pca stuff.ipynb

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    "Make some data and do PCA on it."
   ]
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   "cell_type": "markdown",
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   "source": [
    "## set up distribution, generate data"
   ]
  },
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from numpy.random import normal\n",
    "\n",
    "a = 1\n",
    "b = 10\n",
    "\n",
    "y = lambda x: a*x + b + normal()\n",
    "\n",
    "n = 100\n",
    "\n",
    "# generate data.\n",
    "xx = normal(0, 1, n)\n",
    "yy = np.array([y(x) for x in xx])\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(xx, yy)\n",
    "plt.show()"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "# standardize.\n",
    "\n",
    "xx_standardized = (xx - np.mean(xx))/np.std(xx)\n",
    "yy_standardized = (yy - np.mean(yy))/np.std(yy)\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(xx_standardized, yy_standardized)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1fada84",
   "metadata": {},
   "outputs": [],
   "source": [
    "# data set.\n",
    "\n",
    "S = np.array([xx_standardized, yy_standardized])\n",
    "u, s, vh = np.linalg.svd(S)\n",
    "print(u)\n",
    "\n",
    "alpha=3\n",
    "\n",
    "plt.figure(figsize=(6.4, 6.4))\n",
    "plt.scatter(xx_standardized, yy_standardized)\n",
    "\n",
    "# shabby way of plotting axis.\n",
    "plt.plot([-alpha*u[0][0], alpha*u[0][0]], [-alpha*u[0][1], alpha*u[0][1]], color='red', label='pc1')\n",
    "plt.plot([-alpha*u[1][0], alpha*u[1][0]], [-alpha*u[1][1], alpha*u[1][1]], color='black', label='pc2')\n",
    "plt.xlim(-4, 4)\n",
    "plt.ylim(-4, 4)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "70185fa4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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