There is one fact that the Mahalanobis distance measure is unable to overcome, though, and this is known as the curse of dimensionality. As the number of dimensions in a dataset rises, every point tends to become equally far from every other point. We can demonstrate this quite simply with the following code:
(defn ex-6-27 []
(let [distances (for [d (range 2 100)
:let [data (->> (dataset-of-dimension d)
(s/mahalanobis-distance)
(map first))]]
[(apply min data) (apply max data)])]
(-> (c/xy-plot (range 2 101) (map first distances)
:x-label "Number of Dimensions"
:y-label "Distance Between Points"
:series-label "Minimum Distance"
:legend true)
(c/add-lines (range 2 101) (map second distances)
:series-label "Maximum Distance...