Separability.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Balanced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "separated_means = [[-3, 2], [-1.5, 2], [0, 2], [1.5, 2], [3, 2], [-3, 0], [-1.5, 0], [0, 0], [1.5, 0], [3, 0]]\n",
    "overlapped_means = [[-2, 1], [-1.5, 1], [0, 1], [1.5, 1], [2, 1], [-2, 0], [-1.5, 0], [0, 0], [1.5, 0], [2, 0]]\n",
    "highly_overlapped_means = [[-2, 1], [-1.5, 1], [-1, 1], [-0.5, 1], [0, 1], [-2, 0], [-1.5, 0], [-1, 0], [-0.5, 0], [0, 0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "size_per_category = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "palette = ['red', 'green', 'blue', 'cyan', 'magenta', 'orange', 'yellow', 'lightgreen', 'skyblue', 'orchid']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def generate_distribution(mean_array, size_per_category):\n",
    "    points = pd.DataFrame()\n",
    "    x = []\n",
    "    y = []\n",
    "    category = []\n",
    "    index = 0\n",
    "    for mean in mean_array:\n",
    "        gaussian_normal_points = np.random.normal(loc=mean, scale=[0.3,0.3], size=[size_per_category, 2])\n",
    "        x += list(gaussian_normal_points[:, 0])\n",
    "        y += list(gaussian_normal_points[:, 1])\n",
    "        category += [index] * size_per_category\n",
    "        index += 1\n",
    "    points['x'] = x\n",
    "    points['y'] = y\n",
    "    points['category'] = category\n",
    "    return points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_distribution(distribution):\n",
    "    legend = [('Category '+ str(index+1)) for index in range(10)]\n",
    "    plt.figure(figsize=(15,8))\n",
    "    for index in range(10):\n",
    "        data = distribution[distribution['category'] == index]\n",
    "        plt.scatter(data['x'], data['y'], c=palette[index], s=5)\n",
    "        plt.xlabel('x')\n",
    "        plt.ylabel('y')\n",
    "        plt.legend((legend), loc=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "separated = generate_distribution(separated_means, size_per_category)\n",
    "#plot_distribution(separated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "overlapped = generate_distribution(overlapped_means, size_per_category)\n",
    "#plot_distribution(overlapped)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "highly_overlapped = generate_distribution(highly_overlapped_means, size_per_category)\n",
    "#plot_distribution(highly_overlapped)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imbalanced"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run for r in [0.01, 0.05, 0.1, 0.5, 0.9] and m in [1,9]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulating for one test case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m = 2\n",
    "r = 0.01\n",
    "k = 10\n",
    "imbalanced_size = 2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def sample_imbalanced_data(data, imbalanced_size, m, r, k):\n",
    "    p_min = r/10 #for m classes\n",
    "    p_max = (1 - (p_min * m))/(k - m) #for k-m classes\n",
    "    minority_positions = ([p_min] * m + [p_max] * (k - m))\n",
    "    np.random.shuffle(minority_positions)\n",
    "    class_probabilities = [(proba/size_per_category) for proba in minority_positions]\n",
    "    p = [class_probabilities[category] for category in data['category']]\n",
    "    indices = np.arange(len(data))\n",
    "    selected_indices = np.random.choice(indices, imbalanced_size, p=p)\n",
    "    imbalanced_samples = data.iloc[selected_indices, :]\n",
    "    imbalanced_samples.reset_index(inplace=True, drop=True)\n",
    "    return imbalanced_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "separated_imbalanced = sample_imbalanced_data(separated, imbalanced_size, m, r, k)\n",
    "#plot_distribution(separated_imbalanced)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "overlapped_imbalanced = sample_imbalanced_data(overlapped, imbalanced_size, m, r, k)\n",
    "#plot_distribution(overlapped_imbalanced)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "highly_overlapped_imbalanced = sample_imbalanced_data(highly_overlapped, imbalanced_size, m, r, k)\n",
    "#plot_distribution(highly_overlapped_imbalanced)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def imbalance_ratio(data):\n",
    "    value_counts = data['category'].value_counts()\n",
    "    counts = [count for category, count in value_counts.iteritems()]\n",
    "    count_max = max(counts)\n",
    "    count_min = min(counts)\n",
    "    IR = count_max / count_min\n",
    "    return IR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def hellinger_distance(vec1, vec2):\n",
    "    return np.sqrt(np.sum((np.sqrt(vec1) - np.sqrt(vec2)) ** 2)) / np.sqrt(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def imbalance_degree(data, c):\n",
    "    value_counts = data['category'].value_counts()\n",
    "    counts = [count for category, count in value_counts.iteritems()]\n",
    "    size = len(data)\n",
    "    p = np.array(counts) / size\n",
    "    if (len(p) < c):\n",
    "        p = np.concatenate((p, [0] * (c-len(p))))\n",
    "    b = [1/c] * c\n",
    "    m = 0\n",
    "    for prob in (p-b):\n",
    "        if prob < 0:\n",
    "            m +=1\n",
    "    p_m = [0] * m + [1/c] * (c-m-1) + [1-(c-m-1)/c]\n",
    "    ID = (hellinger_distance(p,b) / hellinger_distance(p_m,b)) + (m-1)\n",
    "    return ID"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def log_likelihood_index(data):\n",
    "    c = len(np.unique(data['category']))\n",
    "    b = np.array([1/c] * c)\n",
    "    value_counts = data['category'].value_counts()\n",
    "    size = len(data)\n",
    "    proba = [(count/size) for category, count in value_counts.iteritems()]\n",
    "    n = [count for _, count in value_counts.iteritems()]\n",
    "    summation = np.sum([(p*np.log(p*c)) for p in proba])\n",
    "    LLI = 2 * summation\n",
    "    return LLI"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "def tangential_imbalance_degree(data):\n",
    "    c = len(np.unique(data['category']))\n",
    "    b = np.array([1/c] * c)\n",
    "    value_counts = data['category'].value_counts()\n",
    "    size = len(data)\n",
    "    proba = [(count/size) for category, count in value_counts.iteritems()]\n",
    "    n = [count for _, count in value_counts.iteritems()]\n",
    "    TID = np.sum(proba * np.tan(proba-b))\n",
    "    return TID"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tangential_imbalance_degree(data):\n",
    "    targets = data['category']\n",
    "    unique, n = np.unique(targets, return_counts=True)\n",
    "    c = len(unique)\n",
    "    N = len(targets)\n",
    "    b = [1/c] * c\n",
    "    p = n / N\n",
    "    unique = unique\n",
    "    counts = n\n",
    "    ic = -2 * p*np.tan(b-p)\n",
    "    signs = np.array([-1 if x < 0 else 1 for x in ic])\n",
    "    #ic = np.sqrt(np.absolute(ic)) * signs\n",
    "    tid = np.absolute(np.sum(ic))\n",
    "    return tid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulating for all values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def compute_graphs(distribution, imbalanced_size, k):\n",
    "    results = []\n",
    "    for m in range(1,k):\n",
    "        IR = []\n",
    "        ID = []\n",
    "        LLI = []\n",
    "        TID = []\n",
    "        for r in [0.01, 0.05, 0.1, 0.5, 0.9]:\n",
    "            imbalanced_data = sample_imbalanced_data(distribution, imbalanced_size, m, r, k)\n",
    "            IR.append(imbalance_ratio(imbalanced_data))\n",
    "            ID.append(imbalance_degree(imbalanced_data, k))\n",
    "            LLI.append(log_likelihood_index(imbalanced_data))\n",
    "            TID.append(tangential_imbalance_degree(imbalanced_data))\n",
    "        result = {}\n",
    "        result['ir'] = IR\n",
    "        result['id'] = ID\n",
    "        result['lli'] = LLI\n",
    "        result['tid'] = TID\n",
    "        results.append(result)\n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_graph(distribution, metric, legend, k=10, imbalanced_size=5000):\n",
    "    data_points = compute_graphs(distribution, imbalanced_size, k)\n",
    "    #plt.figure(figsize=(10,6))\n",
    "    index = 0\n",
    "    r_values = [0.01, 0.05, 0.1, 0.5, 0.9999]\n",
    "    legend = [('m = ' + str(i)) for i in range(1,10)]\n",
    "    for category in data_points:\n",
    "        scores = category[metric]\n",
    "        plt.plot(r_values, scores)\n",
    "        plt.xlabel('r')\n",
    "        plt.ylabel(metric.upper())\n",
    "        #print(scores)\n",
    "    plt.legend((legend), loc=1, fontsize='medium', framealpha=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SluePE3xvGt5Jlz6RRmkpKSkkJCSwb98+9u7dS1VVFQsWLGDGjBmo1e73APpK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x99534639e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_graph(highly_overlapped, 'lli', legend=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rP1Kxfxgqleu6pNPpiu8FGDk/YmwwXOxAc8WFQqGBgQG2b99Od3c3fX19BINB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\nREREkVCIiIgioRAREcW/uWbSJ9wuazQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x99556ba5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_graph(highly_overlapped, 'tid', legend=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}