What is "dual form"

Question

I am reading up on AI and now read https://en.wikipedia.org/wiki/Kernel_perceptron

It says:

To derive a kernelized version of the perceptron algorithm, we must first formulate it in dual form, starting from the observation that the weight vector w can be expressed as a linear combination of the n training samples.

But what is "dual form"?

ististyle · Accepted Answer · 2019-07-20T16:12:23.583

0

The word "dual" is widely used throughout mathematics. The meaning of the word depends on the context, and usually refers to the object whose properties are reversed. In the above context, it means that the problem of finding $\mathbf{w}$ has been reversed to the problem of finding $\alpha$.

edited Jul 20 '19 at 16:12

answered Jul 20 '19 at 15:55

ististyle

460

Thank you. "Dual" here does not mean "two" but means "duality". Looking op duality in Wikipedia gives an additional explanation. – Paul Ogilvie Jul 20 '19 at 16:06
In mathematics, "dual" is an adjectival form of "duality". For example, in a matrix, the dual of a column vector is a row vector. It is duality of linear algebra. – ististyle Jul 20 '19 at 16:20

What is "dual form"

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