As in all Boosting classifiers, the final classification function is of the form
where are non-negative weightings for weak classifiers . Each individual weak classifier may be just a little bit better than random, but the resulting linear combination of many weak classifiers can perform very well.
LPBoost constructs by starting with an empty set of weak classifiers. Iteratively, a single weak classifier to add to the set of considered weak classifiers is selected, added and all the weights for the current set of weak classifiers are adjusted. This is repeated until no weak classifiers to add remain.
The property that all classifier weights are adjusted in each iteration is known as totally-corrective property. Early Boosting methods, such as AdaBoost do not have this property and converge slower.
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