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  {
   "cell_type": "markdown",
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   "source": [
    "# Dimension Reduction\n",
    "\n",
    "Dimension reduction has a close relation to feature engineering. Before performing the clustering, we wish to keep the main features of data instead of dumping the whole raw data into the clustering models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "\n",
    "pd.set_option(\"display.max_rows\", 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Preparation\n",
    "\n",
    "When we have the raw data of discrete particle velocities at a given location, we first need to convert that into a distribution function. Here we take advantage of the Kernel Density Estimation (KDE) technique implemented in scikit-learn. Note that an alternative implementation exists in `seaborn` but for plotting purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KernelDensity\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from vdfpy.generator import make_clusters\n",
    "\n",
    "df = make_clusters(n_clusters=3, n_dims=1, n_points=100, n_samples=50, random_state=1)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_features = 200\n",
    "X_plot = np.linspace(-4, 4, n_features)[:, np.newaxis]\n",
    "\n",
    "density = np.zeros(shape=(df[\"particle velocity\"].size, n_features))\n",
    "\n",
    "for isample, pv in enumerate(df[\"particle velocity\"]):\n",
    "    kde = KernelDensity(bandwidth=\"silverman\").fit(pv.values)\n",
    "    log_den = kde.score_samples(X_plot)\n",
    "    density[isample,:] = np.exp(log_den)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 3), layout=\"constrained\")\n",
    "\n",
    "ax.plot(X_plot[:, 0], np.transpose(density), alpha=0.6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "n_components = 2\n",
    "pca = PCA(n_components=n_components)\n",
    "pca.fit(density)\n",
    "X = pca.transform(density)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4), layout=\"constrained\")\n",
    "ax.scatter(X[:,0], X[:,1], s=10, c=df[\"class\"], cmap=\"Set1\")\n",
    "ax.set_xlabel(\"1st Principle Component\", fontsize=14)\n",
    "ax.set_ylabel(\"2nd Principle Component\", fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import umap\n",
    "\n",
    "reducer = umap.UMAP(n_components=2)\n",
    "\n",
    "X = reducer.fit_transform(density)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4), layout=\"constrained\")\n",
    "ax.scatter(X[:,0], X[:,1], s=10, c=df[\"class\"], cmap=\"Set1\")\n",
    "xax = ax.axes.get_xaxis()\n",
    "xax.set_visible(False)\n",
    "yax = ax.axes.get_yaxis()\n",
    "yax.set_visible(False)\n",
    "plt.title(\"UMAP projection\", fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that `umap` has its own [plotting support](https://umap-learn.readthedocs.io/en/latest/plotting.html#) with some extra dependencies."
   ]
  }
 ],
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