{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "HF8AJZP6PG"
    }
  ],
  "body": "\n## Summary\n\nThe Mahalanobis distance measures how far a point lies from the centre of a multivariate distribution.\nIts units are adapted to the spread and the correlations of the distribution.\nIt is the [[Euclidean distance|0NPPGHQNXQ]] after the data are transformed so that the [[covariance matrix|0V7G6WMFK0]] becomes the identity.\nIt is used to detect outliers and in [[linear discriminant analysis|ZATS7NV9WD]].\nThe density of a [[multivariate normal distribution|0XN3K7RSZY]] is constant on the sets of constant Mahalanobis distance.\n\n## Explanations\n\n### L1 human\n\nA point that is two units from the mean is unusual in a direction where the data hardly vary, but ordinary in a direction where they vary a lot.\nThe Mahalanobis distance takes this into account by dividing each direction by its own spread.\nIts level sets are ellipses around the mean instead of circles.\nLet the first coordinate have variance $4$ and the second variance $1$, with no correlation.\nThen the points $(2, 0)$ and $(0, 1)$ are both at Mahalanobis distance $1$ from the origin.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "62H30",
      "62H20"
    ],
    "name": "Mahalanobis distance",
    "same_as": {
      "wikidata": "Q1334846",
      "wikipedia": "Mahalanobis distance"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Mahalanobis_distance"
      }
    ],
    "tag": "P546TSFBK2"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/P546TSFBK2/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/P546TSFBK2.md",
  "msc": [
    "62H30",
    "62H20"
  ],
  "name": "Mahalanobis distance",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/P54/P546TSFBK2.md",
  "status": null,
  "tag": "P546TSFBK2",
  "uri": "m2://P546TSFBK2",
  "url": "https://tamnd.github.io/math2/wiki/mahalanobis-distance/",
  "writing": {
    "tag": "P546TSFBK2",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}