Learning the Mean Vector

Suppose that we have a collection of n examples, all from the same class. Then if the feature vectors for these examples are { x(1), x(2), ... , x(n) }, the obvious way to estimate the mean vector m is by averaging:

m(n) = [ x(1) + x(2) + ... + x(n) ] / n .

In some applications, new examples regularly appear, and we can improve our estimate of m by including this new data. Since n m(n) is the sum of the first n examples, the sum of the first (n+1) examples is n m(n) + x(n+1). Dividing by n+1, we obtain the following useful recursive formula for sequential learning* of the mean:

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