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Error-Correcting Codes for Multiclass Classification

  • Originally designed to correct errors during data transmission for communication tasks by exploring data redundancy
  • Example
    • A 7-bit codeword associated with classes 1-4  
    • Given a unknown tuple X, the 7-trained classifiers output: 0001010 
    • Hamming distance: # of different bits between two codewords
    • H( X , C1) = 5, by checking # of bits between [1111111] & [0001010]
    • H( X , C2) = 3, H( X , C3) = 3, H( X , C4) = 1, thus C4 as the label for X
  • Error-correcting codes can correct up to (h-1)/h 1-bit error, where h is the minimum Hamming distance between any two codewords
  • If we use 1-bit per class, it is equiv. to one-vs.-all approach, the code are insufficient to self-correct
  • When selecting error-correcting codes, there should be good row-wise and col.-wise separation between the codewords

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