1. Multi-Valued Neuron with Sigmoid Activation Function Shin-Fu Wu 2013/6/21

2. MVN-sig Review 

3. Outlines  Stopping Criteria  Parameter C  Learning Rule for Parameter C  Simulation Results  Binary Classification  MVN-P approach  Simulation Results  Complex-output Model  Model Architecture  Simulation Results  Future Work

4. Stopping Criteria 

5. Training acc. - EpochSquared error - Epoch

6. Training acc. - EpochSquared error - Epoch

7. Training acc. - EpochSquared error - Epoch

8. Parameter C 

9. Simulation Results  Wine Dataset MVN EpochSec.Acc. 38.60.213793.39 43.60.227595.52 31.40.183592.80 35.20.206493.28 35.80.202793.50 36.920.206893.698 MVN-sig (C=5) EpochSec.Acc. 92.61.739992.80 80.41.082294.34 650.435195.04 550.597494.34 94.41.593694.93 77.481.089694.29 MVN-sig (learned C) EpochSec.Acc. 83.80.384393.75 540.278892.21 60.40.281693.28 101.81.373591.04 1231.031691.51 84.60.669992.358

10. Simulation Results  Glass Identification Dataset MVN EpochSec.Acc. 101.40.588689.69 96.60.556189.69 101.80.566689.69 118.80.625189.21 109.20.595489.21 105.560.586489.50 MVN-sig (C=5) EpochSec.Acc. 226.81.731792.59 254.21.541892.15 148.62.178292.55 2792.164792.03 305.85.481590.17 242.882.619691.90 MVN-sig (learned C) EpochSec.Acc. 873.45.785591.12 512.44.541992.11 3853.158093.93 20659138.0593.50 1385138.4290.64 7256.237.9992.26

11. Binary Classification  MVN-P approach  k=2, l=2, m=k*l=4  About 10% worse than MVN-P … WHY?

12. Simulation Results MVN-PMVN-sig-P Breast Cancer96.14%89% ~ 95.94% Parkinson's89.19%68.51% ~ 82.35% heart76.78%59.52% ~ 73.04%

13. Complex-output Model 

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16. Simulation Results  Wine Dataset MVN EpochSec.Acc. 38.60.213793.39 43.60.227595.52 31.40.183592.80 35.20.206493.28 35.80.202793.50 36.920.206893.698 MVN-sig (C=5) EpochSec.Acc. 92.61.739992.80 80.41.082294.34 650.435195.04 550.597494.34 94.41.593694.93 77.481.089694.29 Complex MVN-sig (C=5) EpochSec.Acc. 56.21.412095.52 68.41.201095.52 151.41.316894.57 67.21.324095.52 520.806394.34 79.041.212095.094

17. Simulation Results  Iris Dataset MVN (96% trained) EpochSec.Acc. 9.40.048194.00 10.40.053293.33 9.60.053391.33 11.60.058193.33 80.045194.00 9.80.051693.20 MVN-sig (C=5) EpochSec.Acc. 6.60.027396.00 17.40.073893.33 9.80.032396.00 14.20.080297.33 10.40.047692.67 11.680.052295.066 Complex MVN-sig (C=5) EpochSec.Acc. 29.80.569796.00 150.240696.00 33.80.620495.33 16.20.132196.67 20.40.177095.33 23.040.348095.87

18. Future Works  Synthetic Data Analysis  Why the binary classification failed?  Why this model is feasible?  Regression Problem  How to solve regression problems?  Multilayer Structure  Construct MLMVN using complex-output MVN-sig  How to choose the activation functions in the hidden layer?