{"id":2022,"date":"2019-10-17T22:59:44","date_gmt":"2019-10-17T13:59:44","guid":{"rendered":"http:\/\/141.164.34.82\/?p=2022"},"modified":"2019-10-18T14:09:20","modified_gmt":"2019-10-18T05:09:20","slug":"correlation-coefficient-and-euclidean-distance","status":"publish","type":"post","link":"http:\/\/ds.sumeun.org\/?p=2022","title":{"rendered":"\ub450 \ubcc0\uc218\uc758 \uc0c1\uad00\uacc4\uc218\uc640 \uc720\ud074\ub9ac\ub4dc \uac70\ub9ac"},"content":{"rendered":"<h2>Correlation coefficient and Euclidean distance<\/h2>\n<p>\uc774\uc0b0\ud655\ub960\ubcc0\uc218 \\(X\\) , \\(Y\\) \ub97c \uac00\uc815\ud558\ub2e4. \uc774\ub54c \\(X=x_i\\), \\(Y=y_i\\) \uc758 \ud655\ub960\uc740 \ubaa8\ub450 \\(1\/n\\) \uc73c\ub85c \uade0\uc77c\ud558\ub2e4\uace0 \uac00\uc815\ud574\ubcf4\uc790.<\/p>\n<p>\uadf8\ub9ac\uace0 \uc774\uc0b0\ud655\ub960\ubcc0\uc218 \\(X\\) \uc640 \\(Y\\) \ub97c \ubaa8\ub450 \ud3c9\uade0 \\(0\\), \ubd84\uc0b0 \\(1\\) \ub85c \ud45c\uc900\ud654\ud558\uc5ec, \uc0c8\ub85c\uc6b4 \ud655\ub960 \ubcc0\uc218 \\(X^*\\) \uc640 \\(Y^*\\) \uc744 \ub9cc\ub4e4\uc790.<\/p>\n<p>\\[X^* = \\frac{X-\\mu_X}{\\sigma_X}\\]<br \/>\n\\[x_i^* = \\frac{x_i-\\sum_i x_i \/n}{\\sum_i (x_i-\\sum_i x_i)^2 \/n}\\]<\/p>\n<p>\ud655\ub960\ubcc0\uc218 \\(Y\\) \ub3c4 \ub9c8\ucc2c\uac00\uc9c0\ub85c \ud45c\uc900\ud654\ud560 \uc218 \uc788\ub2e4. \uc774\ub54c \ud655\ub960\ubcc0\uc218 \\(X^*\\) \uc640 \\(Y^*\\) \uc758 \uc0c1\uad00\uacc4\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4. <\/p>\n<p>\\[\\text{r}(X,Y) = \\textrm{r}(X^*,Y^*) = \\frac{\\sum_i x_i^* y_i^*}{n}\\]<\/p>\n<p>\ubaa8\ub4e0 \\(x_i^*\\) \uc744 \ubaa8\ub450 \ud558\ub098\uc758 \ubca1\ud130\ub85c \ub098\ud0c0\ub0b4\uba74, \\(\\vec{x}^* = (x_1^*, x_2^*, \\cdots, x_n^*)\\) \uac00 \ub41c\ub2e4.<\/p>\n<p>\ub450 \ubca1\ud130 \\(\\vec{x}^*\\) \uc640 \\(\\vec{y}^*\\) \uc758 \uc720\ud074\ub9ac\ub4dc \uac70\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4. <\/p>\n<p>\\[\\textrm{d}(\\vec{x}^*, \\vec{y}^*) = \\sqrt{(x_1^*-y_1^*)^2 + ( x_2^*-y_2^*)^2 + \\cdots + (x_n^*-y_n^*)^2}\\]<\/p>\n<p>\uc880 \ub354 \uac04\ub2e8\ud788 \uc4f0\uba74,<\/p>\n<p>\\[\\textrm{d}(\\vec{x}^*, \\vec{y}^*)^2 = \\sum_i(x_i^*-y_i^*)^2 = \\sum_i({(x_i^*)}^2 &#8211; 2x_i^*y_i^*+{(y_i^*)}^2)\\]<\/p>\n<p>\uc5ec\uae30\uc11c \\(x_i^*\\) \uacfc \\(y_i^*\\) \ub294 \ubaa8\ub450 \ud3c9\uade0 0, \ubd84\uc0b0 1\ub85c \ud45c\uc900\ud654\ub418\uc5c8\uae30 \ub54c\ubb38\uc5d0, \\(\\sum_i x_i=0\\) \uadf8\ub9ac\uace0 \\(\\sum_i {(x_i^*)}^2=1\\) \uc774\ub2e4. \uc774\ub97c \uc801\uc6a9\ud574\uc11c \uc815\ub9ac\ud558\uba74, <\/p>\n<p>\\[\\textrm{d}(\\vec{x}^*, \\vec{y}^*)^2 = \\sum_i({(x_i^*)}^2 &#8211; 2x_i^* y_i^* + {(y_i^*)}^2) = 2 &#8211; 2 \\sum_i(x_i^* y_i^*)\\]<\/p>\n<p>\uc774\uc81c \uc55e\uc5d0\uc11c \uad6c\ud588\ub358 \uc0c1\uad00\uacc4\uc218 \uc2dd \\(\\textrm{r}(X^*,Y^*) = \\frac{\\sum_i x_i^* y_i^*}{n}\\) \uacfc \\(\\textrm{d}(\\vec{x}^*, \\vec{y}^*)^2 = 2 &#8211; 2 \\sum_i(x_i^* y_i^*)\\) \uc744 \uacf5\ud1b5 \ubd80\ubd84 \\(\\sum_i x_i^* y_i^*\\) \uc744 \ud1b5\ud574 \ud569\uccd0\ubcf4\uba74,<\/p>\n<p>\\[\\textrm{d}(\\vec{x}^*, \\vec{y}^*)^2 = 2 &#8211; 2 n \\textrm{r}(X^*,Y^*) = 2(1-n \\cdot \\textrm{r}(X^*,Y^*)).\\]<\/p>\n<p>\ub610\ub294 \ub2e4\uc74c\uc758 \uc2dd\uc744 \uc5bb\ub294\ub2e4.<\/p>\n<p>\\[\\textrm{r}(X^*,Y^*) = 1-\\frac{\\textrm{d}(\\vec{x}^*, \\vec{y}^*)^2}{2n}.\\]<\/p>\n<ul>\n<li>\ucd9c\ucc98 : <a href=\"https:\/\/cmci.colorado.edu\/classes\/INFO-1301\/fa16\/files\/borgatti.htm\">https:\/\/cmci.colorado.edu\/classes\/INFO-1301\/fa16\/files\/borgatti.htm<\/a><\/li>\n<\/ul>\n<h3>R\uc5d0\uc11c \ud655\uc778<\/h3>\n<p>\uc0c1\uad00\uacc4\uc218\uc640 \ub450 \ubcc0\uc218\uc758 \uc720\ud074\ub9ac\ub4dc \uac70\ub9ac\uc758 \uad00\uacc4\ub97c R\uc5d0\uc11c \ud655\uc778\ud574\ubcf4\uc790.[<sup>1]<\/sup><\/p>\n<p>[<sup>1]:<\/sup> \uc774\ub54c \uc720\ud074\ub9ac\ub4dc \uac70\ub9ac\ub294 \ub2e8\uc21c\ud788 \ub450 \uc810\uc5d0\uc11c\uc758 \uac70\ub9ac\uac00 \uc544\ub2c8\ub77c \ub450 \ud655\ub960\ubcc0\uc218\uc5d0\uc11c \uc815\uc758\ub41c \uac70\ub9ac\uc784\uc744 \uc720\uc758\ud558\uc790. \uc55e\uc758 \uc608\uc5d0\uc11c \\((x,y)\\) \uac00 \\(n\\) \uac1c\uc77c \ub54c, \\(n\\) &#8211; \ucc28\uc6d0 \uacf5\uac04 \uc0c1\uc5d0\uc11c \ub450 \uc810 \\((x_1, x_2, \\cdots, x_n)\\) \uacfc \\((y_1, y_2, \\cdots, y_n)\\) \uc758 \uac70\ub9ac\uc774\ub2e4.<\/p>\n<pre><code class=\"r\">library(dplyr)\n\n# sampling x, y\nN &lt;- 100\nx &lt;- runif(N, min=-3, max=2)\ny &lt;- 1*x + rnorm(N, mean=1, sd=1.4)\n\nplot(y ~ x)\n<\/code><\/pre>\n<p><img src=\"data:image\/png;base64,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\" alt=\"plot of chunk unnamed-chunk-1\"\/><\/p>\n<pre><code class=\"r\"># scale x, y to x2, y2\nx2 &lt;- scale(x)\ny2 &lt;- scale(y)\n\n# correlation\ncor(x,y)\n<\/code><\/pre>\n<pre>## [1] 0.5890677\n<\/pre>\n<pre><code class=\"r\"># Euclidean distance between scaled x, y\nd2 = sum((x2-y2)^2)\n\n1-d2\/(2*N)\n<\/code><\/pre>\n<pre>## [1] 0.5931771\n<\/pre>\n<p>\ub450 \uac12\uc5d0 \uc57d\uac04 \ucc28\uc774\uac00 \ub098\uc9c0\ub9cc, \ube44\uc2b7\ud558\ub2e4. \ub9cc\uc57d <code>N<\/code>\uc744 <code>1000<\/code>, <code>10000<\/code>\uc73c\ub85c \ub298\ub9ac\uba74, \uadf8 \ucc28\uc774\uac00 \ub354\uc6b1 \uc904\uc5b4\ub4e0\ub2e4. <\/p>\n<p>\uc774 \ucc28\uc774\ub294 <code>scale<\/code> \ud568\uc218\uac00 \uc8fc\uc5b4\uc9c4 \ubcc0\uc218\ub97c \ud3c9\uade0\uc73c\ub85c \ube7c\uace0, \ud45c\uc900\ud3b8\ucc28\ub85c \ub098\ub20c \ub54c, \ud45c\ubcf8\ud45c\uc900\ud3b8\ucc28\ub97c \uc4f0\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n<p>\ub9cc\uc57d \uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130\ub97c \ubaa8\uc9d1\ub2e8\uc73c\ub85c \uc0dd\uac01\ud558\uace0 \ubaa8\ud45c\uc900\ud3b8\ucc28( \\(n-1\\) \ub300\uc2e0 \\(n\\) )\uc744 \uc0ac\uc6a9\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \ub450 \uac12\uc774 \uac19\ub2e4.<\/p>\n<pre><code class=\"r\">x3 &lt;- (x-mean(x)) \/ sqrt(sum(((x-mean(x))\/sqrt(N))^2))\n# scale uses N-1 instead of N\ny3 &lt;- (y-mean(y)) \/ sqrt(sum(((y-mean(y))\/sqrt(N))^2))\n\n# correlation\ncor(x,y)\n<\/code><\/pre>\n<pre>## [1] 0.5890677\n<\/pre>\n<pre><code class=\"r\"># Euclidean distance between scaled x, y\nd2 = sum((x3-y3)^2)\n1-d2\/(2*N)\n<\/code><\/pre>\n<pre>## [1] 0.5890677\n<\/pre>\n<h2>\uc5f0\uc18d \ubcc0\uc218\ub85c\uc758 \ud655\uc7a5<\/h2>\n<p>\ub9cc\uc57d \ub450 \ub450 \ud655\ub960 \ubcc0\uc218\uc758 \uac70\ub9ac\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4\uba74,<\/p>\n<p>\\[\\textrm{d}(X^*, Y^*) = \\sqrt{\\int_{x^*} \\int_{y^*} |x^*-y^*|^2 f_{X^*, Y^*}(x^*, y^*) d{x^*}d{y^*}}\\]<\/p>\n<p>\ub2e4\uc74c\uc758 \uc2dd\uc744 \uc131\ub9bd\ud560 \uac83\uc774\ub2e4. <\/p>\n<p>\\[\\textrm{r}(X^*,Y^*) = 1-\\frac{\\textrm{d}(X^*, Y^*)^2}{2}.\\]<\/p>\n<p>\uc5f0\uc18d\ud655\ub960\uc758 \uadfc\uc0ac\ub85c \uc784\uc758\uc758 \uc774\uc0b0\ud655\ub960\ubd84\ud3ec\ub97c \uc0dd\uc131\ud55c \ud6c4 \uc704\uc758 \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud558\ub294\uc9c0 \ud655\uc778\ud574 \ubcf4\uc790. <\/p>\n<pre><code class=\"r\">x &lt;- 1:100\ny &lt;- 1:100\ndf = expand.grid(x=x,y=y)\ndf$prob = rpois(25, 3)\n\ndf &lt;- df %&gt;% mutate(prob = ifelse(x&gt;y, 0, prob))\n# random variable x, y has clear relationship\n\ndf$prob = df$prob \/ sum(df$prob)\n\nmx &lt;- sum(df$x * df$prob)\nmy &lt;- sum(df$y * df$prob)\nvarx &lt;- sum((df$x - mx)^2 * df$prob)\nvary &lt;- sum((df$y - my)^2 * df$prob)\n\ndf &lt;- df %&gt;% mutate(x2 = (x-mx)\/sqrt(varx),\n                    y2 = (y-my)\/sqrt(vary))\n\n# Check if appropriately standardized\n#sum(df$x2*df$prob)\n#sum(df$x2^2*df$prob)\n#sum(df$y2*df$prob)\n#sum(df$y2^2*df$prob)\n\ndf &lt;- df %&gt;% mutate(d=(x2-y2)^2*prob) \nd2 = sum(df$d)\n\nsum(df$x2 * df$y2 * df$prob)\n<\/code><\/pre>\n<pre>## [1] 0.5001581\n<\/pre>\n<pre><code class=\"r\">1-d2\/2\n<\/code><\/pre>\n<pre>## [1] 0.5001581\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Correlation coefficient and Euclidean distance \uc774\uc0b0\ud655\ub960\ubcc0\uc218 \\(X\\) , \\(Y\\) \ub97c \uac00\uc815\ud558\ub2e4. \uc774\ub54c \\(X=x_i\\), \\(Y=y_i\\) \uc758 \ud655\ub960\uc740 \ubaa8\ub450 \\(1\/n\\) \uc73c\ub85c \uade0\uc77c\ud558\ub2e4\uace0 \uac00\uc815\ud574\ubcf4\uc790. \uadf8\ub9ac\uace0 \uc774\uc0b0\ud655\ub960\ubcc0\uc218 \\(X\\) \uc640 \\(Y\\) \ub97c \ubaa8\ub450 \ud3c9\uade0 \\(0\\), \ubd84\uc0b0 \\(1\\) \ub85c \ud45c\uc900\ud654\ud558\uc5ec, \uc0c8\ub85c\uc6b4 \ud655\ub960 \ubcc0\uc218 \\(X^*\\) \uc640 \\(Y^*\\) \uc744 \ub9cc\ub4e4\uc790. \\[X^* = \\frac{X-\\mu_X}{\\sigma_X}\\] \\[x_i^* = \\frac{x_i-\\sum_i x_i \/n}{\\sum_i (x_i-\\sum_i x_i)^2 \/n}\\] \ud655\ub960\ubcc0\uc218 \\(Y\\) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2025,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[146,319],"tags":[405,288,404,406],"jetpack_featured_media_url":"http:\/\/ds.sumeun.org\/wp-content\/uploads\/2019\/10\/correlation_and_distance.png","_links":{"self":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/2022"}],"collection":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2022"}],"version-history":[{"count":4,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/2022\/revisions"}],"predecessor-version":[{"id":2027,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/2022\/revisions\/2027"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/media\/2025"}],"wp:attachment":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2022"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2022"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}