Final Report for CS5611 (Fuzzy Sets: Theory and Applications):

Input Selection of ANFIS, with Application to MPG Prediction

張智星 (mr830000, 資碩三)
陳俊傑 (mr844339, 資碩二)
吳志銘 (mr854306, 資碩一)

Table of Contents

Abstract	Problem Definition	Data Set Description	Our Approach
Simulation Results	Conclusions	Computer Programs	Division of labor
References

• Origin: This dataset was original from the StatLib library which is maintained at Carnegie Mellon University. Now that data set is also kept at UCI Machine Learning Repository. FTP access to the data set is via ftp://ftp.ics.uci.edu/pub/machine-learning-databases/auto-mpg/.
• Description: The data concerns city-cycle fuel consumption in miles per gallon (MPG), to be predicted in terms of 3 multivalued discrete and 5 continuous inputs. There are totally 398 instances, each with 8 inputs and 1 output:
  • Input 1: cylinders (multi-valued discrete)
  • Input 2: displacement (continuous)
  • Input 3: horsepower (continuous)
  • Input 4: weight (continuous)
  • Input 5: acceleration (continuous)
  • Input 6: model year (multi-valued discrete)
  • Input 7: origin (multi-valued discrete)
  • Input 8: car name (string, unique for each instance)
  • Output: MPG (continuous)
  There are 6 missing values in horsepower.
• Past Usage:
  1. The dataset was used in the 1983 American Statistical Association Exposition.
  2. The dataset was also used by Quinlan [Quinlan93] and Jang [Jang97].

• Data Preprocessing:
  • Data screening: Input-output pairs with missing values were eliminated and there remains 392 valid instances for NN training. Also input 8 was deleted from the data set since it is a unique string for each instance, which is not usable for NN training.
  • Input normalization: none.
  • Output normalization: All outputs are linearly normalized to [-1, 1].
  • Data reduction: none
  • Others: none
• Input selection: ...
• Data utilization:
  • Training data: Odd-indexed entries
  • Test data: Even-indexed entries
• ANFIS Structure:
  Describe your network architecture, such as
  • 2-input 4-rule ANFIS
  • 2-input 9-rule ANFIS
  • 3-input 8-rule ANFIS
  • 3-input 27-rule ANFIS
• Training method:
  Describe your training methods, such as
  • Vanilla backpropagation:
    • steepest descent: simple (or normalized)
    • eta: fixed at 0.1
    • alpha: fixed at 0.9
  • Enhanced backpropagation:
    • steepest descent: simple (or normalized)
    • eta: adaptive according to ...
    • alpha: adaptive according to ...
  • Gauss Newton method:
    • eta: adaptive according to ...
  • Levenberg Marquardt method:
    • eta: adaptive according to ...
    • lambda: adaptive according to ...
  • Genetic algorithms:
    • population size
    • crossover and mutation rate
    • number of generations
  • Simulated Annealing:
    • move set
    • cooling schedule
• Training Results:
  • Input selection plot:
    

    Input selection curves.

    
    
  • Training and test RMSE plot:
    

    Training and test RMSE curves.

    
    
  • Data distribution plot:
    

    Data distribution plot.

    
    
  • NN surface plot:
    

    NN's input/output surface.

    
    
  • Comparisons with other approaches:
    (Describe any other methods you tried on the data set.)
    • I also tried the simple linear regression method and found that it is slightly worse then the NN approaches but much faster...
  • Others:
    Describe any simulation details not covered above.
    

  Concluding Remarks and Future Work

  (Describe anything you want to say here.)
  • Concluding Remarks:
    (Describe your conclusion from your simulation.)
    NNs is useful because ...
    NNs is not really useful because ...
    
  • Future Work:
    (If you have more time and energy, what extension to your work might be interesting and potentially useful?)

  Computer Programs

  • All the computer programs (including C and MATLAB) for this project are available at: ftp://ftp.cs.nthu.edu.tw/pub/CS/papers/jang/public/select-input.tar.gz
  • Function of each program: ...
  • How to run my program: ...
  • Others: ...

  Division of Labor

  • 張智星: Project presentation, C coding
  • 陳俊傑: MATLAB Coding, simulation
  • 吳志銘: Software collection, report writing

  References

  • [Jang93] J.-S. R. Jang, `` ANFIS: Adaptive-Network-based Fuzzy Inference Systems,'' IEEE Trans. on Systems, Man, and Cybernetics, vol. 23, pp. 665-685, May 1993.
  • [Quinlan93] R. Quinlan, ``Combining Instance-Based and Model-Based Learning,'' in Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst, 1993.
  • [Jang97] J.-S. R. Jang, C.-T. Sun, and E. Mizutani, `` Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence,'' Prentice Hall, 1997.