This animation derives the soft-margin SVM dual from its Lagrangian, showing how weights alpha_i obey 0<=alpha_i<=C and sum(alpha_i*y_i)=0. It visualizes the classifier as a kernel-weighted sum plus bias, highlighting nonzero-alpha samples. A worked two-point SMO example (x1=-1, x2=1) shows the dual objective 2a-2a^2 maximized over [0,1], comparing C=1 and C=0.25 cases, and clarifies that alpha=C does not imply misclassification. Suited for first-year AI students studying SVM optimization.
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# The SVM dual turns learning into weighted sample interactions Start from the soft-margin SVM objective and show how its Lagrangian leads to weights alpha_i satisfying 0 <= alpha_i <= C and sum(alpha_i*y_i)=0. The classifier becomes a weighted sum of kernel evaluations plus a bias, making nonzero-alpha samples visually prominent. Explain the dual objective as a balance between the sum of alphas and their pairwise kernel interactions. Demonstrate SMO's two-variable idea with two one-dimensional samples: x1=-1,y1=-1 and x2=1,y2=1. The equality constraint forces both alphas to equal a. With C=1, maximize 2a-2a squared over [0,1], obtaining a=.5, w=1, and b=0. If C=.25, the optimum is clipped to .25 and w becomes .5. Clarify that alpha=C does not automatically mean a sample is misclassified. Use black backgrounds, a readable one-dimensional objective curve, and synchronized constraint highlighting. Audience: 一年级人工智能专业学生