10 in Algorithm 2). This action is then added to the premise of the rule (line 11 in Algorithm 2).
3.3. Recommendation Induction
3.3.1. Meta-Table
3.3.2. Final Recommendation
4. Experiments and Results
- The XGBoost model is trained on the training data.
- For each test example x, the survival curve is determined, which represents the conclusion of the recommendation.
- The example is passed to the trained XGBoost model with attribute values modified according to the recommendation algorithm.
- The XGBoost model assigns the survival curve to the example .
- The difference between the curves and is examined; if the curves are not significantly different, then the rule action model is assumed to be working correctly.
4.1. Case Studies
4.1.1. Maintenance Dataset
- pressureInd
- moistureInd
- temperatureInd
- provider
- team
- time
- status
- number of conditions,
- number of actions,
- the percentage of all examples that the left part of the rule covers,
- the percentage of all examples that the right part of the rule covers,
- p-value of the log-rank test between the Kaplan–Meier curves of the left and right sides of the rule,
- median survival time for examples covered by the left rule (time for probability = ),
- median survival time for examples covered by the right rule,
- difference between the median survival times of the left side of the rule and the right side of the rule.
4.1.2. Comparative Study
Dataset
Detailed Example
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
BMI | Body Mass Index |
CF | counterfactual explanations |
KM | Kaplan–Meier |
RUL | survival action rules |
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1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | |
0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
Dataset | Miss | Cens | ||
---|---|---|---|---|
FD001 [61] | 100 | 24 | 0.00 | 19.00 |
FD002 [61] | 260 | 24 | 0.00 | 19.69 |
FD003 [61] | 100 | 24 | 0.00 | 20.00 |
FD004 [61] | 249 | 24 | 0.00 | 19.76 |
GBSG2 [62] | 686 | 8 | 0.00 | 56.41 |
melanoma [63] | 205 | 7 | 0.00 | 65.37 |
actg320 [64] | 1151 | 11 | 0.00 | 91.66 |
bmt-ch [65] | 187 | 35 | 1.24 | 54.55 |
follic [66] | 541 | 4 | 0.00 | 35.67 |
hd [66] | 865 | 6 | 0.00 | 50.75 |
lung [67] | 1032 | 7 | 2.60 | 25.97 |
maintenance [68] | 1000 | 3 | 0.00 | 19.00 |
mgus [69] | 241 | 9 | 19.59 | 23.65 |
pbc [70] | 418 | 17 | 14.54 | 61.48 |
std [71] | 877 | 21 | 0.00 | 60.43 |
uis [64] | 575 | 13 | 0.00 | 19.30 |
whas1 [64] | 481 | 7 | 0.00 | 48.23 |
whas500 [64] | 500 | 13 | 0.00 | 57.00 |
zinc [72] | 431 | 55 | 57.17 | 81.21 |
Dataset | |||||||||
---|---|---|---|---|---|---|---|---|---|
FD001 | 2.0 | 2.45 | 0.15 | 100 | 100 | 34.72 | 36.44 | 1.0 | 1.0 |
FD002 | 6.8 | 3.05 | 0.39 | 91 | 86 | 24.43 | 26.13 | 3.6 | 3.1 |
FD003 | 2.0 | 4.00 | 1.30 | 100 | 100 | 35.06 | 41.50 | 1.0 | 1.0 |
FD004 | 6.5 | 3.49 | 0.79 | 100 | 100 | 28.48 | 29.94 | 3.4 | 3.1 |
GBSG2 | 13.8 | 3.31 | 0.47 | 100 | 100 | 27.41 | 33.16 | 11.5 | 2.3 |
melanoma | 3.9 | 2.62 | 0.63 | 100 | 100 | 32.62 | 38.82 | 2.6 | 1.3 |
actg320 | 18.4 | 4.00 | 1.96 | 99 | 99 | 22.48 | 39.29 | 16.1 | 2.2 |
bmt-ch | 4.7 | 2.50 | 0.60 | 100 | 100 | 30.63 | 40.34 | 2.9 | 1.8 |
follic | 7.2 | 1.86 | 0.45 | 98 | 98 | 33.26 | 22.61 | 4.2 | 3.0 |
hd | 10.1 | 1.22 | 0.21 | 87 | 81 | 22.10 | 40.01 | 8.0 | 2.1 |
lung | 7.1 | 2.79 | 0.71 | 100 | 100 | 35.59 | 36.49 | 3.5 | 3.6 |
maintenance | 20.8 | 2.56 | 0.03 | 98 | 91 | 22.27 | 12.10 | 12.7 | 8.1 |
mgus | 4.1 | 3.27 | 0.91 | 100 | 100 | 31.00 | 21.63 | 2.8 | 1.3 |
pbc | 6.8 | 2.73 | 0.49 | 100 | 100 | 29.88 | 45.10 | 5.7 | 1.1 |
std | 15.1 | 4.18 | 2.10 | 100 | 100 | 23.72 | 28.36 | 7.4 | 7.7 |
uis | 8.0 | 3.49 | 1.55 | 100 | 100 | 26.80 | 45.86 | 7.0 | 1.0 |
whas1 | 6.9 | 2.52 | 0.07 | 100 | 100 | 27.58 | 34.88 | 4.9 | 2.0 |
whas500 | 7.9 | 4.33 | 0.43 | 100 | 100 | 29.33 | 33.44 | 6.6 | 1.3 |
zinc | 6.9 | 2.59 | 0.90 | 67 | 53 | 21.61 | 39.53 | 4.9 | 2.0 |
Dataset | Cs0.05 | Cs0.01 |
---|---|---|
FD001 | 80 | 66 |
FD002 | 97 | 95 |
FD003 | 93 | 86 |
FD004 | 98 | 95 |
GBSG2 | 100 | 100 |
melanoma | 100 | 100 |
actg320 | 96 | 96 |
bmt-ch | 100 | 100 |
follic | 100 | 99 |
hd | 100 | 100 |
lung | 100 | 100 |
maintenance | 92 | 84 |
mgus | 99 | 99 |
pbc | 100 | 100 |
std | 100 | 100 |
uis | 100 | 100 |
whas1 | 99 | 98 |
whas500 | 100 | 100 |
zinc | 100 | 100 |
Dataset | ||
---|---|---|
FD001 | 2.69 | 14.62 |
FD002 | 2.36 | 21.92 |
FD003 | 2.92 | 21.54 |
FD004 | 2.40 | 26.92 |
GBSG2 | 1.76 | 46.00 |
melanoma | 2.01 | 42.22 |
actg320 | 1.36 | 33.08 |
bmt-ch | 2.36 | 16.76 |
follic | 1.97 | 45.00 |
hd | 1.70 | 38.75 |
lung | 3.35 | 63.33 |
maintenance | 1.02 | 46.00 |
mgus | 2.21 | 35.45 |
pbc | 1.68 | 19.47 |
std | 3.22 | 49.57 |
uis | 2.65 | 33.33 |
whas1 | 1.18 | 42.22 |
whas500 | 1.82 | 29.33 |
zinc | 1.29 | 3.51 |
Number of examples | 900 |
Minimum number of examples covered by rule | 30 |
Stable attributes | None |
Number of rules | 23 |
Number of rules without any action in premise | 0 |
Conditions count | 63 |
Actions count | 63 |
Average conditions per rule | 2.74 |
Average actions per rule | 2.74 |
Percent of examples covered by left and right rules | 66.67 |
Percent of examples covered by left rule | 94.78 |
Percent of examples covered by right rule | 67.11 |
Id | Premise |
---|---|
r1 | (pressureInd, [103.79, 143.68) → (-inf, 95.80)) ∧ (temperatureInd, [45.46, 123.85) → [86.05, 106.59)) ∧ (moistureInd, [75.70, inf) → [94.84, inf)) |
r2 | (pressureInd, [103.79, 135.02) → [75.67, 96.13)) ∧ (temperatureInd, (-inf, 160.28) → (-inf, 106.59)) ∧ (moistureInd, [89.64, inf) → ANY) |
r3 | (pressureInd, [101.14, inf) → [36.36, 96.13)) ∧ (temperatureInd, [71.62, 116.04) → [86.05, 106.60)) ∧ (moistureInd, [76.57, inf) → [88.97, inf)) |
r4 | (pressureInd, [100.32, inf) → (-inf, 96.13)) ∧ (temperatureInd, (-inf, 132.94) → (-inf, 106.59)) |
Id | p | ||||||||
---|---|---|---|---|---|---|---|---|---|
r1 | 3 | 3 | 0 | 33.11 | 12.89 | 0.00 | 56.00 | 67.00 | −11.00 |
r2 | 3 | 3 | 1 | 30.33 | 21.44 | 0.00 | 56.00 | 65.00 | −9.00 |
r3 | 3 | 3 | 0 | 31.89 | 15.67 | 0.00 | 56.00 | 66.00 | −10.00 |
r4 | 2 | 2 | 0 | 42.89 | 28.00 | 0.00 | 58.00 | 65.00 | −7.00 |
Id | Recommendation |
---|---|
73 | (temperatureInd, (79.57, 85.54] → (45.46, 106.14]) ∧ (moistureInd, (106.22, 110.00] → (112.84, 114.75]) |
74 | (temperatureInd, (86.82, 106.14] → (85.54, 86.82]) |
75 | (temperatureInd, (61.19, 68.84] → (70.81, 160.28]) ∧ (moistureInd, (94.84, 99.71] → (94.21, 94.83]) |
76 | (temperatureInd, (106.64, 108.03] → (85.54, 86.82]) |
PressureInd | MoistureInd | TemperatureInd | Time | Status |
---|---|---|---|---|
57.46 | 104.98 | 100.53 | 12 | 1 |
Method | p-Value ≤ 0.05 |
---|---|
recommendation algorithm | 60.8 |
counterfactuals () | 81.1 |
counterfactuals () | 74.7 |
Method | Execution Time |
---|---|
recommendation algorithm | 00:03:36 |
counterfactuals | 03:16:07 |
((temperatureInd, (86.82, 106.14) → (temperatureInd, (85.54, 86.82)) |
PressureInd | MoistureInd | TemperatureInd |
---|---|---|
57.46 | 104.98 | 86.25 |
PressureInd | MoistureInd | TemperatureInd |
---|---|---|
70.11 | 103.78 | 98.84 |
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Hermansa, M.; Sikora, M.; Sikora, B.; Wróbel, Ł. Recommendation Algorithm Based on Survival Action Rules. Appl. Sci. 2024, 14, 2939. https://doi.org/10.3390/app14072939
Hermansa M, Sikora M, Sikora B, Wróbel Ł. Recommendation Algorithm Based on Survival Action Rules. Applied Sciences. 2024; 14(7):2939. https://doi.org/10.3390/app14072939
Chicago/Turabian StyleHermansa, Marek, Marek Sikora, Beata Sikora, and Łukasz Wróbel. 2024. "Recommendation Algorithm Based on Survival Action Rules" Applied Sciences 14, no. 7: 2939. https://doi.org/10.3390/app14072939