ftes / de.ftes.uon.comp6380.ha1

Q1 Variations of the Two-Spiral Task

a) Original Dataset

Steps

1. data obtained from http://wiki.cs.brynmawr.edu/?page=TwoSpiralsProblem
   1. version on blackboard did not contain class identifiers
   2. according to the code in the original paper, this seems to be the correct format
2. converted spaces to tabs
3. processed with Pybrain (pybrain-classify.py)
   1. followed tutorial
   2. used two binary output neurons (dataset._convertToOneOfMany(bounds=[0.,1.]))
   3. used ideas from Beherey et al.
      1. network layout: 2 hidden layers with 77 neurons each
      2. activation: tanh for hidden layers, linear for output
      3. RPROP as training algorithm, because it converges faster than back propagation

Result

• reproduce by running pybrain-classify.py
• visualization of final result not available (plot stopped responding)
  • 
• training error achieved after 5000 epochs: 0.52% (1 misclassified)
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b) Self-generated dataset

Steps

1. generated data set using algorithm in blackboard
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   1. far denser spirals
   2. 1920 (10x as many) data points
2. trained feed-forward net with same characteristics as in a) on new data

Result

• 10 times as many data points leads to longer training times per epoch
• faster conversion
  • zero classification errors after 598 epochs
  • 
• smoother learning curve
  • 

c) Four Spirals

Steps

1. adapted spiral generation script to generate two additional spirals (rotated 90 degrees against original ones)
   • 
2. trained feed-forward net with same characteristics as in a) (but 4 classes instead of only two) on new data

Result

• due to time constraints canceled training after 2000 epochs
  • classification error at this point: 28.42%
  • 
  • 
• up to this point promising: with enough time, the ANN should hopefully generalize

d) ANNs vs SVMs

General Discussion

• as discussed in class, SVMs can be seen as a generalisation of neural networks
  • with a good kernel, the spiral data can be transformed into a linearly separable form

Results

• as suggested in the background reading paper, we used radial basis function kernels
• far lower training times than ANNs for the spiral task