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roc.html
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<html>
<head>
<meta charset="UTF-8">
<link rel="stylesheet" type="text/css" href="style/bootstrap.min.css"/>
<link rel="stylesheet" type="text/css" href="style/style.css"/>
<link href="http://cdn.jsdelivr.net/gh/joungkyun/font-d2coding/d2coding.css" rel="stylesheet" type="text/css">
<style>
/* https://stackoverflow.com/questions/7525977/how-to-write-fraction-value-using-html */
.frac {
display: inline-block;
position: relative;
vertical-align: middle;
letter-spacing: 0.001em;
text-align: center;
}
.frac > span {
display: block;
padding: 0.1em;
}
.frac span.bottom {
border-top: thin solid black;
}
.frac span.symbol {
display: none;
}
</style>
</head>
<body style="background-color:#F9F9F9;">
<div class="container" style="border:0px solid #FF0000;padding-top:3px;">
<div class="row" style="border:0px solid #FFCC12;"><!--가우시안 그래프-->
<div class="col-12" style="border:0px solid #FF0000;margin-top:0px;"></div>
<div class="card" style="margin-top:10px;">
<!--div class="card-header">Two classes distribution</div-->
<div class="card-body" style="padding-top:0px;padding-bottom:0px;">
<div id="graph1" style="border:0px solid #FF0000;margin-top:10px;"></div>
</div>
</div>
</div>
</div>
<div class="row" style="border:0px solid #FF0000;"><!--슬라이더-->
<div class="col-md-3 offset-md-5" style="border:0px solid #FF0000;">
<div class="card" style="border:0px solid #FF0000;margin-top:5px;">
<div class="card-body">
<h5 class="card-title">C<sub>2</sub> mean=<span id="mu_C2_label"></span></h5>
<form class="customizing"></form>
<input type="range" min="0" max="100" value="50" class="custom-range" id="mu_C2">
</form>
</div>
</div>
</div>
</div>
<div class="row">
<div class="container" style="border:0px solid #00FF00;">
<div class="row">
<div class="col-6" style="padding-left:20px;border:0px solid #FF0000;">
<div class="card" style="margin-top:10px;">
<div class="card-header">정밀도Precision, 재현율Recall(TPR), 특이도Specificity(TNR)</div>
<div class="card-body">
<!--Precision-->
<div class="row"><!--계산값들-->
<div class="frac" style="margin-left:10px;">
<span>TP</span>
<span class="symbol">/</span>
<span class="bottom">TP + FP</span>
</div>
<span style="padding-top:15px;">=</span>
<div class="frac">
<span id="pcs_n_tp"></span>
<span class="symbol">/</span>
<span class="bottom">
<span id="pcs_d_tp"></span>+<span id="pcs_d_fp"></span>
</span>
</div>
<span style="padding-top:15px;">=</span><span style="padding-top:15px;" id="pcs"></span>
<span style="margin-left:10px;padding-top:15px;">Precision</span>
</div>
<!--Recall-->
<div class="row">
<div class="frac" style="margin-left:10px;">
<span>TP</span>
<span class="symbol">/</span>
<span class="bottom">TP + FN</span>
</div>
<span style="padding-top:15px;">=</span>
<div class="frac">
<span id="rcl_n_tp"></span>
<span class="symbol">/</span>
<span class="bottom">
<span id="rcl_d_tp"></span>+<span id="rcl_d_fn"></span>
</span>
</div>
<span style="padding-top:15px;">=</span> <span style="padding-top:15px;" id="rcl"></span>
<span style="margin-left:10px;padding-top:15px;">Recall(TPR)</span>
</div>
<!--TNR-->
<div class="row">
<div class="frac" style="margin-left:10px;">
<span>TN</span>
<span class="symbol">/</span>
<span class="bottom">TN + FP</span>
</div>
<span style="padding-top:15px;">=</span>
<div class="frac">
<span id="spc_n_tn"></span>
<span class="symbol">/</span>
<span class="bottom">
<span id="spc_d_tn"></span>+<span id="spc_d_fp"></span>
</span>
</div>
<span style="padding-top:15px;">=</span> <span style="padding-top:15px;" id="spc"></span>
<span style="margin-left:10px;padding-top:15px;">Specificity(TNR)</span>
</div>
</div><!--card-body-->
</div><!--card-->
</div><!--col-->
<div class="col-6"><!--ROC-->
<div class="card" style="margin-top:10px;">
<div class="card-header">ROC(Receiver Operating Characteristic)</div>
<div class="card-body">
<div id="graph2" style="border:0px solid #FF0000;margin-top:10px;"></div>
</div>
</div>
</div>
</div><!--row-->
</div>
</div>
</div>
<script src="https://code.jquery.com/jquery-3.2.1.min.js"></script>
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.min.js"></script>
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<!--script src="https://cdn.jsdelivr.net/gh/nicolaspanel/[email protected]/dist/numjs.min.js"></script-->
<script>
/*
* numpy.linspace() 함수의 구현
* https://gist.github.com/joates/6584908
*/
var linspace = function(a, b, n) {
if(typeof n === "undefined") n = Math.max(Math.round(b-a)+1,1);
if(n<2) { return n===1 ? [a] : []; }
var i,ret = Array(n);
n--;
for(i=n; i>=0; i--) { ret[i] = (i*b+(n-i)*a)/n; }
return ret;
}
function gaussian_(x, mu, variance) {
sigma = Math.sqrt(variance);
return (1. / sigma*Math.sqrt(2*Math.PI)) * Math.exp( (-1/2)*(Math.pow((x-mu)/sigma, 2)) );
}
/*
* https://stackoverflow.com/questions/5259421/cumulative-distribution-function-in-javascript
*/
function normalcdf(mean, sigma, to)
{
var z = (to-mean)/Math.sqrt(2*sigma*sigma);
var t = 1/(1+0.3275911*Math.abs(z));
var a1 = 0.254829592;
var a2 = -0.284496736;
var a3 = 1.421413741;
var a4 = -1.453152027;
var a5 = 1.061405429;
var erf = 1-(((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*Math.exp(-z*z);
var sign = 1;
if(z < 0)
{
sign = -1;
}
return (1/2)*(1+sign*erf);
}
/*
* https://stackoverflow.com/questions/3730510/javascript-sort-array-and-return-an-array-of-indicies-that-indicates-the-positi
*/
var make_sort_index = function(test){
var test_with_index = [];
for (var i in test) {
test_with_index.push([test[i], i]);
}
test_with_index.sort(function(left, right) {
return left[0] < right[0] ? -1 : 1;
});
var indexes = [];
test = [];
for (var j in test_with_index) {
test.push(test_with_index[j][0]);
indexes.push(test_with_index[j][1]);
}
return indexes;
}
$( document ).ready(function() {
var GRAPH1 = document.getElementById('graph1');
var GRAPH2 = document.getElementById('graph2');
var mu_C1 = 3.;
var variance_C1 = 1.;
var mu_C2 = (3./100.)*parseFloat($('#mu_C2').val()) + 5.;
var variance_C2 = 1.3;
// console.log($('#mu_C2').val());
// console.log(mu_C2);
// 노란색 세로바의 초기 위치
var init_x_hat = 5.;
var x_hat = init_x_hat;
var x_left = linspace(0, x_hat, 100);
var x_right = linspace(x_hat, 12, 100);
var p_C1 = 0.7;
var p_C2 = 0.3;
// 두 가우시안이 이루는 영역 4개에 대한 적분값
var tn, tp, fn, fp;
tn = normalcdf(mu_C1, Math.sqrt(variance_C1), x_hat)*p_C1;
fp = (1-normalcdf(mu_C1, Math.sqrt(variance_C1), x_hat))*p_C1;
fn = normalcdf(mu_C2, Math.sqrt(variance_C2), x_hat)*p_C2;
tp = (1-normalcdf(mu_C2, Math.sqrt(variance_C2), x_hat))*p_C2;
var gaussian = function(x, mu, variance, prior) {
// prior
// |
// p(x,y) = p(x|y) * p(y)
// |
// class conditional prob.
return x.map(function(value, index) { return prior*gaussian_(value, mu, variance); });
}
// Joint를 구역 4개로 나눠서 준비함.
var p_x_C1_l = {
x: x_left,
y: gaussian(x_left, mu_C1, variance_C1, p_C1),
name: 'p(x,C1)',
type: 'scatter',
marker: {color:'#348ABD'},
};
var p_x_C1_r = {
x: x_right,
y: gaussian(x_right, mu_C1, variance_C1, p_C1),
name: 'False Positive',
type: 'scatter',
marker: {color:'#348ABD'},
fill: 'tozeroy'
};
var p_x_C2_l = {
x: x_left,
y: gaussian(x_left, mu_C2, variance_C2, p_C2),
name: 'False Negative',
type: 'scatter',
marker: {color:'#A60628'},
fill: 'tozeroy'
};
var p_x_C2_r = {
x: x_right,
y: gaussian(x_right, mu_C2, variance_C2, p_C2),
name: 'p(x,C2)',
type: 'scatter',
marker: {color:'#A60628'},
};
var roc_x = [];
var roc_y = [];
var roc_xy = {
x: roc_x,
y: roc_y,
//mode: 'markers',
//type: 'scatter'
};
var data = [ p_x_C1_l, p_x_C2_l, p_x_C1_r, p_x_C2_r ];
var data_roc = [ roc_xy ];
// https://community.plot.ly/t/moving-shapes-with-mouse-in-plotly-js-reactjs/11457/7
// https://codepen.io/fingerpori/pen/GGLWoz
// https://plot.ly/javascript/plotlyjs-events/
// https://plotly.com/javascript/setting-graph-size/
// https://plotly.com/javascript/configuration-options/
var layout = {
autosize: true,
title: 'Two classes distribution',
width: 1100,
height: 400,
xaxis: { title:'x', fixedrange: true },
yaxis: { range:[0,2], title:'Prob. density', fixedrange: true },
shapes: [{ //노란색 라인
'type': 'line',
'x0': x_hat,
'y0': -10,
'x1': x_hat,
'y1': 10,
'line': {
'color': '#F0E442',
'width': 3,
}
}]
};
var layout_roc = {
autosize: false,
width: 400,
height: 300,
xaxis: {range:[-0.1,1], title:'1-Specificity(FPR)'},
yaxis: {range:[0, 1.1], title:'Sensitivity(TPR)'},
margin: {
l: 40, r: 5, b: 30, t: 5, pad: 0
}
};
Plotly.newPlot(GRAPH1, data, layout, {editable: true, displayModeBar: false});
Plotly.newPlot(GRAPH2, data_roc, layout_roc);
$('#mu_C2').on("change mousemove", function() { // 슬라이더 움직일 때...
mu_C2 = (3./100.)*parseFloat($(this).val()) + 5.;
$('#mu_C2_label').html(mu_C2.toFixed(3));
// console.log('slider, mu_C2:', mu_C2);
// console.log('slider, x_left:', x_left[99]);
// console.log('slider, x_right:', x_right[0]);
update = { x: [ x_left, x_left, x_right, x_right ],
y: [ gaussian(x_left, mu_C1, variance_C1, p_C1),
gaussian(x_left, mu_C2, variance_C2, p_C2),
gaussian(x_right, mu_C1, variance_C1, p_C1),
gaussian(x_right, mu_C2, variance_C2, p_C2) ]
}
Plotly.restyle(GRAPH1, update, [0,1,2,3]);
//update = {x: [x_left], y: [gaussian(x_left, mu_C1, variance_C1, p_C1)] }
//Plotly.restyle(GRAPH1, update, 0);
//update = {x: [x_left], y: [gaussian(x_left, mu_C2, variance_C2, p_C2)] }
//Plotly.restyle(GRAPH1, update, 1);
//update = {x: [x_right], y: [gaussian(x_right, mu_C1, variance_C1, p_C1)] }
//Plotly.restyle(GRAPH1, update, 2);
//update = {x: [x_right], y: [gaussian(x_right, mu_C2, variance_C2, p_C2)] }
//Plotly.restyle(GRAPH1, update, 3);
// ROC 초기화
// console.log('init roc');
roc_x = [];
roc_y = [];
});
/*
$("#mu_C2").slider({
value : 50,
min : 0,
max : 100,
step : 1,
slide: function (e, ui) {
console.log("dragging");
mu_C2 = (3./100.)*parseFloat($(this).val()) + init_x_hat;
// redraw
y = gaussian(x_left, mu_C2, variance_C2, p_C2);
update = { y: [y] }
Plotly.restyle(GRAPH1, update, 1);
y = gaussian(x_right, mu_C2, variance_C2, p_C2);
update = { y: [y] }
Plotly.restyle(GRAPH1, update, 3);
},
stop: function (e, ui) { //슬라이더 놓을 때
console.log("dropped");
// ROC 그래프 초기화
}
});
*/
GRAPH1.on('plotly_afterplot', function(){
if(x_hat != layout.shapes[0].x0) {
// retrieve the new line position
x_hat = layout.shapes[0].x0;
//console.log('afterplot, x_hat:', x_hat);
// for restyle
x_left = linspace(0, x_hat, 100);
x_right = linspace(x_hat, 12, 100);
// 여기서 업데이트하면 무한루프 빠짐
var update = { x: [ x_left, x_left, x_right, x_right ],
y: [ gaussian(x_left, mu_C1, variance_C1, p_C1),
gaussian(x_left, mu_C2, variance_C2, p_C2),
gaussian(x_right, mu_C1, variance_C1, p_C1),
gaussian(x_right, mu_C2, variance_C2, p_C2) ]
}
Plotly.restyle(GRAPH1, update, [0,1,2,3]);
//}
tn = normalcdf(mu_C1, Math.sqrt(variance_C1), x_hat)*p_C1;
fp = (1-normalcdf(mu_C1, Math.sqrt(variance_C1), x_hat))*p_C1;
fn = normalcdf(mu_C2, Math.sqrt(variance_C2), x_hat)*p_C2;
tp = (1-normalcdf(mu_C2, Math.sqrt(variance_C2), x_hat))*p_C2;
$('#pcs_n_tp').html(tp.toFixed(3));
$('#pcs_d_tp').html(tp.toFixed(3));
$('#pcs_d_fp').html(fp.toFixed(3));
$('#pcs').html((tp / (tp+fp)).toFixed(3));
$('#rcl_n_tp').html(tp.toFixed(3));
$('#rcl_d_tp').html(tp.toFixed(3));
$('#rcl_d_fn').html(fn.toFixed(3));
$('#rcl').html((tp / (tp+fn)).toFixed(3));
$('#spc_n_tn').html(tn.toFixed(3));
$('#spc_d_tn').html(tn.toFixed(3));
$('#spc_d_fp').html(fp.toFixed(3));
$('#spc').html((tn / (tn+fp)).toFixed(3));
// ROC커브에 점찍기
TPR = tp / (tp+fn); // y
FPR = 1 - (tn / (tn+fp)); // x
roc_x.push(FPR);
roc_y.push(TPR);
// console.log('roc_x', roc_x);
// console.log('roc_y', roc_y);
// 여기서 FPR값을 기준으로 roc_x, roc_y를 정렬해야 된다.
sort_idx = make_sort_index(roc_x);
// console.log('sort_idx', sort_idx);
ordered_roc_x = [];
ordered_roc_y = [];
sort_idx.forEach(function(e){
ordered_roc_x.push(roc_x[e]);
ordered_roc_y.push(roc_y[e]);
})
// console.log('ordered_x', ordered_roc_x);
// console.log('ordered_y', ordered_roc_y);
var update = {
x: [ ordered_roc_x ],
y: [ ordered_roc_y ]
}
Plotly.restyle(GRAPH2, update, [0]);
}
});
// p(x , C), 진단장비의 결과(TP, TN, FP, FN)
console.log('p(D=Neg, C=C1)=' + tn);
console.log('p(D=Pos, C=C1)=' + fp);
console.log('p(D=Neg, C=C2)=' + fn);
console.log('p(D=Pos, C=C2)=' + tp);
// p(x | C), 진단장비의 스펙
console.log('p(D=Neg | C=C1)=' + (tn / p_C1));
console.log('p(D=Pos | C=C1)=' + (fp / p_C1));
console.log('p(D=Neg | C=C2)=' + (fn / p_C2));
console.log('p(D=Pos | C=C2)=' + (tp / p_C2));
// prior, 유병률
console.log('p(C=C1)=' + (tn+fp));
console.log('p(C=C2)=' + (fn+tp));
// =1
console.log(tn+fp+fn+tp);
});
</script>
</body>
</html>