MOTiFS: Monte Carlo Tree Search Based Feature Selection
Abstract
:1. Introduction
- The novel feature selection algorithm, MOTiFS, is proposed which combines the robustness of MCTS with the accuracy of wrapper methods.
- MOTiFS searches through the feature space efficiently and find the best feature subset within a few iterations, relatively.
- Only two hyper-parameters, scaling factor and termination criteria, are required to be tuned, making MOTiFS simple and flexible to handle.
- MOTiFS is tested on 25 benchmark datasets and results are also compared with other established methods. The promising results demonstrate the superiority of MOTiFS.
2. Literature Review
3. Background
3.1. Working Procedure of Monte Carlo Tree Search (MCTS)
- Selection: Starting from the root node, the algorithm traverses the tree by selecting nodes with the highest approximated values, until a non-terminal node with unexpanded children is reached.
- Expansion: A new child node is added to expand the tree, according to the available set of actions.
- Simulation: From the new child node, a random simulation is performed until the terminal node is reached, to approximate the reward.
- Backpropagation: The simulation result (reward) is backpropagated through the selected nodes to update the tree.
3.2. Upper Confidence Bounds for Trees (UCT) Algorithm
4. MOTiFS (Monte Carlo Tree Search Based Feature Selection)
- The root is , which means no features are selected.
- Any node at levelhas two children,and, where.
4.1. Feature Subset Generation
4.1.1. Selection
4.1.2. Expansion
4.1.3. Simulation
4.2. Reward Calculation and Backpropagation
Algorithm 1 The MOTiFS Algorithm |
Load dataset and preprocess Initialize SCALAR, BUDGET //Scaling factor & Number of MCTS simulations (hyper parameters) function MOTiFS (featuresList) create rootNode maxReward, bestFeatureSubset ← UCTSEARCH (rootNode) return (maxReward, bestFeatureSubset) function UCTSEARCH (rootNode) Initialize maxReward, bestFeatureSubset while within computational budget do frontNode ← TREEPOLICY (rootNode) reward, featureSubset ← DEFAULTPOLICY (frontNode.state) BACKUP (frontNode, reward) if reward is greater than maxReward then maxReward ← reward bestFeatureSubset ← featureSubset return (maxReward, bestFeatureSubset) function TREEPOLICY (node) while node is non-terminal do if node not fully expanded then return EXPAND (node) else node ← BESTCHILD (node, SCALAR) return node function EXPAND (node) choose a untried actions from A(node.state) add a newChild with f(node.state, a) return newChild function BESTCHILD (, ) return function DEFAULTPOLICY (state) while state is non-terminal do choose a A(state) uniformly at random state ← f(state, a) traverse state.path if ai is equal to fi+1 then featureSubset ← INCLUDE (fi+1) reward ← REWARD (featureSubset) return (reward, featureSubset) function BACKUP (node, reward) while node is not null do node.visits ← node.visits + 1 if reward > node.reward then node.reward ← reward node ← node.parent return |
5. Experiment and Results
5.1. Datasets
5.2. Experimental Procedure and Parameter Setup for MOTiFS
5.3. Comparison Methods
5.4. Results and Comparisons
5.5. Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Notation | Interpretation |
---|---|
Original feature set | |
Total number of features | |
Node at tree level | |
Action taken at | |
Simulation reward |
# | Dataset | No. of Features | No. of Instances | No. of Classes |
---|---|---|---|---|
1 | Spambase | 57 | 4701 | 2 |
2 | WBC | 9 | 699 | 2 |
3 | Ionosphere | 34 | 351 | 2 |
4 | Arrhythmia | 195 | 452 | 16 |
5 | Multiple features | 649 | 2000 | 10 |
6 | Waveform | 40 | 5000 | 3 |
7 | WBDC | 30 | 569 | 2 |
8 | Glass | 9 | 214 | 6 |
9 | Wine | 13 | 178 | 3 |
10 | Australian | 14 | 690 | 2 |
11 | German number | 24 | 1000 | 2 |
12 | Zoo | 17 | 101 | 7 |
13 | Breast cancer | 10 | 683 | 2 |
14 | DNA | 180 | 2000 | 2 |
15 | Vehicle | 18 | 846 | 4 |
16 | Sonar | 60 | 208 | 2 |
17 | Hillvalley | 100 | 606 | 2 |
18 | Musk 1 | 166 | 476 | 2 |
19 | Splice | 60 | 1000 | 2 |
20 | KRFP * | 4860 | 215 | 2 |
21 | Soybean-small | 35 | 47 | 4 |
22 | Liver disorders | 6 | 345 | 2 |
23 | Credit | 15 | 690 | 2 |
24 | Tic-tac-toe | 9 | 985 | 2 |
25 | Libras movement | 90 | 360 | 15 |
Parameter | Values Used for Different Datasets |
---|---|
Scaling factor, C | (0.1, 0.05, 0.02) |
Termination criteria | (500, 1000, 10,000) iterations |
Method | Description |
---|---|
SFS, SBS | Sequential Forward Selection and Sequential Backward Selection * [22] (2015) |
FS-FS | Feature Similarity Technique [49] (2002) |
FR-FS | Fuzzy Rule Based Technique [50] (2012) |
SFSW | An Evolutionary Multi-Objective Optimization Approach [22] (2015) |
DEMOFS | Differential Evolution Based Multi-Objective Feature Selection * [22] (2014) |
BA | Bat Algorithm and Optimum-Path Forest Based Wrapper Approach [26] (2014) |
PSO | Particle Swarm Optimization Based Method * [26] (2014) |
SCE, CCE | Shannon’s Entropy Reduction, Complementary Entropy Reduction * [39] (2016) |
PDE-2 | Partition Differential Entropy Based Method [39] (2016) |
Dataset | Avg. Acc. # Sel. Feat. | ||||||||
---|---|---|---|---|---|---|---|---|---|
MOTiFS | SFSW [22] | SFS [22] | SBS [22] | FS-FS [49] | FR-FS [50] | DEMOFS [22] | BA [26] | PSO [26] | |
Spambase | 0.907 ± 0.003 | 0.885 | 0.874 | 0.870 | 0.900 | ||||
31.5 | 26.0 | 35.7 | 37.3 | 29.0 | |||||
WBC | 0.968 ± 0.001 | 0.961 | 0.960 | 0.951 | 0.956 | ||||
5.52 | 4.2 | 6.4 | 7.3 | 4.0 | |||||
Ionosphere | 0.889 ± 0.007 | 0.883 | 0.887 | 0.859 | 0.788 | 0.844 | 0.780 | 0.790 | |
12.32 | 11.5 | 1.2 | 9.1 | 16.0 | 4.33 | 21.0 | 14.0 | ||
Arrhythmia | 0.650 ± 0.003 | 0.658 | 0.599 | 0.580 | 0.589 | ||||
94.4 | 100.0 | 89.4 | 49.2 | 100.0 | |||||
Multiple features | 0.980 ± 0.001 | 0.979 | 0.903 | 0.912 | 0.783 | ||||
321.84 | 270.0 | 210.0 | 305.0 | 325.0 | |||||
Waveform | 0.816 ±0.002 | 0.837 | 0.778 | 0.785 | 0.752 | ||||
19.42 | 16.0 | 18.4 | 18.3 | 20.0 | |||||
WBDC | 0.967 ± 0.004 | 0.941 | 0.901 | 0.898 | 0.936 | ||||
15.42 | 13.5 | 13.9 | 17.8 | 2.14 | |||||
Glass | 0.705 ± 0.003 | 0.678 | 0.631 | 0.636 | 0.615 | ||||
4.80 | 4.4 | 5.8 | 7.0 | 6.96 | |||||
Wine | 0.963 ± 0.004 | 0.961 | 0.914 | 0.914 | 0.955 | 0.897 | |||
7.52 | 6.9 | 6.0 | 7.5 | 4.38 | 6.0 | ||||
Australian | 0.850 ± 0.002 | 0.846 | 0.830 | 0.828 | 0.773 | ||||
6.98 | 4.7 | 3.7 | 3.0 | 4.0 | |||||
German number | 0.725 ± 0.008 | 0.713 | 0.682 | 0.658 | 0.701 | ||||
11.46 | 10.5 | 12.2 | 10.8 | 1.0 | |||||
Zoo | 0.920 ± 0.022 | 0.954 | 0.949 | 0.980 | 0.954 | ||||
9.06 | 11.0 | 9.0 | 13.0 | 11.0 | |||||
Breast cancer | 0.967 ± 0.003 | 0.965 | 0.951 | 0.949 | 0.940 | 0.930 | |||
6.14 | 4.3 | 6.10 | 6.10 | 5.0 | 5.0 | ||||
DNA | 0.810 ± 0.006 | 0.831 | 0.822 | 0.823 | 0.760 | 0.760 | |||
89.26 | 71.8 | 18.8 | 20.6 | 96.0 | 91.0 | ||||
Vehicle | 0.721 ± 0.008 | 0.653 | 0.686 | 0.673 | |||||
10.14 | 9.1 | 10.8 | 10.7 | ||||||
Sonar | 0.850 ± 0.002 | 0.827 | 0.729 | 0.786 | |||||
28.96 | 20.0 | 5.85 | 10.0 | ||||||
Hillvalley | 0.535 ± 0.003 | 0.575 | 0.605 | ||||||
45.18 | 40.0 | 26.0 | |||||||
Musk 1 | 0.852 ± 0.003 | 0.815 | 0.835 | ||||||
81.34 | 59.3 | 58.0 | |||||||
Splice | 0.778 ± 0.002 | 0.680 | 0.670 | ||||||
25.66 | 28.0 | 28.0 | |||||||
KRFP | 0.896 ± 0.001 | 0.842 * | 0.884 * | ||||||
2390.2 | 6.0 | 1866 |
Dataset | Avg. Acc. # Sel. Feat. | Avg. Acc. | ||
---|---|---|---|---|
MOTiFS | SCE [39] | CCE [39] | PDE-2 [39] | |
Soybean-small | 0.988 ± 0.015 | 1.000 | 1.000 | 1.000 |
12.18 | ||||
Liver-disorders | 0.645 ± 0.012 | 0.602 | 0.592 | 0.590 |
3.94 | ||||
Credit | 0.845 ± 0.007 | 0.646 | 0.654 | 0.659 |
8.22 | ||||
Tic-tac-toe | 0.794 ± 0.006 | 0.774 | 0.747 | 0.757 |
7.18 | ||||
Libras movement | 0.807 ± 0.011 | 0.538 | 0.552 | 0.554 |
44.94 |
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Chaudhry, M.U.; Lee, J.-H. MOTiFS: Monte Carlo Tree Search Based Feature Selection. Entropy 2018, 20, 385. https://doi.org/10.3390/e20050385
Chaudhry MU, Lee J-H. MOTiFS: Monte Carlo Tree Search Based Feature Selection. Entropy. 2018; 20(5):385. https://doi.org/10.3390/e20050385
Chicago/Turabian StyleChaudhry, Muhammad Umar, and Jee-Hyong Lee. 2018. "MOTiFS: Monte Carlo Tree Search Based Feature Selection" Entropy 20, no. 5: 385. https://doi.org/10.3390/e20050385