support vector machine
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A support vector machine separates two groups by drawing the boundary with the widest possible buffer between them. Imagine red and blue marbles scattered on a table, and you must draw a line splitting them. Many lines would work, but the SVM picks the one that leaves the largest empty margin on both sides — the line that keeps the nearest marbles of each color as far from it as possible. The intuition: a boundary with breathing room is more likely to hold up on marbles it hasn't seen.
Only a few points actually matter — the ones sitting right on the edge of the margin, closest to the other group. These are the "support vectors," and they alone pin the boundary in place; you could delete every other point and the line wouldn't move. That focus on the hardest, borderline cases is what gives the method its name and much of its robustness. A "soft margin" setting lets a few stubborn points sit on the wrong side, trading a perfect split for a boundary that generalizes better.
On its own an SVM draws a straight boundary, but paired with the kernel trick it can curve and twist to separate tangled data, which made it one of the most powerful classifiers of the 1990s and 2000s. It shines when you have many features but only modest amounts of data — text classification was a classic stronghold. Its limits: it can be slow to train on very large datasets, it doesn't naturally hand you probabilities, and choosing the kernel and its settings takes care. For huge image or language tasks, neural networks have since taken the crown.
Sorting emails into spam vs. real using two features. Hundreds of dots, two clusters with some overlap. The SVM ignores the comfortable middle of each cluster and obsesses over the few borderline emails between them — those support vectors fix the dividing line, with the widest gap they allow.
Only the borderline points — the support vectors — fix the widest-margin boundary.
The boundary is pinned only by the support vectors — the points hugging the margin — so most of your data has no direct effect on it. Without the kernel trick an SVM can only draw straight boundaries; that pairing is what gives it its curve-fitting power.