PCA-code.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "from sklearn.decomposition import PCA\n",
    "from numpy import linalg as LA\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape X:  (200, 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
    "print(\"Shape X: \", X.shape)\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  3.72125118 151.9275557 ]\n",
      "[0.01860626 0.75963778]\n",
      "[[ 0.3280512  -0.94465994]\n",
      " [-0.94465994 -0.3280512 ]]\n"
     ]
    }
   ],
   "source": [
    "w, v = LA.eigh(X.T@X)\n",
    "w_prime = w/X.shape[0]\n",
    "print(w)\n",
    "print(w_prime)\n",
    "print(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.023908 0.976092]\n"
     ]
    }
   ],
   "source": [
    "print((w)/sum(w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.7625315 0.0184779]\n"
     ]
    }
   ],
   "source": [
    "print (pca.explained_variance_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean:  [ 0.03351168 -0.00408072]\n"
     ]
    }
   ],
   "source": [
    "mean = np.mean(X, axis = 0)\n",
    "print(\"Mean: \", mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.94446029 -0.32862557]\n",
      " [-0.32862557  0.94446029]]\n"
     ]
    }
   ],
   "source": [
    "print(pca.components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_vector(v0, v1, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    arrowprops=dict(arrowstyle='->',\n",
    "                    linewidth=2,\n",
    "                    shrinkA=0, shrinkB=0, color = 'black')\n",
    "    ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
    "\n",
    "# plot data\n",
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    draw_vector(pca.mean_, pca.mean_ + v)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hola\n"
     ]
    }
   ],
   "source": [
    "str_ = \"string\"\n",
    "\n",
    "if str_ == \"string\":\n",
    "    print(\"hola\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}