Support Vector Machines: An Introduction by de Almeida Marcelo Barros

Author:de Almeida, Marcelo Barros [de Almeida, Marcelo Barros]
Language: eng
Format: epub
Published: 2015-01-17T16:00:00+00:00

The gradient ascent method, using an initial estimation of the Lagrange multipliers, updates one Lagrange multiplier per turn. Due to the convexity of the problem, at each iteration, the objective function is monotonically increased, until its maximum is reached.

Consider the following quadratic function

(4.1)

and suppose that α N is the next Lagrange multiplier to be optimized. Separating α N , last equation can be rewritten as:

(4.2)

where K ij = K (x i , x j ).

Grouping all constant terms in , Equation 4.2 becomes

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