SKEDSOFT

Introduction:-The LVQ is a supervised learning procedure. A teaching input that tells the learning procedure whether the classification of the input pattern is right or wrong: In other words, we have to know in advance the number of classes to be represented or the number of codebook vectors.

The procedure of learning:-Learning works according to a simple scheme. We have (since learning is supervised)a set P of |P| training samples. Additionally, we already know that classes are predefined; too, i.e. we also have a set of classes C. A codebook vector is clearly assigned to each class. Thus, we can say that the set of classes |C| contains many codebook vectors C1, C2…C|C|. This leads to the structure of the training samples: They are of the form (p, c) and therefore contain the training input vector p and its class affiliation c. For the class affiliation c ϵ{1, 2, . . . , |C|}

Holds, which means that it clearly assigns the training sample to a class or a codebook vector.

The fundamental LVQ learning procedure:-

Initialization: We place set of codebook vectors on random positions in the input space.

Training sample: A training sample p of our training set P is selected and presented.

Distance measurement: We measure the distance ||p − C|| between all codebook vectors C1,C2, . . . ,C|C| and our input p.

Winter: The closest codebook vector wins, i.e. the one with

Learning process: The learning process takes place according to the rule

---(1)

--(2)

Which we now want to break down.

• We have already seen that the first factor ɳ(t) is a time-dependent learning rate allowing us to differentiate between large learning steps and fine tuning.
• The last factor (p − C_i)is obviously the direction toward which the codebook vector is moved.
•  But the function h(p,C_i)is the core of the rule: It implements a distinction of cases.

Assignment is correct: The winner vector is the codebook vector of the class that includes p. In this case, the function provides positive values and the codebook vector moves towards p.

Assignment is wrong: The winner vector does not represent the class that includes p. Therefore it moves away from p.Our definition of the function h was not precise enough. With good reason: From here on, the LVQ is divided into different nuances, dependent of how exactly h and the learning rate should be defined (called LVQ1, LVQ2, LVQ3,OLVQ, etc). The differences are, for instance, in the strength of the codebook vector movements. They are not all based on the same/.