Normalized Hamming distance

The literature also mentions a normalized Hamming distance, which is then equal to either ... 

The Hamming distance has some disadvantages for vectors with only a few components containing 1 s. An alternative is the Tanimoto distance which is a normalized Hamming distance C3983. 

A number of similarity metrics have been proposed for binary descriptors [6]. The most frequently used ones are the normalized Hamming distance ... 

The two master sequences have a Hamming distance d(l, 2) = 2. The normalized concentrations are then... 

In order to show that this procedure leads to acceptable results, reference is briefly made to the normal coordinate transformation mentioned at the end of Section 2.2. By this transformation the set of coordinates of junction points is transformed into a set of normal coordinates. These coordinates describe the normal modes of motion of the model chain. It can be proved that the lowest modes, in which large parts of the chain move simultaneously, are virtually uninfluenced by the chosen length of the subchains. This statement remains valid even when the subchains are chosen so short that their end-to-end distances no longer display a Gaussian distribution in a stationary system [cf. a proof given in the appendix of a paper by Ham (75)]. As a consequence, the first (longest or terminal) relaxation time and some of the following relaxation times will be quite insensitive for the details of the chain... 

The normalized distance is independent of the number of dimensions C1753 the Hamming and Tanimoto distances are suitable for binary encoded patterns C353, 356, 3573. 

---