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index.html
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<html>
<head>
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<script type="application/javascript">
var x_min = 0.0;
var y_min = 0.0;
var x_max = 1.0;
var y_max = 1.0;
var xs = [];
var ys = [];
for (var x = x_min; x <= x_max; x += 0.01)
xs.push(x);
for (var y = y_min; y <= y_max; y += 0.01)
ys.push(y);
var colors = ['blue', 'red'];
var zs = new Array(ys.length).fill(0.0).map(x => new Array(xs.length).fill(0.0));
//import numpy as np
//
//class SVM:
// def __init__(self, kernel='linear', C=10000.0, max_iter=100000, degree=3, gamma=1):
// self.kernel = {'poly' : lambda x,y: np.dot(x, y.T)**degree,
// 'rbf' : lambda x,y: np.exp(-gamma*np.sum((y - x[:,np.newaxis])**2, axis=-1)),
// 'linear': lambda x,y: np.dot(x, y.T)}[kernel]
// self.C = C
// self.max_iter = max_iter
//
// def restrict_to_square(self, t, v0, u):
// t = (np.clip(v0 + t*u, 0, self.C) - v0)[1]/u[1]
// return (np.clip(v0 + t*u, 0, self.C) - v0)[0]/u[0]
//
// def fit(self, X, y):
// self.X = X.copy()
// self.y = y * 2 - 1
// self.lambdas = np.zeros_like(self.y, dtype=float)
// self.K = self.kernel(self.X, self.X) * self.y[:,np.newaxis] * self.y
//
// for _ in range(self.max_iter):
// for idxM in range(len(self.lambdas)):
// idxL = np.random.randint(0, len(self.lambdas))
// Q = self.K[[[idxM, idxM], [idxL, idxL]], [[idxM, idxL], [idxM, idxL]]]
// v0 = self.lambdas[[idxM, idxL]]
// k0 = 1 - np.sum(self.lambdas * self.K[[idxM, idxL]], axis=1)
// u = np.array([-self.y[idxL], self.y[idxM]])
// t_max = np.dot(k0, u) / (np.dot(np.dot(Q, u), u) + 1E-15)
// self.lambdas[[idxM, idxL]] = v0 + u * self.restrict_to_square(t_max, v0, u)
//
// idx, = np.nonzero(self.lambdas > 1E-15)
// self.b = np.sum((1.0 - np.sum(self.K[idx] * self.lambdas, axis=1)) * self.y[idx]) / len(idx)
//
// def decision_function(self, X):
// return np.sum(self.kernel(X, self.X) * self.y * self.lambdas, axis=1) + self.b
var max_iter = 100;
var C = 100.0;
var degree = 3;
var gamma = 5;
var poly_ker = function(x, y) {
return (x[0] * y[0] + x[1] * y[1])**degree;
}
var rbf_ker = function(x, y) {
const d = [x[0] - y[0], x[1] - y[1]];
return Math.exp(- gamma * (d[0] * d[0] + d[1] * d[1]));
}
var lin_ker = function(x, y) {
return x[0] * y[0] + x[1] * y[1];
}
var ker = lin_ker;
//ef restrict_to_square(self , t, v0 , u):
// t = (np.clip(v0 + t*u, 0, self.C) - v0)[1]/u[1]
// return (np.clip(v0 + t*u, 0, self.C) - v0)[0]/u[0]
function restrict_t(t, v0, u) {
var clip = x => x < 0 ? 0.0 : (x > C ? C : x);
t = (clip(v0[1] + t * u[1]) - v0[1]) / u[1];
t = (clip(v0[0] + t * u[0]) - v0[0]) / u[0];
return t;
}
function get_K_matrix() {
var K = new Array(points.length);
for (var i = 0; i < points.length; ++i) {
var row = new Array(points.length);
for (var j = 0; j < points.length; ++j) {
row[j] = ker(points[i], points[j]) * (2 * points[i][2] - 1) * (2 * points[j][2] - 1);
}
K[i] = row;
}
return K;
}
function get_k0(K, lambdas, idxM, idxL) {
var k0 = [1.0, 1.0];
for (var idx = 0; idx < lambdas.length; ++idx) {
k0[0] -= lambdas[idx] * K[idxM][idx];
k0[1] -= lambdas[idx] * K[idxL][idx];
}
return k0;
}
function get_lambdas() {
var lambdas = new Array(points.length).fill(0.0);
const K = get_K_matrix();
for (var i = 0; i < max_iter; ++i) {
for (var idx_M = 0; idx_M < lambdas.length; ++idx_M) {
const idx_L = Math.floor(Math.random() * Math.floor(lambdas.length));
const k0 = get_k0(K, lambdas, idx_M, idx_L);
const u = [-(2 * points[idx_L][2] - 1), 2 * points[idx_M][2] - 1];
const t_max = (u[0] * k0[0] + u[1] * k0[1]) / (K[idx_L][idx_L] * u[1] * u[1] + K[idx_M][idx_M] * u[0] * u[0] + 2 * K[idx_L][idx_M] * u[0] * u[1] + 1E-15);
const t_restr = restrict_t(t_max, [lambdas[idx_M], lambdas[idx_L]], u);
lambdas[idx_M] += u[0] * t_restr;
lambdas[idx_L] += u[1] * t_restr;
}
}
var b = 0.0;
var items = 0;
for (var k = 0; k < lambdas.length; ++k) {
if (lambdas[k] < 1E-10)
continue;
items += 1;
var y_k = 2.0 * points[k][2] - 1;
for (var i = 0; i < lambdas.length; ++i)
b -= lambdas[i] * y_k * K[k][i];
b += y_k;
}
b /= items;
return [lambdas, b];
}
function loss_function_2d() {
var data = get_lambdas();
var lambdas = data[0];
var b = data[1];
var blue_x = [];
var blue_y = [];
var red_x = [];
var red_y = [];
for (var i = 0; i < points.length; ++i) {
if (points[i][2]) {
blue_x.push(points[i][0]);
blue_y.push(points[i][1]);
} else {
red_x.push(points[i][0]);
red_y.push(points[i][1]);
}
}
data = [];
// datapoints
data.push({
x: red_x, y: red_y,
showscale: false, opacity: 1.0, type: 'scatter', mode: 'markers',
name: 'red class datapoints',
marker: {size: 12, color: 'red'},
});
data.push({
x: blue_x, y: blue_y,
showscale: false, opacity: 1.0, type: 'scatter', mode: 'markers',
name: 'red class datapoints',
marker: {size: 12, color: 'blue'},
});
var support_x = [];
var support_y = [];
for (var i = 0; i < points.length; ++i) {
if (lambdas[i] > 1E-10) {
support_x.push(points[i][0]);
support_y.push(points[i][1]);
}
}
data.push({
x: support_x, y: support_y,
showscale: false, opacity: 1.0, type: 'scatter', mode: 'markers',
name: 'support vectors',
marker: {size: 3, color: 'yellow'},
});
for (var i = 0; i < ys.length; ++i) {
for (var j = 0; j < xs.length; ++j) {
zs[i][j] = 0.0;
for (var k = 0; k < lambdas.length; ++k)
zs[i][j] += lambdas[k] * (2.0 * points[k][2] - 1) * ker(points[k], [xs[j], ys[i]]);
zs[i][j] += b;
//zs[i][j] = 1 / (1 + Math.exp(-zs[i][j]));
//if (zs[i][j] > 0)
// zs[i][j] = 1.0;
//else
// zs[i][j] = 0.0;
}
}
var colorscaleValue = [
[0, '#FF000044'],
[1, '#008efba0']
];
data.push({
x: xs,
y: ys,
z: zs,
type: 'contour',
colorscale: colorscaleValue,
showscale: false,
contours: {start: 0.0, end: 0.0, size: 3.0},
line: {width: 2, color: 'black'},
});
data.push({
x: xs,
y: ys,
z: zs,
type: 'contour',
showscale: false,
contours: {start: -1.0, end: 1.0, size: 1.0, coloring: 'none'},
line: {
width: 1,
color: 'black'
},
});
var cell_for_plot = document.getElementById("for_right_plot");
var layout = {
title: 'Decision Tree',
xaxis: {'range': [x_min, x_max], 'domain': [0.0, 1.0], 'fixedrange': true},
yaxis: {'range': [y_min, y_max], 'domain': [0.0, 1.0], 'fixedrange': true},
width: 600,
height: 600,
autosize: false,
showlegend: false,
margin: {l: 0, r: 0, b: 0, t: 0 }
};
Plotly.newPlot(cell_for_plot, data, layout);
}
points = [];
canvas_handles = {
handle_down: null,
handle_move: null,
handle_up: null,
};
function add_pts(cls) {
canvas_handles.handle_down = function(x, y) { points.push([x, y, cls]); };
canvas_handles.handle_move = null;
canvas_handles.handle_up = null;
}
function move_pts() {
canvas_handles.handle_down = function(x, y) {
for (var i = 0; i < points.length; ++i)
if ((x - points[i][0])*(x - points[i][0]) + (y - points[i][1])*(y - points[i][1]) < 0.001)
{
canvas_handles.handle_move = function(x, y) {
if (x < x_min || x > x_max || y < y_min || y > y_max)
return;
points[i][0] = x;
points[i][1] = y;
}
break;
}
};
canvas_handles.handle_move = null;
canvas_handles.handle_up = function(x, y) { canvas_handles.handle_move = null; };
}
function del_pts() {
canvas_handles.handle_down = function(x, y) {
var idx = -1;
for (var i = 0; i < points.length; ++i)
if ((x - points[i][0])*(x - points[i][0]) + (y - points[i][1])*(y - points[i][1]) < 0.001)
idx = i;
points.splice(idx, 1);
};
canvas_handles.handle_move = null;
canvas_handles.handle_up = null;
}
function extract_coordinates(event) {
event.stopPropagation();
var x = event.offsetX;
var y = event.offsetY;
var canvas = document.getElementById("paint");
var w = canvas.width;
var h = canvas.height;
var plot_x = x / w * (x_max - x_min) + x_min;
var plot_y = (1.0 - y / h) * (y_max - y_min) + y_min;
return [plot_x, plot_y];
}
function mdown_handle(event) {
var pts = extract_coordinates(event);
if (canvas_handles.handle_down)
canvas_handles.handle_down(pts[0], pts[1]);
loss_function_2d();
}
function mmove_handle(event) {
var pts = extract_coordinates(event);
if (canvas_handles.handle_move) {
canvas_handles.handle_move(pts[0], pts[1]);
loss_function_2d();
}
}
function mup_handle(event) {
var pts = extract_coordinates(event);
if (canvas_handles.handle_up)
canvas_handles.handle_up(pts[0], pts[1]);
loss_function_2d();
}
function adjust_canvas() {
var plt_div = document.getElementById('for_right_plot');
var el = plt_div.getElementsByClassName('xy')[0];
el = el.childNodes[0];
if (!el)
return [600, 600];
var rect = el.getBoundingClientRect();
var canvas = document.getElementById("paint");
//console.log(rect);
canvas.style.cssText = "position:absolute; top:" + parseInt(rect.top)
+ "px; left: " + parseInt(rect.left)
+ "px; width:" + parseInt(rect.width)
+ "px; height:" + parseInt(rect.height)
+ "px; z-index:1000;";
canvas.width = rect.width;
canvas.height = rect.height;
var ctx = canvas.getContext('2d');
ctx.clearRect(0, 0, canvas.width, canvas.height);
//loss_function_2d();
return [canvas.width, canvas.height];
}
function clear_field() {
points = [];
loss_function_2d();
}
function C_change(val) {
var l = document.getElementById('c_val');
l.innerHTML = (val/10.0).toFixed(1);
C = 10**(val/10.0);
loss_function_2d();
}
function ker_change(val) {
if (val == 'linear') {
ker = lin_ker;
document.getElementById('gamma').style = 'display: none';
document.getElementById('polyn').style = 'display: none';
}
if (val == 'poly') {
ker = poly_ker;
document.getElementById('gamma').style = 'display: none';
document.getElementById('polyn').style = 'display: block';
}
if (val == 'rbf') {
ker = rbf_ker;
document.getElementById('gamma').style = 'display: block';
document.getElementById('polyn').style = 'display: none';
}
loss_function_2d();
}
function gamma_change(val) {
gamma = val / 2.0 + 0.5;
document.getElementById('glabel').innerHTML = gamma.toFixed(1);
loss_function_2d();
}
function n_change(val) {
degree = val;
document.getElementById('nlabel').innerHTML = degree;
loss_function_2d();
}
</script>
</head>
<body>
<div id="everything" style="height:600px; width:625px;">
<div id="for_right_plot">
</div>
<div id="for_left_plot" style="position:absolute; top:50px; left:800px" >
<input type="radio" id="root_add_red" name="root_node" checked="checked" onchange="add_pts(0); loss_function_2d(); ">
<label for="root_add_red">Add red data point</label><br>
<input type="radio" id="root_add_blue" name="root_node" onchange="add_pts(1); loss_function_2d(); ">
<label for="root_add_blue">Add blue data point</label><br>
<input type="radio" id="root_move" name="root_node" onchange="move_pts(); loss_function_2d(); ">
<label for="root_move">Move data point</label><br>
<input type="radio" id="root_del" name="root_node" onchange="del_pts(); loss_function_2d(); ">
<label for="root_del">Delete data point</label><br>
<input type="range" min="-30" max="50" value="10" oninput="C_change(this.value)">
<label>C = 10<sup id="c_val">1</sup></label><br>
Kernel:
<select id="select_kernel" onchange="ker_change(this.value)">
<option value="linear">Linear</option>
<option value="poly">Polynomial</option>
<option value="rbf">Radial Basis Functions</option>
</select><br>
<div id='gamma' style='display: none'>
<input type="range" min="0" max="10" value="5" oninput="gamma_change(this.value)">
gamma = <label id='glabel'>3.0</label><br>
</div>
<div id='polyn' style='display: none'>
<input type="range" min="2" max="7" value="3" oninput="n_change(this.value)">
n = <label id='nlabel'>3</label><br>
</div>
</div>
</div>
<canvas id="paint" width=600 height=600
onmousedown="mdown_handle(event)"
onmousemove="mmove_handle(event)"
onmouseup="mup_handle(event)">
</canvas>
</body>
<script>
function init()
{
loss_function_2d();
adjust_canvas();
add_pts(0);
setInterval(adjust_canvas, 1000);
}
init();
</script>
</html>