SML homework template Q3

hw3_template.ipynb

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    "# Q1\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import linalg as LA\n",
    "from matplotlib.patches import Ellipse\n",
    "from sklearn.datasets.samples_generator import make_blobs \n",
    "from scipy.stats import multivariate_normal\n",
    "\n",
    "K = 3\n",
    "NUMDATAPTS = 150\n",
    "\n",
    "X, y = make_blobs(n_samples=NUMDATAPTS, centers=K, shuffle=False, random_state=0, cluster_std=0.6)\n",
    "\n",
    "g1 = np.asarray([[2.0, 0], [-0.9, 1]])\n",
    "g2 = np.asarray([[1.4, 0], [0.5, 0.7]])\n",
    "\n",
    "mean1 = np.mean(X[:int(NUMDATAPTS/K)])\n",
    "mean2 = np.mean(X[int(NUMDATAPTS/K):2*int(NUMDATAPTS/K)])\n",
    "\n",
    "X[:int(NUMDATAPTS/K)] = np.einsum('nj,ij->ni', X[:int(NUMDATAPTS/K)] - mean1, g1) + mean1\n",
    "X[int(NUMDATAPTS/K):2*int(NUMDATAPTS/K)] = np.einsum('nj,ij->ni', X[int(NUMDATAPTS/K):2*int(NUMDATAPTS/K)] - mean2, g2) + mean2\n",
    "X[:,1] -= 4\n",
    "\n",
    "\n",
    "def E_step():\n",
    "    gamma = np.zeros((NUMDATAPTS, K))\n",
    "    # your steps here\n",
    "    return gamma\n",
    "\n",
    "def M_step(gamma): \n",
    "    # your steps here\n",
    "    return None\n",
    "\n",
    "\n",
    "def plot_result(gamma=None):\n",
    "    ax = plt.subplot (111 , aspect='equal')\n",
    "    ax.set_xlim([-5, 5])\n",
    "    ax.set_ylim([-5, 5])\n",
    "    ax.scatter(X[:, 0], X[:, 1], c=gamma, s=50, cmap=None)\n",
    "    for k in range(K):\n",
    "        l, v = LA.eig(cov[k])\n",
    "        theta = np.arctan(v[1,0]/v[0,0])\n",
    "        e = Ellipse((mu[k, 0], mu[k, 1]), 6*l[0], 6*l[1], theta*180 / np.pi)\n",
    "        e.set_alpha(0.5) \n",
    "        ax.add_artist(e)\n",
    "        plt.show()"
   ]
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   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Q4\n",
    "\n",
    "import numpy as np\n",
    "from sklearn import decomposition\n",
    "from sklearn import datasets\n",
    "X = datasets.load_diabetes().data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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