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| (ns knn.distance)
(use '[knn.op :as op])
(use '[knn.norm :as norm])
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Util Function to be used to compute Bray Curtis Distance
Function between two vectors
| (defn- bray-curtis-distance-denominator
[first-vector second-vector]
(reduce + (map #(Math/abs (+ %1 %2)) first-vector second-vector)))
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Manhattan Distance between two vectors, called l_1 distance as well
Formula: sum(abs(x - y))
| (defn manhattan-distance
"Manhattan Distance between two vectors, called l_1 distance as well\n
Formula: sum(abs(x - y))"
[first-vector second-vector]
(reduce + (map #(Math/abs (- %1 %2)) first-vector second-vector)))
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Euclidean distance between two vectors
Formula: sqrt(sum((x - y) .^ 2))
| (defn euclidean-distance
"Euclidean distance between two vectors\n
Formula: sqrt(sum((x - y) .^ 2))"
[first-vector second-vector]
(Math/sqrt (reduce + (map #(Math/pow (- %1 %2) 2) first-vector second-vector))))
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Squared Euclidean Distance between two vectors
Formula: sum((x - y) .^ 2)
| (defn squared-euclidean-distance
"Squared Euclidean Distance between two vectors\n
Formula: sum((x - y) .^ 2)"
[first-vector second-vector]
(* (euclidean-distance first-vector second-vector) (euclidean-distance first-vector second-vector)))
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Minkowski Distance, known as l-p distance
Most Generic form of l-p distances, covers l_1(manhattan)
and l_2(euclidean distances) as well
Formula: sum(abs(x - y).^p) ^ (1/p)
| (defn minkowski-distance
"Minkowski Distance, known as l-p distance
Most Generic form of l-p distances, covers l_1(manhattan)
and l_2(euclidean distances) as well\n
Formula: sum(abs(x - y).^p) ^ (1/p)"
[first-vector second-vector p]
(Math/pow (reduce + (map #(Math/pow (Math/abs (- %1 %2)) p) first-vector second-vector)) (/ p)))
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Weighted Minkowski Distance, with different weights
on the difference between observations
Formula: sum(abs(x - y).^p .* w) ^ (1/p)
| (defn weighted-minkowski-distance
"Weighted Minkowski Distance, with different weights
on the difference between observations\n
Formula: sum(abs(x - y).^p .* w) ^ (1/p)"
[first-vector second-vector weight-vector p]
(Math/pow
(reduce + (map #(* (Math/pow (Math/abs (- %1 %2)) p) %3) first-vector second-vector weight-vector))
(/ p)))
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Chebyshev Distance
It is a form of l_p distance when p -> /Infinity
Formula: max(abs(x - y))
| (defn chebyshev-distance
"Chebyshev Distance
It is a form of l_p distance when p -> /Infinity\n
Formula: max(abs(x - y))"
[first-vector second-vector]
(apply max (map #(Math/abs (- %1 %2)) first-vector second-vector)))
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Hamming Distance between two vectors
Formula: sum(x .!= y)
| (defn hamming-distance
"Hamming Distance between two vectors\n
Formula: sum(x .!= y)"
[first-vector second-vector]
(count
(filter true? (map #(not= %1 %2) first-vector second-vector))))
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Bray Curtis Distance Function
| (defn bray-curtis-distance
[first-vector second-vector]
(/ (manhattan-distance first-vector second-vector) (bray-curtis-distance-denominator first-vector second-vector)))
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Canberra Distance
| (defn canberra-distance
[first-vector second-vector]
(reduce + (map #(/ (Math/abs (- %1 %2)) (+ (Math/abs %1) (Math/abs %2))) first-vector second-vector)))
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Cosine distance between two vectors
Formula: 1 - dot(x, y) / (norm(x) * norm(y))
| (defn cosine-distance
"Cosine distance between two vectors\n
Formula: 1 - dot(x, y) / (norm(x) * norm(y))"
[first-vector second-vector]
(- 1 (/ (op/dot first-vector second-vector) (* (norm/euclidean-norm first-vector) (norm/euclidean-norm second-vector) ))))
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Correlation distance between two vectors
Formula: cosine-distance(x - mean(x), y - mean(y))
| (defn correlation-distance
"Correlation distance between two vectors\n
Formula: cosine-distance(x - mean(x), y - mean(y))"
[first-vector second-vector]
(cosine-distance (op/scalar-subtract first-vector (op/mean first-vector))
(op/scalar-subtract second-vector (op/mean second-vector))))
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Chi Squared Distance between two vectors
Formula: sum((x - y).^2 / (x + y))
| (defn chi-squared-distance
"Chi Squared Distance between two vectors\n
Formula: sum((x - y).^2 / (x + y))"
[first-vector second-vector]
(reduce + (map #(/ (* (- %1 %2) (- %1 %2) ) (+ %1 %2)) first-vector second-vector)))
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Kullback-Leibler Divergence of two vectors with a function
that is mapped to the ratio
| (defn- kl-div
[first-vector second-vector func]
(reduce + (op/mult first-vector (map func (op/div first-vector second-vector)))))
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Kullback-Leibler Divergence with a normal Log function
Formula: sum(p .* log(p ./ q))
| (defn kl-divergence
"Kullback-Leibler Divergence with a normal Log function\n
Formula: sum(p .* log(p ./ q))"
[first-vector second-vector]
(kl-div first-vector second-vector #(Math/log %)))
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JS Divergence of two vectors
Formula: KL(x, m) / 2 + KL(y, m) / 2 where
m = (x + y) / 2
| (defn js-divergence
"JS Divergence of two vectors\n
Formula: KL(x, m) / 2 + KL(y, m) / 2 where
m = (x + y) / 2"
[first-vector second-vector]
(let [m (op/scalar-div (op/add first-vector second-vector) 2)]
(+ (kl-divergence first-vector m) (kl-divergence second-vector m))))
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Span-norm distance between two vectors
Formula: max(x - y) - min(x - y)
| (defn span-norm-distance
"Span-norm distance between two vectors\n
Formula: max(x - y) - min(x - y)"
[first-vector second-vector]
(- (apply max (op/subtract first-vector second-vector)) (apply min (op/subtract first-vector second-vector))))
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Bhattacharyya Distance between two vectors
Formula: -log(sum(sqrt(x .* y) / sqrt(sum(x) * sum(y)))
| (defn bhattacharyya-distance
"Bhattacharyya Distance between two vectors\n
Formula: -log(sum(sqrt(x .* y) / sqrt(sum(x) * sum(y)))"
[first-vector second-vector]
(- (Math/log
(reduce + (map #(/ (Math/sqrt (* %1 %2)) (Math/pow (* (reduce + first-vector)
(reduce + second-vector)) 0.5)) first-vector second-vector)))))
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| (defn hellinger-distance
[first-vector second-vector]
(Math/pow (- 1.0 (reduce + (map #(/ (Math/sqrt (* %1 %2)) (Math/pow (* (reduce + first-vector)
(reduce + second-vector)) 0.5)) first-vector second-vector))) 0.5))
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