05.Unsupervised Learning.ipynb

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   "cell_type": "markdown",
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   "source": [
    "## Learning Algorithms - Unsupervised Learning\n",
    "<img src='imgs/ml_process_by_micheleenharris.png' alt=\"Smiley face\" width=\"400\"><br>\n",
    ">  Reminder:  In machine learning, the problem of unsupervised learning is that of trying to find hidden structure in unlabeled data. Since the training set given to the learner is unlabeled, there is no error or reward signal to evaluate a potential solution. Basically, we are just finding a way to represent the data and get as much information from it that we can.\n",
    "\n",
    "HEY!  Remember PCA from above?  PCA is actually considered unsupervised learning.  We just put it up there because it's a good way to visualize data at the beginning of the ML process.\n",
    "\n",
    "Let's revisit it in a little more detail using the `iris` dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "source": [
    "# Imports for python 2/3 compatibility\n",
    "\n",
    "from __future__ import absolute_import, division, print_function, unicode_literals\n",
    "\n",
    "# For python 2, comment these out:\n",
    "# from builtins import range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA revisited"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "from sklearn.datasets import load_iris\n",
    "\n",
    "iris = load_iris()\n",
    "\n",
    "# subset data to have only sepal width (cm) and petal length (cm) for simplification\n",
    "X = iris.data[:, 1:3]\n",
    "print(iris.feature_names[1:3])\n",
    "\n",
    "pca = PCA(n_components = 2)\n",
    "pca.fit(X)\n",
    "\n",
    "print(\"% of variance attributed to components: \"+ \\\n",
    "      ', '.join(['%.2f' % (x * 100) for x in pca.explained_variance_ratio_]))\n",
    "print('\\ncomponents of each feature:', pca.components_)\n",
    "\n",
    "print(list(zip(pca.explained_variance_, pca.components_)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `pca.explained_variance_` is like the magnitude of a components influence (amount of variance explained) and the `pca.components_` is like the direction of influence for each feature in each component.\n",
    "\n",
    "<p style=\"text-align:right\"><i>Code in next cell adapted from Jake VanderPlas's code [here](https://github.com/jakevdp/sklearn_pycon2015)</i></p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "# plot the original data in X (before PCA)\n",
    "plt.plot(X[:, 0], X[:, 1], 'o', alpha=0.5)\n",
    "\n",
    "# grab the component means to get the center point for the plot below\n",
    "means = pca.mean_\n",
    "\n",
    "# here we use the direction of the components in pca.components_\n",
    "#  and the magnitude of the variance explained by that component in\n",
    "#  pca.explained_variance_\n",
    "\n",
    "# we plot the vector (magnitude and direction) of the components\n",
    "#  on top of the original data in X\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    print([means[0], v[0]+means[0]], [means[1], v[1]+means[1]])\n",
    "    plt.plot([means[0], v[0]+means[0]], [means[1], v[1]+means[1]], '-k', lw=3)\n",
    "\n",
    "\n",
    "# axis limits\n",
    "plt.xlim(0, max(X[:, 0])+3)\n",
    "plt.ylim(0, max(X[:, 1])+3)\n",
    "\n",
    "# original feature labels of our data X\n",
    "plt.xlabel(iris.feature_names[1])\n",
    "plt.ylabel(iris.feature_names[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "QUESTION:  In which direction in the data is the most variance explained?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall, in the ML 101 module: unsupervised models have a `fit()`, `transform()` and/or `fit_transform()` in `sklearn`.\n",
    "\n",
    "\n",
    "If you want to both get a fit and new dataset with reduced dimensionality, which would you use below? (Fill in blank in code)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# get back to our 4D dataset\n",
    "X, y = iris.data, iris.target\n",
    "\n",
    "pca = PCA(n_components = 0.95) # keep 95% of variance\n",
    "X_trans = pca.___(X) # <- fill in the blank\n",
    "print(X.shape)\n",
    "print(X_trans.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "plt.scatter(X_trans[:, 0], X_trans[:, 1], c=iris.target, edgecolor='none', alpha=0.5,\n",
    "           cmap=plt.cm.get_cmap('spring', 10))\n",
    "plt.ylabel('Component 2')\n",
    "plt.xlabel('Component 1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering\n",
    "KMeans finds cluster centers that are the mean of the points within them.  Likewise, a point is in a cluster because the cluster center is the closest cluster center for that point.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> If you don't have ipywidgets package installed, go ahead and install it now by running the cell below uncommented."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "!pip install ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from ipywidgets import interact\n",
    "from sklearn.metrics.pairwise import euclidean_distances\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "iris = load_iris()\n",
    "X, y = iris.data, iris.target\n",
    "pca = PCA(n_components = 2) # keep 2 components which explain most variance\n",
    "X = pca.fit_transform(X)\n",
    "\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# I have to tell KMeans how many cluster centers I want\n",
    "n_clusters  = 3\n",
    "\n",
    "# for consistent results when running the methods below\n",
    "random_state = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:right\"><i>Code in next cell adapted from Jake VanderPlas's code [here](https://github.com/jakevdp/sklearn_pycon2015)</i></p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def _kmeans_step(frame=0, n_clusters=n_clusters):\n",
    "    rng = np.random.RandomState(random_state)\n",
    "    labels = np.zeros(X.shape[0])\n",
    "    centers = rng.randn(n_clusters, 2)\n",
    "\n",
    "    nsteps = frame // 3\n",
    "\n",
    "    for i in range(nsteps + 1):\n",
    "        old_centers = centers\n",
    "        if i < nsteps or frame % 3 > 0:\n",
    "            dist = euclidean_distances(X, centers)\n",
    "            labels = dist.argmin(1)\n",
    "\n",
    "        if i < nsteps or frame % 3 > 1:\n",
    "            centers = np.array([X[labels == j].mean(0)\n",
    "                                for j in range(n_clusters)])\n",
    "            nans = np.isnan(centers)\n",
    "            centers[nans] = old_centers[nans]\n",
    "\n",
    "\n",
    "    # plot the data and cluster centers\n",
    "    plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='rainbow',\n",
    "                vmin=0, vmax=n_clusters - 1);\n",
    "    plt.scatter(old_centers[:, 0], old_centers[:, 1], marker='o',\n",
    "                c=np.arange(n_clusters),\n",
    "                s=200, cmap='rainbow')\n",
    "    plt.scatter(old_centers[:, 0], old_centers[:, 1], marker='o',\n",
    "                c='black', s=50)\n",
    "\n",
    "    # plot new centers if third frame\n",
    "    if frame % 3 == 2:\n",
    "        for i in range(n_clusters):\n",
    "            plt.annotate('', centers[i], old_centers[i], \n",
    "                         arrowprops=dict(arrowstyle='->', linewidth=1))\n",
    "        plt.scatter(centers[:, 0], centers[:, 1], marker='o',\n",
    "                    c=np.arange(n_clusters),\n",
    "                    s=200, cmap='rainbow')\n",
    "        plt.scatter(centers[:, 0], centers[:, 1], marker='o',\n",
    "                    c='black', s=50)\n",
    "\n",
    "    plt.xlim(-4, 5)\n",
    "    plt.ylim(-2, 2)\n",
    "    plt.ylabel('PC 2')\n",
    "    plt.xlabel('PC 1')\n",
    "\n",
    "    if frame % 3 == 1:\n",
    "        plt.text(4.5, 1.7, \"1. Reassign points to nearest centroid\",\n",
    "                 ha='right', va='top', size=8)\n",
    "    elif frame % 3 == 2:\n",
    "        plt.text(4.5, 1.7, \"2. Update centroids to cluster means\",\n",
    "                 ha='right', va='top', size=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "KMeans employ the <i>Expectation-Maximization</i> algorithm which works as follows: \n",
    "\n",
    "1. Guess cluster centers\n",
    "* Assign points to nearest cluster\n",
    "* Set cluster centers to the mean of points\n",
    "* Repeat 1-3 until converged"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# suppress future warning\n",
    "# import warnings\n",
    "# warnings.filterwarnings('ignore')\n",
    "\n",
    "min_clusters, max_clusters = 1, 6\n",
    "interact(_kmeans_step, frame=[0, 20],\n",
    "                    n_clusters=[min_clusters, max_clusters])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> <b>Warning</b>! There is absolutely no guarantee of recovering a ground truth. First, choosing the right number of clusters is hard. Second, the algorithm is sensitive to initialization, and can fall into local minima, although scikit-learn employs several tricks to mitigate this issue.<br>  --Taken directly from sklearn docs\n",
    "\n",
    "<img src='imgs/pca1.png' alt=\"Original PCA with Labels\" align=\"center\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Novelty detection aka anomaly detection\n",
    "QUICK QUESTION:\n",
    "What is the difference between outlier detection and anomaly detection?\n",
    "\n",
    "Below we will use a one-class support vector machine classifier to decide if a point is weird or not given our original data. (The code was adapted from the sklearn docs [here](http://scikit-learn.org/stable/auto_examples/svm/plot_oneclass.html#example-svm-plot-oneclass-py))"
   ]
  },
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raZk//viDxo0bY2NjYyrTqlWrLKEyo4SEBO7fv0+bNm1M03Q6HYGBgcTHx5um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ag/cCzwQ+Am4HxgXzIWgAAWN8KYUSOYOHEiABMnTmT09vUsbtzy2NKlS7nwwgtZunTpVo/Fe17U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\nd85Fx44sMLO38f+fDgaeC7p5f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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106854550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import rcParams, font_manager\n",
    "rcParams['figure.figsize'] = (14.0, 7.0)\n",
    "fprop = font_manager.FontProperties(size=14)\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.font_manager\n",
    "from sklearn import svm\n",
    "\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.cross_validation import train_test_split\n",
    "\n",
    "xx, yy = np.meshgrid(np.linspace(-2, 9, 500), np.linspace(-2,9, 500))\n",
    "\n",
    "# Iris data\n",
    "iris = load_iris()\n",
    "X, y = iris.data, iris.target\n",
    "labels = iris.feature_names[1:3]\n",
    "X = X[:, 1:3]\n",
    "\n",
    "# split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state = 0)\n",
    "\n",
    "# make some outliers\n",
    "X_weird = np.random.uniform(low=-2, high=9, size=(20, 2))\n",
    "\n",
    "# fit the model\n",
    "clf = svm.OneClassSVM(nu=0.1, kernel=\"rbf\", gamma=1, random_state = 0)\n",
    "clf.fit(X_train)\n",
    "\n",
    "# predict labels\n",
    "y_pred_train = clf.predict(X_train)\n",
    "y_pred_test = clf.predict(X_test)\n",
    "y_pred_outliers = clf.predict(X_weird)\n",
    "\n",
    "\n",
    "n_error_train = y_pred_train[y_pred_train == -1].size\n",
    "n_error_test = y_pred_test[y_pred_test == -1].size\n",
    "n_error_outliers = y_pred_outliers[y_pred_outliers == 1].size\n",
    "\n",
    "\n",
    "# plot the line, the points, and the nearest vectors to the plane\n",
    "Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])\n",
    "Z = Z.reshape(xx.shape)\n",
    "\n",
    "plt.title(\"Novelty Detection aka Anomaly Detection\")\n",
    "plt.contourf(xx, yy, Z, levels=np.linspace(Z.min(), 0, 7), cmap=plt.cm.Blues_r)\n",
    "a = plt.contour(xx, yy, Z, levels=[0], linewidths=2, colors='red')\n",
    "plt.contourf(xx, yy, Z, levels=[0, Z.max()], colors='orange')\n",
    "\n",
    "b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c='white')\n",
    "b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c='green')\n",
    "c = plt.scatter(X_weird[:, 0], X_weird[:, 1], c='red')\n",
    "plt.axis('tight')\n",
    "plt.xlim((-2, 9))\n",
    "plt.ylim((-2, 9))\n",
    "plt.ylabel(labels[1], fontsize = 14)\n",
    "plt.legend([a.collections[0], b1, b2, c],\n",
    "           [\"learned frontier\", \"training observations\",\n",
    "            \"new regular observations\", \"new abnormal observations\"],\n",
    "           loc=\"best\",\n",
    "           prop=fprop)\n",
    "plt.xlabel(\n",
    "    \"%s\\nerror train: %d/200 ; errors novel regular: %d/40 ; \"\n",
    "    \"errors novel abnormal: %d/10\"\n",
    "    % (labels[0], n_error_train, n_error_test, n_error_outliers), fontsize = 14)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "TRY changing the value of the parameters in the SVM classifier above especially `gamma`.  More information on `gamma` and support vector machine classifiers [here](http://scikit-learn.org/stable/auto_examples/svm/plot_rbf_parameters.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Created by a Microsoft Employee.\n",
    "\t\n",
    "The MIT License (MIT)<br>\n",
    "Copyright (c) 2016 Micheleen Harris"
   ]
  }
 ],
 "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": "3.4.3"
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 },
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