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  "body": "\n## Summary\n\nLinear discriminant analysis assigns an observation to one of several classes with a rule whose decision boundaries are hyperplanes.\nIt is the optimal rule when each class has a [[multivariate normal distribution|0XN3K7RSZY]] and all classes share one [[covariance matrix|0V7G6WMFK0]].\nIn practice the means and the common covariance are estimated from labelled data.\nIt is closely tied to Fisher's linear discriminant, which also gives a dimension reduction.\n\n## Explanations\n\n### L1 human\n\nTwo kinds of flowers differ on average in petal length and width, but the measurements overlap.\nLinear discriminant analysis draws a straight line through the plane of measurements and calls every flower on one side the first kind.\nThe line is placed using the class averages and the shared spread, measured by the [[Mahalanobis distance|P546TSFBK2]].\nFor one measurement with class means $-1$ and $1$, equal variances and equal sizes, the rule simply looks at the sign of the measurement.\n",
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