= Kernel support vector machine
A kernel support vector machine trains a <support vector machine> using a <positive-definite kernel> instead of explicit feature coordinates. The <kernel trick> evaluates all required feature inner products through the training <Gram matrix>; prediction is $\sum_i\alpha_i y_i k(x_i,x)+b$. Nonzero dual coefficients identify <support vectors>. An unpenalized intercept supplies the dual equality $\sum_i\alpha_i y_i=0$. The <Reproducing-kernel Hilbert space> construction explains why a positive-semidefinite kernel defines valid feature geometry.
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