Example 7.8 showed the use of error-correcting codes for a multiclass classification problem having four classes.

a. Suppose that, given an unknown tuple to label, the seven trained binary classifiers collectively output the codeword 0101110, which does not match a codeword for any of the four classes. Using error correction, what class label should be assigned to the tuple?

b. Explain why using a 4-bit vector for the codewords is insufficient for error correction.

Example 7.8. Multiclass classification with error-correcting codes. Consider the 7-bit codewords associated with classes C to C4 in Fig. 7.25. Suppose that, given an unknown tuple to label, the seven trained binary classifiers collectively output the codeword 0001010, which does not match a codeword for any of the four classes. A classification error has obviously occurred, but can we figure out what the classification most likely should be? We can try by using the Hamming distance, which is the number of different bits between two codewords. The Hamming distance between the output codeword and the codeword for C is 5 because five bits-namely, the first, second, third, fifth, and seventh-differ. Similarly, the Hamming distance between the output code and the codewords for C through C4 are 3, 3, and 1, respectively. Note that the output codeword is closest to the codeword for C4. That is, the FIGURE 7.25 Class Error-correcting codeword C C C3 C4 1111111 0000111 0011001 0101010