Hamming resemblance

The Hamming similarity (after Richard Hamming ) is a rudimentary similarity measure that is used in machine case - based reasoning . It is used to determine the degree of similarity between two cases (e.g. clinical pictures, legal cases, business management). If the similarity between two cases is great, the solution of one case can also be used in the other. One can therefore search for a case that is as similar as possible for a given case by means of the Hamming similarity in a case base.

The Hamming similarity is based on the Hamming distance . One can imagine that the individual thereby bits which are compared in determining the Hamming distance, features constitute a case, each of the expression  0 or 1, or another bivalent can accept expression. If the Hamming distance is related to the number of features, the Hamming similarity is obtained, which represents a rough measure of the similarity of the two cases under consideration (in the features under consideration). Formally, one writes x and y with n features for two cases:

${\displaystyle \mathrm {Hamming{-}Aehnlichkeit} (x,y)=1-{\frac {\mathrm {Hamming{-}Distanz} (x,y)}{n}}}$

A variant of the Hamming similarity works with weighting of the individual features. This takes into account that some features may be more important than others. Instead of setting the Hamming distance in relation to the number of features as above, individual weights are added up for each feature. We speak of weighted Hamming similarity : ${\displaystyle w_{i}}$

${\displaystyle \mathrm {Hamming{-}Aehnlichkeit} ^{\mathrm {gewichtet} }(x,y)=1-{\frac {\sum _{i=1}^{n}w_{i}\mathrm {Hamming{-}Distanz} (x_{i},y_{i})}{\sum _{i=1}^{n}w_{i}}}}$

As can be seen, the Hamming similarity can only be used as a measure of similarity if the features can only assume two different values. However, the method can be generalized and then also used for any feature values.

literature

• Christoph Beierle, Gabriele Kern-Isberner: Methods of knowledge-based systems. Basics - Algorithms - Applications, 5th edition, Springer Fachmedien, Wiesbaden 2014, ISBN 978-3-8348-1896-6 .
• Martin Werner: Information and Coding. Basics and Applications, 2nd edition, Vieweg + Teubner Verlag, Wiesbaden 2008, ISBN 978-3-8348-0232-3 .

Web links

• Hamming Codes (accessed February 16, 2018)
• Intelligent Systems Case-Based Closing (accessed February 16, 2018)
• Web Application Hashing (accessed February 16, 2018)