U1-M1-L2-prep-discretization.ipynb

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    "Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
    "\n",
    "**IMPORTANT: DO NOT COPY OR SPLIT CELLS.** If you do, you'll mess the autograder. If need more cells to work or test things out, create a new cell. You may add as many new cells as you need.\n",
    "\n",
    "Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your name and group below:"
   ]
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  {
   "cell_type": "code",
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   "metadata": {},
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   "source": [
    "COURSE = \"Unsupervised Learning 2021\"\n",
    "GROUP = \"D8A\"\n",
    "NAME = \"Tokiyomi\" # Match your GitHub Classroom ID"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
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   "source": [
    "# Standard imports\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from utils import print_class_limits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assignment: Discretization\n",
    "\n",
    "In this assignment, you'll be required to implement different discretization strategies, as reviewed in the lectures. You may check your work against the expected outcome in the lecture notes.\n",
    "\n",
    "- Equal frequency (2 pt)\n",
    "- Clustering using 1D k-means (4 pts)\n",
    "- Kernel density estimation (4 pts)\n",
    "\n",
    "As in the lectures, we begin with the creation of some synthetic data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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   "outputs": [
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# taken from sklearn docs: https://scikit-learn.org/stable/auto_examples/preprocessing/plot_discretization_strategies.html#sphx-glr-auto-examples-preprocessing-plot-discretization-strategies-py\n",
    "\n",
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "n_samples = 200\n",
    "centers_0 = np.array([[0, 0], [0, 5], [2, 4], [8, 8]])\n",
    "centers_1 = np.array([[0, 0], [3, 1]])\n",
    "\n",
    "random_state = 42\n",
    "X_list = [\n",
    "    np.random.RandomState(random_state).uniform(-3, 3, size=(n_samples, 2)),\n",
    "    make_blobs(n_samples=[n_samples // 10, n_samples * 4 // 10,\n",
    "                          n_samples // 10, n_samples * 4 // 10],\n",
    "               cluster_std=0.5, centers=centers_0,\n",
    "               random_state=random_state)[0],\n",
    "    make_blobs(n_samples=[n_samples // 5, n_samples * 4 // 5],\n",
    "               cluster_std=0.5, centers=centers_1,\n",
    "               random_state=random_state)[0],\n",
    "]\n",
    "\n",
    "figure = plt.figure(figsize=(6.4*3, 4.8))\n",
    "for idx, X in enumerate(X_list):\n",
    "    ax = plt.subplot(1, len(X_list), idx+1)\n",
    "    ax.scatter(X[:, 0], X[:, 1], edgecolors='k')\n",
    "\n",
    "    ax.set_xticks(())\n",
    "    ax.set_yticks(())\n",
    "    ax.set_xlim(np.min(X[:,0]), np.max(X[:,0]))\n",
    "    ax.set_ylim(np.min(X[:,1]), np.max(X[:,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Equal frecuency (2 pt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "ffae1ee056477db6e6ff0655167595b5",
     "grade": false,
     "grade_id": "cell-fa0b21ee97e705af",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Implement equal frecuency discretization below\n",
    "\n",
    "def disc_eq_freq(X, k):\n",
    "    # Implement equal frequency discretization with k bins.\n",
    "    # Each feature should be discretized individually (univariate discretization).\n",
    "    # Your code should work with a data matrix X with an arbitrary number of unsorted features.\n",
    "    \n",
    "    m, n = X.shape\n",
    "    \n",
    "    # Find class limits.\n",
    "    # Hint: use -inf and +inf as the first and last limit\n",
    "\n",
    "    clims = []\n",
    "    quantiles = np.linspace(0, 100, k + 1) # compute k + 1 quantiles to have k intervals\n",
    "\n",
    "    for i in range(n): # for each column\n",
    "        \n",
    "        clims.append((np.percentile(X[:,i], quantiles))) # compute the corresponding value of each quantile using percentile\n",
    "    \n",
    "    clims = np.array(clims)\n",
    "    clims[:,0] = np.NINF\n",
    "    clims[:,-1] = np.Inf\n",
    "    \n",
    "    X_disc = np.zeros(X.shape)\n",
    "\n",
    "    for i in range(n): # compute the discretization for each column\n",
    "        X_disc[:,i] = np.searchsorted(clims[i], X[:,i], side='right') - 1\n",
    "        \n",
    "    # Return the discretized labels in a matrix the same shape as X.\n",
    "    # Return the limits in a matrix which rows are the interval classes of each feature.\n",
    "    return X_disc, clims"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test the function employ the following test matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "61b6df12a9206736b299c38d3e7bd1ca",
     "grade": true,
     "grade_id": "cell-755a3a7461850f7f",
     "locked": true,
     "points": 2,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The discretized matrix is:\n[[0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [2. 2. 2. 2.]\n [3. 3. 3. 3.]]\nExpected answer:\n[[0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [2. 2. 2. 2.]\n [3. 3. 3. 3.]]\n\nThe bin edges are:\n[[  -inf -1.25  -0.5    0.25     inf]\n [  -inf  1.75   2.5    3.25     inf]\n [  -inf -3.25  -2.5   -1.75     inf]\n [  -inf -0.625  0.     0.875    inf]]\nExpected edges:\n[[  -inf -1.25  -0.5    0.25     inf]\n [  -inf  1.75   2.5    3.25     inf]\n [  -inf -3.25  -2.5   -1.75     inf]\n [  -inf -0.625  0.     0.875    inf]]\n\n"
     ]
    }
   ],
   "source": [
    "X_test = np.array([[-2, 1, -4,   -1],\n",
    "                   [-1, 2, -3, -0.5],\n",
    "                   [ 0, 3, -2,  0.5],\n",
    "                   [ 1, 4, -1,    2]])\n",
    "\n",
    "X_disc, bin_edges = disc_eq_freq(X_test, 4)\n",
    "\n",
    "print(\"The discretized matrix is:\")\n",
    "print(X_disc)\n",
    "print(\"Expected answer:\")\n",
    "print(\"\"\"[[0. 0. 0. 0.]\n",
    " [1. 1. 1. 1.]\n",
    " [2. 2. 2. 2.]\n",
    " [3. 3. 3. 3.]]\"\"\")\n",
    "print()\n",
    "\n",
    "print(\"The bin edges are:\")\n",
    "print(bin_edges)\n",
    "print(\"Expected edges:\")\n",
    "print(\"\"\"[[  -inf -1.25  -0.5    0.25     inf]\n",
    " [  -inf  1.75   2.5    3.25     inf]\n",
    " [  -inf -3.25  -2.5   -1.75     inf]\n",
    " [  -inf -0.625  0.     0.875    inf]]\n",
    "\"\"\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code plots the sample data sets and the equal frequency partition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "5c37431a014efb220ef16166abbfad1c",
     "grade": false,
     "grade_id": "cell-c352e9d6c47aee09",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "bin_edges = [disc_eq_freq(X, 4)[1][:,1:-1] for X in X_list]\n",
    "\n",
    "figure = plt.figure(figsize=(6.4*3, 4.8))\n",
    "for idx, X in enumerate(X_list):\n",
    "    ax = plt.subplot(1, len(X_list), idx+1)\n",
    "    ax.scatter(X[:, 0], X[:, 1], edgecolors='k')\n",
    "    \n",
    "    ax.set_xlim(np.min(X[:,0]), np.max(X[:,0]))\n",
    "    ax.set_ylim(np.min(X[:,1]), np.max(X[:,1]))\n",
    "    \n",
    "    for x in bin_edges[idx][0]:\n",
    "        ax.axvline(x)\n",
    "    for y in bin_edges[idx][1]:\n",
    "        ax.axhline(y)\n",
    "    \n",
    "    ax.set_xticks(())\n",
    "    ax.set_yticks(())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discretization by clustering (4 pts)\n",
    "\n",
    "Remember to follow the paper by Daniela Joita, attatched."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "fedd7b5e06f61a1a4d637ddaffc7a0af",
     "grade": false,
     "grade_id": "cell-1bc52659604d965c",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Implement 1D k-means below\n",
    "\n",
    "def k_means_1D(x, k):\n",
    "    \"\"\" Implmentes K-means discretization.\n",
    "    \n",
    "    INPUT:\n",
    "        x: one dimensional numpy array with the features to discretize\n",
    "        k: number of bins\n",
    "        \n",
    "    OUTPUT:\n",
    "        b: the bin edges\n",
    "    \"\"\"\n",
    "    n = len(x)\n",
    "    x = np.array(x)\n",
    "    \n",
    "    # We need an array for the cluster index of each point\n",
    "    cluster = np.zeros(n, dtype=int)\n",
    "    \n",
    "    # Bin edges\n",
    "    b = np.zeros(k + 1)\n",
    "    \n",
    "    # This variable monitors the reallocation of clusters.\n",
    "    # change = true if at least one value is being moved to a different cluster.\n",
    "    change = False\n",
    "    \n",
    "    # Initialize cluster centers to first unique k elements in x\n",
    "    C = []\n",
    "    for e in x:\n",
    "        if e in C:\n",
    "            continue\n",
    "        C.append(e)\n",
    "        if len(C) == k:\n",
    "            break\n",
    "    C = np.sort(C)\n",
    "    if len(C) < k:\n",
    "        assert \"Error, not enough unique centers.\"\n",
    "    \n",
    "    # initialize bin edges\n",
    "    b[0] = -np.inf\n",
    "    b[-1] = np.inf\n",
    "    b[1:-1] = (C[1:] + C[:-1])/2\n",
    "\n",
    "    # Assign cluster index in cluster list\n",
    "    \n",
    "    for idx, e in enumerate(x): # for each index and value in dataset\n",
    "        for j in range(1,k+1): # for each cluster edge (start from 1 to avoid list out of index when validating intervals)\n",
    "            if e >= b[j-1] and e < b[j]: # check interval belonging\n",
    "                cluster[idx] = j - 1 # correct the index of the cluster since we started from 1 instead of 0\n",
    "\n",
    "    # Iteration\n",
    "    change = True\n",
    "    while change:\n",
    "        change = False\n",
    "        # Recompute the centers of the clusters as \n",
    "        # the average of the values in each cluster.\n",
    "        for j in range(k): # for each cluster index\n",
    "            temp = [] # create a temporal list to store x's that belong to the same center\n",
    "            for idx, e in enumerate(x): # for each index,value in dataset\n",
    "                if cluster[idx] == j: # if the cluster label is equal to the current cluster j\n",
    "                    temp.append(e) # store the value in temp\n",
    "            mean = sum(temp)/len(temp) # compute the average of all the x's that share the same center\n",
    "            C[j] = mean # recompute center of the cluster with average value\n",
    "\n",
    "        # Find the closest cluster to e from the possible clusters {j-1, j, j+1} .\n",
    "        for idx, e in enumerate(x):\n",
    "\n",
    "            j = cluster[idx] # start assigning the current cluster label to j\n",
    "\n",
    "            # as C is an ordered array, we just make two more verifications using the left and right neighbours {j-1, j, j+1} to know if we are in the correct cluster\n",
    "\n",
    "            if (j > 0) and (e < C[j]) and ((e - C[j-1]) < (C[j] - e)): # if the left is the correct then change the label\n",
    "                cluster[idx] = j - 1\n",
    "                change = True # keep in the while for recomputing centers with new cluster labels\n",
    "\n",
    "            if (j < k-1) and ( e > C[j]) and ((C[j+1] - e) < (e - C[j])):  # if the right is the correct then change the label\n",
    "                cluster[idx] = j + 1 \n",
    "                change = True # keep in the while for recomputing centers with new cluster labels\n",
    "\n",
    "        \n",
    "    # Determination of the cut points\n",
    "    b[0] = x.min()\n",
    "    b[-1] = x.max()\n",
    "    b[1:-1] = (C[1:] + C[:-1])/2\n",
    "    \n",
    "    return b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def disc_k_means(X, k):\n",
    "    \"\"\" Implmentes K-means discretization.\n",
    "    \n",
    "    INPUT:\n",
    "        X: data matrix as a numpy array\n",
    "        k: number of bins\n",
    "    \"\"\"\n",
    "    m, n = X.shape\n",
    "    X_disc = np.zeros(X.shape)\n",
    "    clims = []\n",
    "    \n",
    "    for i in range(n):\n",
    "        bin_edges = k_means_1D(X[:,i], k)\n",
    "        bin_edges[0] = -np.inf\n",
    "        bin_edges[-1] = np.inf\n",
    "        clims.append(list(bin_edges))\n",
    "        X_disc[:,i] = np.searchsorted(bin_edges, X[:,i], side='right') - 1\n",
    "        \n",
    "    return X_disc, np.array(clims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test the function employ the following test matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "0529ab957b46a8f6c6377883b5cb4286",
     "grade": true,
     "grade_id": "cell-6df3f09d755f5084",
     "locked": true,
     "points": 4,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The discretized matrix is:\n[[0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [2. 2. 2. 2.]\n [3. 3. 3. 3.]]\nExpected answer:\n[[0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [2. 2. 2. 2.]\n [3. 3. 3. 3.]]\n\nThe bin edges are:\n[[ -inf -1.5  -0.5   0.5    inf]\n [ -inf  1.5   2.5   3.5    inf]\n [ -inf -3.5  -2.5  -1.5    inf]\n [ -inf -0.75  0.    1.25   inf]]\nExpected edges:\n[[ -inf -1.5  -0.5   0.5    inf]\n [ -inf  1.5   2.5   3.5    inf]\n [ -inf -3.5  -2.5  -1.5    inf]\n [ -inf -0.75  0.    1.25   inf]]\n\n"
     ]
    }
   ],
   "source": [
    "X_test = np.array([[-2, 1, -4,   -1],\n",
    "                   [-1, 2, -3, -0.5],\n",
    "                   [ 0, 3, -2,  0.5],\n",
    "                   [ 1, 4, -1,    2]])\n",
    "\n",
    "X_disc, bin_edges = disc_k_means(X_test, 4)\n",
    "\n",
    "print(\"The discretized matrix is:\")\n",
    "print(X_disc)\n",
    "print(\"Expected answer:\")\n",
    "print(\"\"\"[[0. 0. 0. 0.]\n",
    " [1. 1. 1. 1.]\n",
    " [2. 2. 2. 2.]\n",
    " [3. 3. 3. 3.]]\"\"\")\n",
    "print()\n",
    "\n",
    "print(\"The bin edges are:\")\n",
    "print(bin_edges)\n",
    "print(\"Expected edges:\")\n",
    "print(\"\"\"[[ -inf -1.5  -0.5   0.5    inf]\n",
    " [ -inf  1.5   2.5   3.5    inf]\n",
    " [ -inf -3.5  -2.5  -1.5    inf]\n",
    " [ -inf -0.75  0.    1.25   inf]]\n",
    "\"\"\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code plots the sample data sets with the found partitions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "bin_edges = [disc_k_means(X, 4)[1][:,1:-1] for X in X_list]\n",
    "\n",
    "figure = plt.figure(figsize=(6.4*3, 4.8))\n",
    "for idx, X in enumerate(X_list):\n",
    "    ax = plt.subplot(1, len(X_list), idx+1)\n",
    "    ax.scatter(X[:, 0], X[:, 1], edgecolors='k')\n",
    "    \n",
    "    ax.set_xlim(np.min(X[:,0]), np.max(X[:,0]))\n",
    "    ax.set_ylim(np.min(X[:,1]), np.max(X[:,1]))\n",
    "    \n",
    "    for x in bin_edges[idx][0]:\n",
    "        ax.axvline(x)\n",
    "    for y in bin_edges[idx][1]:\n",
    "        ax.axhline(y)\n",
    "    \n",
    "    ax.set_xticks(())\n",
    "    ax.set_yticks(())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kernel density estimation (4 pts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
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     "locked": false,
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   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KernelDensity\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "def disc_kde_1D(x, plot=False):\n",
    "    \"\"\" Implmentes KDE discretization.\n",
    "    \n",
    "    INPUT:\n",
    "        x: one dimensional numpy array with the features to discretize\n",
    "               \n",
    "    OUTPUT:\n",
    "        b: the bin edges\n",
    "    \"\"\"\n",
    "    \n",
    "    n = len(x)\n",
    "    x = np.array(x)\n",
    "    x.sort()\n",
    "    \n",
    "    # Select an appropiate bw candidates\n",
    "    xmin = x[0]\n",
    "    xmax = x[-1]\n",
    "    xrange = xmax - xmin\n",
    "    bw_l = np.linspace(0.01*xrange, xrange, 100)\n",
    "    bw_scores = np.zeros(len(bw_l))\n",
    "   \n",
    "    # Use 10-fold CV. Find the corresponding train and test for each fold.\n",
    "    # Note: Since x is ordered, maybe systematic sampling would give better cv results.\n",
    "    folds = list(KFold(n_splits=10, shuffle=True, random_state=11).split(x))\n",
    "\n",
    "    best_params = GridSearchCV(KernelDensity(kernel='gaussian'), {'bandwidth': bw_l}, cv=folds).fit(x.reshape(-1, 1)).best_params_\n",
    "\n",
    "    # Iterating over each fold by hand (same result as above)\n",
    "    \"\"\"for i, bw in enumerate(bw_l):\n",
    "        \n",
    "        scores = []\n",
    "        for train_index, test_index in folds:\n",
    "            kernel = KernelDensity(bandwidth=bw, kernel='gaussian').fit(x[train_index].reshape(-1,1))\n",
    "            scores.append(kernel.score(x[test_index].reshape(-1,1)))\n",
    "\n",
    "        bw_scores[i] = np.mean(scores)\"\"\"\n",
    "\n",
    "    # It seems the best bw benefits from some smoothing, need to explore this more, systematic sampling may solve this.\n",
    "    #best_bw = 1.5*bw_l[np.argmax(bw_scores)]\n",
    "    best_bw = 1.5*best_params['bandwidth']\n",
    "    \n",
    "\n",
    "    # List to store bin edges\n",
    "    bin_edges = [xmin]\n",
    "    \n",
    "    # Find local minima using a grid, other option is to use data poitns.\n",
    "    grid_x = np.linspace(xmin, xmax, 100)\n",
    "    kde_full = KernelDensity(bandwidth=best_bw, kernel='gaussian').fit(x.reshape(-1,1)).score_samples(grid_x.reshape(-1,1))\n",
    "\n",
    "    \"\"\"if  (kde_full[0] <  kde_full[1]):\n",
    "        bin_edges.append(grid_x[0])\"\"\"\n",
    "\n",
    "    for i in range(1, len(kde_full)-1):\n",
    "\n",
    "        if  (kde_full[i-1] >  kde_full[i]) and (kde_full[i] < kde_full[i+1]):\n",
    "            bin_edges.append(grid_x[i])\n",
    "\n",
    "    \"\"\"if (kde_full[-1] <  kde_full[-2]):\n",
    "        bin_edges.append(grid_x[-1])\"\"\"\n",
    "        \n",
    "    bin_edges.append(xmax)\n",
    "    \n",
    "    return np.array(bin_edges)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def disc_kde(X):\n",
    "    m, n = X.shape\n",
    "    X_disc = np.zeros(X.shape)\n",
    "    clims = []\n",
    "    \n",
    "    for i in range(n):\n",
    "        bin_edges = disc_kde_1D(X[:,i])\n",
    "        bin_edges[0] = -np.inf\n",
    "        bin_edges[-1] = np.inf\n",
    "        clims.append(bin_edges)\n",
    "        X_disc[:,i] = np.searchsorted(bin_edges, X[:,i], side='right') - 1\n",
    "    \n",
    "    # Now clims cannot be an array, since there is no guarante\n",
    "    # that all features will have the same number of bins    \n",
    "    return X_disc, clims"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test the function employ the following test matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
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     "locked": true,
     "points": 4,
     "schema_version": 3,
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    },
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The discretized matrix is:\n[[0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [1. 1. 1. 2.]\n [2. 2. 2. 3.]\n [0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [1. 1. 1. 2.]\n [2. 2. 2. 3.]\n [0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [1. 1. 1. 2.]\n [2. 2. 2. 3.]]\nExpected answer:\n[[0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [1. 1. 1. 2.]\n [2. 2. 2. 3.]\n [0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [1. 1. 1. 2.]\n [2. 2. 2. 3.]\n [0. 0. 0. 0.]\n [1. 1. 1. 1.]\n [1. 1. 1. 2.]\n [2. 2. 2. 3.]]\n\nThe bin edges are:\n[       -inf -1.61616162  0.61616162         inf]\n[      -inf 1.61414141 3.58585859        inf]\n[       -inf -3.58585859 -1.61414141         inf]\n[       -inf -0.85656566  0.0020202   1.34141414         inf]\nExpected edges:\n[       -inf -1.61616162  0.61616162         inf]\n[      -inf 1.61414141 3.58585859        inf]\n[       -inf -3.58585859 -1.61414141         inf]\n[       -inf -0.85656566  0.0020202   1.34141414         inf]\n\n"
     ]
    }
   ],
   "source": [
    "X_test = np.array([[-2, 1, -4,   -1],\n",
    "                   [-1, 2, -3, -0.5],\n",
    "                   [ 0, 3, -2,  0.5],\n",
    "                   [ 1, 4, -1,    2],\n",
    "                   [-2.1, 1.1, -4.1,   -1.1],\n",
    "                   [-1.1, 2.1, -3.1, -0.6],\n",
    "                   [ 0.1, 3.1, -2.1,  0.6],\n",
    "                   [ 1.1, 4.1, -1.1,    2.1],\n",
    "                   [-2.2, 1.2, -4.2,   -1.2],\n",
    "                   [-1.2, 2.2, -3.2, -0.7],\n",
    "                   [ 0.2, 3.2, -2.2,  0.7],\n",
    "                   [ 1.2, 4.2, -1.2,    2.2]])\n",
    "\n",
    "X_disc, bin_edges = disc_kde(X_test)\n",
    "\n",
    "print(\"The discretized matrix is:\")\n",
    "print(X_disc)\n",
    "print(\"Expected answer:\")\n",
    "print(\"\"\"[[0. 0. 0. 0.]\n",
    " [1. 1. 1. 1.]\n",
    " [1. 1. 1. 2.]\n",
    " [2. 2. 2. 3.]\n",
    " [0. 0. 0. 0.]\n",
    " [1. 1. 1. 1.]\n",
    " [1. 1. 1. 2.]\n",
    " [2. 2. 2. 3.]\n",
    " [0. 0. 0. 0.]\n",
    " [1. 1. 1. 1.]\n",
    " [1. 1. 1. 2.]\n",
    " [2. 2. 2. 3.]]\"\"\")\n",
    "print()\n",
    "\n",
    "print(\"The bin edges are:\")\n",
    "for b in bin_edges:\n",
    "    print(b)\n",
    "print(\"Expected edges:\")\n",
    "print(\"\"\"[       -inf -1.61616162  0.61616162         inf]\n",
    "[      -inf 1.61414141 3.58585859        inf]\n",
    "[       -inf -3.58585859 -1.61414141         inf]\n",
    "[       -inf -0.85656566  0.0020202   1.34141414         inf]\n",
    "\"\"\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code plots the sample data sets with the found partitions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "bin_edges = [disc_kde(X)[1] for X in X_list]\n",
    "\n",
    "figure = plt.figure(figsize=(6.4*3, 4.8))\n",
    "for idx, X in enumerate(X_list):\n",
    "    ax = plt.subplot(1, len(X_list), idx+1)\n",
    "    ax.scatter(X[:, 0], X[:, 1], edgecolors='k')\n",
    "    \n",
    "    ax.set_xlim(np.min(X[:,0]), np.max(X[:,0]))\n",
    "    ax.set_ylim(np.min(X[:,1]), np.max(X[:,1]))\n",
    "    \n",
    "    for x in bin_edges[idx][0][1:-1]:\n",
    "        ax.axvline(x)\n",
    "    for y in bin_edges[idx][1][1:-1]:\n",
    "        ax.axhline(y)\n",
    "    \n",
    "    ax.set_xticks(())\n",
    "    ax.set_yticks(())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python385jvsc74a57bd076e3749c4d8f143b85e17554ce3ae58a0fcf4212a15be7e0134aaba6048266e3",
   "display_name": "Python 3.8.5 64-bit ('base': conda)"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}