From c45544ed932dc7b513b0d9962c493b0222814fb4 Mon Sep 17 00:00:00 2001 From: Christoph Ruegg Date: Wed, 22 Jan 2014 01:36:49 +0100 Subject: [PATCH] Docs: distance metrics tweaks --- docs/content/Distance.fsx | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/docs/content/Distance.fsx b/docs/content/Distance.fsx index 0a781c02..7fbd8549 100644 --- a/docs/content/Distance.fsx +++ b/docs/content/Distance.fsx @@ -30,7 +30,7 @@ $$$ d_{\mathbf{SAD}} : (x, y) \mapsto \|x-y\|_1 = \sum_{i=1}^{n} |x_i-y_i| [lang=csharp] - double d = Distance.SAD(a, b); + double d = Distance.SAD(x, y); Sum of Squared Difference (SSD) @@ -45,7 +45,7 @@ $$$ d_{\mathbf{SSD}} : (x, y) \mapsto \|x-y\|_2^2 = \langle x-y, x-y\rangle = \sum_{i=1}^{n} (x_i-y_i)^2 [lang=csharp] - double d = Distance.SSD(a, b); + double d = Distance.SSD(x, y); Mean-Absolute Error (MAE) @@ -54,10 +54,10 @@ Mean-Absolute Error (MAE) The mean absolute error is a normalized version of the sum of absolute difference: $$$ -d_{\mathbf{MAD}} : (x, y) \mapsto \frac{d_{\mathbf{SAD}}}{n} = \frac{\|x-y\|_1}{n} = \frac{1}{n}\sum_{i=1}^{n} |x_i-y_i| +d_{\mathbf{MAE}} : (x, y) \mapsto \frac{d_{\mathbf{SAD}}}{n} = \frac{\|x-y\|_1}{n} = \frac{1}{n}\sum_{i=1}^{n} |x_i-y_i| [lang=csharp] - double d = Distance.MAE(a, b); + double d = Distance.MAE(x, y); Mean-Squared Error (MSE) @@ -69,7 +69,7 @@ $$$ d_{\mathbf{MSE}} : (x, y) \mapsto \frac{d_{\mathbf{SSD}}}{n} = \frac{\|x-y\|_2^2}{n} = \frac{1}{n}\sum_{i=1}^{n} (x_i-y_i)^2 [lang=csharp] - double d = Distance.MSE(a, b); + double d = Distance.MSE(x, y); Euclidean Distance @@ -81,7 +81,7 @@ $$$ d_{\mathbf{2}} : (x, y) \mapsto \|x-y\|_2 = \sqrt{d_{\mathbf{SSD}}} = \sqrt{\sum_{i=1}^{n} (x_i-y_i)^2} [lang=csharp] - double d = Distance.Euclidean(a, b); + double d = Distance.Euclidean(x, y); Manhattan Distance @@ -93,7 +93,7 @@ $$$ d_{\mathbf{1}} \equiv d_{\mathbf{SAD}} : (x, y) \mapsto \|x-y\|_1 = \sum_{i=1}^{n} |x_i-y_i| [lang=csharp] - double d = Distance.Manhattan(a, b); + double d = Distance.Manhattan(x, y); Chebyshev Distance @@ -105,7 +105,7 @@ $$$ d_{\mathbf{\infty}} : (x, y) \mapsto \|x-y\|_\infty = \lim_{k \rightarrow \infty}\bigg(\sum_{i=1}^{n} |x_i-y_i|^k\bigg)^\frac{1}{k} = \max_{i} |x_i-y_i| [lang=csharp] - double d = Distance.Chebyshev(a, b); + double d = Distance.Chebyshev(x, y); Minkowski Distance @@ -117,7 +117,7 @@ $$$ d_{\mathbf{p}} : (x, y) \mapsto \|x-y\|_p = \bigg(\sum_{i=1}^{n} |x_i-y_i|^p\bigg)^\frac{1}{p} [lang=csharp] - double d = Distance.Minkowski(p, a, b); + double d = Distance.Minkowski(p, x, y); Canberra Distance @@ -129,7 +129,7 @@ $$$ d_{\mathbf{Canberra}} : (x, y) \mapsto \sum_{i=1}^{n} \frac{|x_i-y_i|}{|x_i|+|y_i|} [lang=csharp] - double d = Distance.Canberra(a, b); + double d = Distance.Canberra(x, y); Pearson's Distance @@ -141,7 +141,7 @@ $$$ d_{\mathbf{Pearson}} : (x, y) \mapsto 1 - \mathbf{Corr}(x, y) [lang=csharp] - double d = Distance.Pearson(a, b); + double d = Distance.Pearson(x, y); Hamming Distance @@ -150,5 +150,5 @@ Hamming Distance The hamming distance represents the number of entries in the two sample vectors which are different. [lang=csharp] - double d = Distance.Hamming(a, b); + double d = Distance.Hamming(x, y); *)