Fuzzy Hamming distance : A new dissimilarity measure

Many problems depend on a reliable measure of the distance or similarity between objects that, frequently, are represented as vectors. We consider here vectors that can be expressed as bit sequences. For such problems, the most heavily used measure is the Hamming distance, perhaps normalized. The value of Hamming distances is limited by the fact that it counts only exact matches, whereas in various applications, corresponding bits that are close by, but not exactly matched, can still be considered to be almost identical. We here define a fuzzy Hamming distance that extends the Hamming concept to give partial credit for near misses, and suggest a dynamic programming algorithm that permits it to be computed efficiently. We envision many uses for such a measure.