Isolation Forests

.block

license: MIT
height: 760
scrolling: no
border: yes

d3.v5.min.js

// https://d3js.org v5.7.0 Copyright 2018 Mike Bostock
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index.html

<!DOCTYPE html>
<html>
  <head>
    <meta charset='UTF-8'>
    <style>
      * {
        font-family: courier;
        margin: 0;
        padding: 0;
      }
      .container {
        text-align: center;
        margin: 20px;
      }
      .iterations {
        margin: 10px;
      }
      input {
        position: relative;
        top: 5px;
      }
      line {
        stroke: rgb(196, 222, 196);
      }
      line.last-line {
        opacity: 1;
        stroke: green;
      }
      text {
        font-size: 9px;
      }
      p {
        text-align: left;
        margin-top: 30px;
        font-family: serif;
      }
      .speed-container {
        opacity: 0.3;
      }
      button {
        padding: 5px;
        background: #efefef;
        border: none;
        font-size: 13px;
        cursor: pointer;
      }
      button.active {
        background: #088000;
        color: #fff;
      }
      #reset {
        margin-left: 100px;
      }
    </style>
  </head>
  <body>
    <div class='container'>
      <div class='controls'>
        <button id='play'>play</button>
        <button id='pause' class='active'>pause</button>
        <button id='step'>step</button>
        <button id='reset'>reset</button>
      </div>
      <div class='iterations'>
        <span>Iterations: </span>
        <span id='iteration'>0</span>
      </div>
      <div id='target'>
        <svg style='height: 500px; width: 500px'></svg>
      </div>
      <div id='speed-container'>
        <label>Speed</label>
        <input type='range' id='speed' name='speed' min='0' max='1000' value='0' />
      </div>
      <p>
        An <a href='https://cs.nju.edu.cn/zhouzh/zhouzh.files/publication/icdm08b.pdf'>Isolation Forest</a> identifies outliers in a dataset by randomly dividing a space until each point is isolated from each other. By repeating this proceedure several times, the Isolation Forest identifies points that are quickly isolated from other points as outliers. The illustration above attempts to illustrate the method by which these outliers are quickly identified. Isolated points are colored and labelled with the iteration on which they were isolated. If you repeat the procedure several times, you'll see the outlier is consistently isolated very quickly, which allows the Isolation Forest to identify the point as an outlier.
      </p>
    </div>
  </body>

  <script src='https://cdnjs.cloudflare.com/ajax/libs/d3/5.7.0/d3.min.js'></script>
  <script>

  // global config
  var w = 500,
      h = 500,
      m = 15,
      total = 100,
      dampen = 6.5,
      centers = [[0.0, 0.0],[1.0, 1.0]],
      outliers = [[0.0, 1.0],[0.5, 0.5],[1.0, 0.0]];

  // state
  var iter = 0,
      groups = [],
      controls = 'pause',
      timeout = null;

  // svg on which all data is painted
  var svg = d3.select('#target').select('svg');

  // create / find elements
  var lineElems = svg.append('g').attr('class', 'lines'),
      pointElems = svg.append('g').attr('class', 'points'),
      textElems = svg.append('g').attr('class', 'texts'),
      speedElem = document.querySelector('#speed'),
      iterElem = document.querySelector('#iteration'),
      container = document.querySelector('.container'),
      speedCElem = document.querySelector('#speed-container'),
      playElem = d3.select('#play'),
      pauseElem = d3.select('#pause'),
      stepElem = d3.select('#step'),
      resetElem = d3.select('#reset');

  // get points and initialize groups as single unit
  var points = getPoints();
  groups = [points];

  // get the data domains
  var xDomain = d3.extent(points, function(d) { return d.x; }),
      yDomain = d3.extent(points, function(d) { return d.y; });

  // get the color scale with which to color points
  var colorDomain = [1, 100];

  var colors = function(val) {
    return d3.interpolateRdYlGn(val / colorDomain[1])
  }

  // x axis scale
  var x = d3.scaleLinear()
    .domain(xDomain)
    .range([2*m, w-(2*m)])

  // y axis scale
  var y = d3.scaleLinear()
    .domain(yDomain)
    .range([2*m, h-(2*m)])

  function initialize() {

    resetState();

    // draw each of the points
    pointElems.selectAll('point').data(points).enter()
      .append('circle')
        .attr('cx', function(d) { return x(d.x) })
        .attr('cy', function(d) { return y(d.y) })
        .attr('id', function(d) { return d.id })
        .attr('r', 3)
        .attr('fill', '#aaa')

    // label the outlier
    textElems.selectAll('.outlier-label').data(outliers).enter()
      .append('text')
        .attr('class', 'outlier-label')
        .attr('x', function(d) { return x(d[0]) + 5})
        .attr('y', function(d) { return y(d[1]) + 8})
        .text('outlier')
        .style('font-size', '12px')
  }

  // draw a new line and further divide the points
  function drawLine(obj) {
    iterElem.innerHTML = ++iter;

    // change the color of the last line
    d3.select('.last-line').classed('last-line', false);

    // use line position args in obj if available, else get random coords
    obj = obj || {};
    var lineX = x(obj.x) || x(getLinePosition('x')),
        lineY = y(obj.y) || y(getLinePosition('y')),
        xMax = x(xDomain[1]),
        yMax = y(yDomain[1]),
        orientation = obj.orientation
          ? obj.orientation
          : Math.random() > 0.5 ? 'v' : 'h';

    lineElems.append('line')
      .attr('class', 'last-line')
      .attr('x1', function(d) { return orientation == 'h' ? 0 : lineX })
      .attr('x2', function(d) { return orientation == 'h' ? xMax : lineX })
      .attr('y1', function(d) { return orientation == 'v' ? 0 : lineY })
      .attr('y2', function(d) { return orientation == 'v' ? yMax : lineY })

    // check if this line separates points into further groups
    var replacements = [];
    for (var i=0; i<groups.length; i++) {
      var above = [],
          below = [];
      for (var j=0; j<groups[i].length; j++) {
        var point = groups[i][j];
        // origin is top-left...
        orientation == 'v'
          ? x(point.x) >= lineX ? above.push(point) : below.push(point)
          : y(point.y) <= lineY ? above.push(point) : below.push(point)
      }
      // if this line split the group, delete the group and add the split groups
      if (above.length && below.length) {
        replacements.push({ groupIdx: i, above: above, below: below })
      }
    }

    // remove all split groups in decreasing order to remove from end of
    // groups array before removing from beginning of groups array
    var sorted = replacements.sort(function(a, b) {
      return b.groupIdx - a.groupIdx;
    })

    for (var i=0; i<sorted.length; i++) {
      var removed = groups.splice(sorted[i].groupIdx, 1);
      groups.push(sorted[i].above);
      groups.push(sorted[i].below);

      // if one of the groups contains only one element, style the point
      // to indicate the point has been isolated
      ['above', 'below'].forEach(function(attr) {
        var group = sorted[i][attr];
        if (group.length === 1) {
          d3.select('#' + group[0].id).style('fill', function() {
            return iter < colorDomain[0]
              ? colors(colorDomain[0])
              : colors(Math.min(colorDomain[1], iter))
          })
          textElems.append('text')
            .attr('x', x(group[0].x) + 3)
            .attr('y', y(group[0].y) - 3)
            .text(iter)
        }
      })
    }

    // draw another line if there are non-isolated points
    if (groups.length != total + outliers.length) {
      if (controls == 'play') {
        timeout = setTimeout(drawLine, 1000 - parseInt(speedElem.value))
      }
    // we're done!
    } else {
      d3.selectAll('button').style('opacity', 0);
      d3.select('#reset').style('opacity', 1);
      deactivateButtons();
    }
  }

  // helper to generate fake data
  function getPoints() {
    var points = [];
    // build up the points array
    for (var i=0; i<centers.length; i++) {
      for (var j=0; j<total/centers.length; j++) {
        points.push({
          x: centers[i][0] + (Math.random() - Math.random()) / dampen,
          y: centers[i][1] + (Math.random() - Math.random()) / dampen,
          group: i,
          id: 'point-' + i + '-' + j,
        })
      }
    }
    // add an outlier
    for (var i=0; i<outliers.length; i++) {
      points.push({
        x: outliers[i][0],
        y: outliers[i][1],
        id: 'outlier-' + i,
        group: 2,
      })
    }
    return points;
  }

  // find the min, max values of all non-isolated points within the
  // `dim` dimension, and return a random value within that domain
  function getLinePosition(dim) {
    var min = Number.POSITIVE_INFINITY,
        max = Number.NEGATIVE_INFINITY;
    for (var i=0; i<groups.length; i++) {
      for (var j=0; j<groups[i].length; j++) {
        var point = groups[i][j];
        if (point[dim] < min) min = point[dim];
        if (point[dim] > max) max = point[dim];
      }
    }
    return (Math.random() * (max-min)) + min;
  }

  // reset all state to prepare for new iteration
  function resetState() {
    if (timeout) clearTimeout(timeout);
    // remove elems
    pointElems.selectAll('circle').remove();
    textElems.selectAll('text').remove();
    lineElems.selectAll('line').remove();
    // reset iterations
    iter = 0;
    iterElem.innerHTML = iter;
    // get and store the points & create one group with all points
    points = window.points || getPoints();
    window.points = points;
    groups = [points];
    // reset button state
    d3.selectAll('button').style('opacity', 1);
    deactivateButtons();
    controls = 'pause';
  }

  // deactivate all button classes
  function deactivateButtons() {
    d3.selectAll('button').classed('active', false)
  }

  /**
  * Controls Event Listeners
  **/

  playElem.on('click', function() {
    deactivateButtons();
    speedCElem.style.opacity = 1;
    playElem.classed('active', true);
    controls = 'play';
    drawLine();
  })

  stepElem.on('click', function() {
    deactivateButtons();
    speedCElem.style.opacity = 0.3;
    stepElem.classed('active', true);
    controls = 'step';
    drawLine();
    setTimeout(function() {
      deactivateButtons();
      pauseElem.classed('active', true);
    }, 100);
  })

  pauseElem.on('click', function() {
    deactivateButtons();
    speedCElem.style.opacity = 0.3;
    pauseElem.classed('active', true);
    controls = 'pause';
  })

  resetElem.on('click', initialize)

  // main
  initialize();

  </script>
</html>

isolation-forest.png

thumbnail.png