Semi-supervised Learning

The same labeled and unlabeled samples shown with two illustrative decision boundaries. The first uses only the labeled examples; the second follows low-density structure revealed by the unlabeled samples. A legend distinguishes samples and boundaries, and the caption states the required cluster assumption.

Gray samples are displayed in both panels for comparison but only inform the second boundary. This assumes that nearby, densely connected samples tend to share a class. Unlabeled data can hurt when that assumption fails; the boundaries are illustrative, not fitted model results.

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Code

semi-supervised-learning.typ (102 lines)

#import "@preview/cetz:0.5.2": canvas, draw
#import draw: circle, line, rect
#set page(width: 660pt, height: auto, margin: 20pt, fill: none)
#set text(font: "Avenir Next", size: 14pt, fill: rgb("#19324f"))
#set par(leading: 0.55em)
#let panel = block.with(
  width: 100%,
  inset: 12pt,
  radius: 7pt,
  fill: rgb("#cdd3da"),
  breakable: false,
)

#let samples = (
  (4.7, 0.1),
  (5.2, 0.1),
  (5.1, -.3),
  (5.6, -.33),
  (5.4, -.7),
  (5.8, -.9),
  (5.9, -1.3),
  (6.4, -1.2),
  (6.9, -1.1),
  (7.4, -1.3),
  (7.45, -1.7),
  (7.8, -1.5),
  (8.2, -1.4),
  (8.3, -1.0),
  (8.6, -1.3),
  (6.1, .8),
  (5.7, .9),
  (5.8, 1.3),
  (5.4, 1.15),
  (5, 1.2),
  (4.8, 1.5),
  (4.3, 1.6),
  (4.2, 1.2),
  (3.8, 1.3),
  (3.4, 1.3),
  (3.4, .8),
  (3.1, 1.1),
  (2.75, .7),
  (2.45, .1),
  (2.35, .45),
  (1.9, -.04),
  (1.85, -.5),
)

#let labeled_samples = (((4.5, .5), red), ((6.5, .5), blue))
#let example(use_unlabeled: false) = canvas(length: 30pt, {
  // Shared bounds keep the same samples aligned in both panels.
  rect((1.2, -2.2), (9.2, 2.2), stroke: none)
  let gray_dot = rgb("#7c858e")
  if use_unlabeled {
    line(
      (1.5, -1),
      (2, -.866),
      (2.5, -.5),
      (3, 0),
      (3.5, .5),
      (4, .866),
      (4.5, 1),
      (5, .866),
      (5.5, .5),
      (6, 0),
      (6.5, -.5),
      (7, -.866),
      (7.5, -1),
      (8, -.866),
      (8.5, -.5),
      (9, 0),
      stroke: (paint: rgb("#19324f"), dash: "dashed", thickness: 1.4pt),
    )
  } else {
    line((5.5, 2), (5.5, -2), stroke: (paint: rgb("#19324f"), dash: "dashed", thickness: 1.4pt))
  }
  for point in samples { circle(point, radius: .15, fill: gray_dot, stroke: none) }
  for (point, color) in labeled_samples { circle(point, radius: .16, fill: color, stroke: none) }
})
#grid(
  columns: (1fr, 1fr),
  gutter: 12pt,
  ..(
    ([1  Labeled data only], false, [Gray samples ignored.]),
    ([2  Include unlabeled data], true, [Boundary follows the low-density gap.]),
  ).map(((title, use_unlabeled, caption)) => panel[
    #text(size: 16pt, weight: "bold", title)
    #v(10pt)
    #align(center, example(use_unlabeled: use_unlabeled))
    #v(8pt)
    #align(center, caption)
  ]),
)
#v(12pt)
#block(
  width: 100%,
  inset: 10pt,
  radius: 5pt,
  fill: rgb("#c6d8d2"),
  breakable: false,
)[Red / blue: labeled · Gray: unlabeled · Dashed: boundary\ Assumption: connected clusters tend to share a class.]