Margins and Support Vectors

The Widest Gap

A separating line can put the two signs on different sides, but max-margin geometry asks for more: it measures the empty gap around the separator. This opening lesson shows only the signed rows so the later checks have a fixed source.

highlighted = computed this step

The signed rows

The displayed rows include (2, 2) with positive label 1 and (0, 0) with label -1.

shown signed rows only\text{shown signed rows only}
Signed SVM pointsOnly the exact signed points are shown.+A-B+C-D

Why the gap matters

Many lines can separate the two signs. The max-margin surface compares the empty gap around a chosen line, not just the side of each point.

separation plus margin geometry\text{separation plus margin geometry}
Signed SVM pointsOnly the exact signed points are shown.+A-B+C-D

Summary

No separator is drawn yet. The point diagram fixes the exact rows that later margin checks must reuse.

exact signed data fixed\text{exact signed data fixed}
Signed SVM pointsOnly the exact signed points are shown.+A-B+C-D