<Dl> <Dd> (1 n ∑ i = 1 n max (0, 1 − y i (w ⋅ x i − b))) + λ ‖ w ‖ 2 . (2) (\ displaystyle \ left ((\ frac (1) (n)) \ sum _ (i = 1) ^ (n) \ max \ left (0, 1 - y_ (i) (w \ cdot x_ (i) - b) \ right) \ right) + \ lambda \ lVert w \ rVert ^ (2). \ qquad (2)) </Dd> </Dl> <Dd> (1 n ∑ i = 1 n max (0, 1 − y i (w ⋅ x i − b))) + λ ‖ w ‖ 2 . (2) (\ displaystyle \ left ((\ frac (1) (n)) \ sum _ (i = 1) ^ (n) \ max \ left (0, 1 - y_ (i) (w \ cdot x_ (i) - b) \ right) \ right) + \ lambda \ lVert w \ rVert ^ (2). \ qquad (2)) </Dd> <P> We focus on the soft - margin classifier since, as noted above, choosing a sufficiently small value for λ (\ displaystyle \ lambda) yields the hard - margin classifier for linearly classifiable input data . The classical approach, which involves reducing (2) to a quadratic programming problem, is detailed below . Then, more recent approaches such as sub-gradient descent and coordinate descent will be discussed . </P> <P> Minimizing (2) can be rewritten as a constrained optimization problem with a differentiable objective function in the following way . </P>

Svm to implement the algorithm in high dimensional space