A very, very brief LVQ tutorial

Since the LVQ approach isn't really covered by the book, this is a very brief and informal tutorial on how the method can be implemented. Note, that there are several variations of LVQ around, and this is just one very simple version. So if you've found something that behaves a bit differently, don't worry. :)

A basic Learning Vector Quantization (LVQ) approach may be defined as:

Take m_i prototype vectors (also often called codebook vectors). There may be one or more prototype vectors per class, usually more than one is used.
Let c = arg min(||x - m_i||) define the nearest m_i to an input vector x, denoted by m_c. When classifying, x is usually taken to belong to the class of it's nearest prototype vector, but m_c is also used in the learning phase.
Now the learning proceeds (with modifying only the nearest prototype m_c(t) for the input x(t) each step t) as in
m_c(t + 1) = m_c(t) + alpha(t)[x(t) - m_c(t)],
if x and m_c belong to the same class

m_c(t + 1) = m_c(t) - alpha(t)[x(t) - m_c(t)],
if x and m_c belong to different classes.
0 < alpha(t) < 1 is the learning coefficient. It may be constant or decrease monotonically with time. For example in the lvq_pak LVQ1, an alpha initially smaller than 0.1 and decreasing linearly with time is used.
The iteration is generally stopped either after a predefined number of steps, when alpha(t) reaches its minumum value or when a desired training set error rate is reached.