Margins and Support Vectors

The Margin Plot

The plot puts the separator, both margin lines, and support-vector marks in one scene. The geometry is recomputed from the same points, w, and b used by the table surface.

highlighted = computed this step

The full margin picture

The solid line is w·x+b=0. The dashed lines are w·x+b=plus-or-minus 1.

w⋅x+b∈{−1,0,1}w\cdot x+b\in\{-1,0,1\}
Margin plotHyperplane, margin lines, and support vectors share the same exact data.SVM margin geometryExact hyperplane and margin lines for the displayed separator.SV+ASV-B+C-Ddash: w·x+b=-1solid: w·x+b=0dash: w·x+b=1

Why the plot is locked

The plot and any SVM table share the same displayed points, w, and b. A mismatch is rejected before rendering.

same points, same w,b\text{same points, same }w,b
Margin plotHyperplane, margin lines, and support vectors share the same exact data.SVM margin geometryExact hyperplane and margin lines for the displayed separator.SV+ASV-B+C-Ddash: w·x+b=-1solid: w·x+b=0dash: w·x+b=1

Summary

The support-vector marks come from exact equality to the margin. Interior points have larger functional margin values.

support means equality at the margin\text{support means equality at the margin}
Margin plotHyperplane, margin lines, and support vectors share the same exact data.SVM margin geometryExact hyperplane and margin lines for the displayed separator.SV+ASV-B+C-Ddash: w·x+b=-1solid: w·x+b=0dash: w·x+b=1