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spearman.cljc
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spearman.cljc
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;; The MIT License (MIT)
;;
;; Copyright (c) 2016 Richard Hull
;;
;; Permission is hereby granted, free of charge, to any person obtaining a copy
;; of this software and associated documentation files (the "Software"), to deal
;; in the Software without restriction, including without limitation the rights
;; to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
;; copies of the Software, and to permit persons to whom the Software is
;; furnished to do so, subject to the following conditions:
;;
;; The above copyright notice and this permission notice shall be included in all
;; copies or substantial portions of the Software.
;;
;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
;; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
;; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
;; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
;; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
;; OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
;; SOFTWARE.
(ns clustering.distance.spearman
"The Spearman correlation coefficient is defined as the Pearson correlation
coefficient between the ranked variables.
See: https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient"
(:require
[clustering.distance.common :refer :all]))
(defn rank-by [key data]
(map #(assoc %1 (keyword (str "rank-" (name key))) %2)
(sort-by key data)
(iterate inc 1)))
(defn correlation-coefficient [xs ys]
(let [n (count xs)
sum-d-sqr (->>
(map #(hash-map :x %1 :y %2) xs ys)
(rank-by :y)
(rank-by :x)
(map #(sqr (- (:rank-x %) (:rank-y %))))
sum)]
(if (zero? n)
0
(- 1 (/ (* 6 sum-d-sqr) (* n (dec (sqr n))))))))