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Distance on Numeric Data: Minkowski Distance

  • Minkowski distance: A popular distance measure

where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are two p-dimensional data objects, and h is the order (the distance so defined is also called L-h norm)

  • Properties
    • d(i, j) > 0 if i ≠ j, and d(i, i) = 0 (Positive definiteness)
    • d(i, j) = d(j, i) (Symmetry)
    • d(i, j) ≤ d(i, k) + d(k, j) (Triangle Inequality)
  • A distance that satisfies these properties is a metric

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