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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Wizualizacja tricku kernelowego"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "W pierwszym kroku generujemy dane które nie są separowalne w przestrzeni 2-D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:53:34.093325Z",
     "start_time": "2020-05-19T15:53:33.908256Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_circles\n",
    "\n",
    "X, y = make_circles(n_samples=100, noise=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:53:34.740342Z",
     "start_time": "2020-05-19T15:53:34.561022Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib notebook\n",
    "\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:53:37.807737Z",
     "start_time": "2020-05-19T15:53:37.805154Z"
    }
   },
   "outputs": [],
   "source": [
    "x1, x2 = X[:, 0], X[:, 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "W następnym kroku posłużymy się trickiem kernelowym żeby przetransformować dane z przestrzeni 2-D (w której dane nie są liniowo separowalne) do przestrzeni 3-D, w której będą liniowo separowalne. Użyjemy następującego kernela (symbol $<>$ oznacza iloczyn skalarny wektorów): $$K(x,y)=<x,y>^2$$ który przeprowadza następującą transformacją: \n",
    "\n",
    "$$<[x_1x_2],[y_1y_2]>^2=(x_1y_1 * x_2y_2)^2=x_1^2y_1^2 + 2x_1y_1x_2y_2 + x_2^2y_2^2 = x_1^2y_1^2 + \\sqrt{2}x_1x_2\\sqrt{2}y_1y_2 + x_2^2y_2^2 = <[x_1^2,\\sqrt{2}x_1x_2,x_2^2],[y_1^2,\\sqrt{2}y_1y_2,y_2^2]>$$\n",
    "\n",
    "$$\\phi([x_1,x_2]=[x_1^2, \\sqrt{2}x_1x_2, x_2^2]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:53:39.652619Z",
     "start_time": "2020-05-19T15:53:39.649058Z"
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   },
   "outputs": [],
   "source": [
    "z1 = x1**2\n",
    "z2 = np.sqrt(2)*x1*x2\n",
    "z3 = x2**2\n",
    "\n",
    "Z = np.column_stack((z1, z2, z3))\n",
    "\n",
    "print(Z[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Po transformacji dane są w sposób oczywisty separowalne w przestrzeni 3-D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:53:40.828850Z",
     "start_time": "2020-05-19T15:53:40.790886Z"
    }
   },
   "outputs": [],
   "source": [
    "plt.clf()\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(z2, z3, z1, c=y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:44:18.413178Z",
     "start_time": "2020-05-19T15:44:18.410349Z"
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   },
   "source": [
    "### dla chętnych\n",
    "\n",
    "Przeprowadź analogiczną wizualizację przy użyciu kernela $K(x,y)=(1+<x,y>)^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Klasyfikacja przy użyciu SVM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do realizacji ćwiczenia posłużymy się klasą [sklearn.svm.SVM](https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html) i sprawdzimy wrażliwość algorytmu na poszczególne parametry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:53:55.300254Z",
     "start_time": "2020-05-19T15:53:55.295645Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_wine\n",
    "wines = load_wine()\n",
    "\n",
    "print(wines['DESCR'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:54:01.813312Z",
     "start_time": "2020-05-19T15:54:01.808455Z"
    }
   },
   "outputs": [],
   "source": [
    "X, y = wines['data'], wines['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:54:02.616414Z",
     "start_time": "2020-05-19T15:54:02.406030Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plt.hist(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:55:20.171512Z",
     "start_time": "2020-05-19T15:55:20.165073Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import classification_report, confusion_matrix\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "scaler = StandardScaler()\n",
    "\n",
    "# https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html\n",
    "svm = SVC(C=1e-2, kernel='poly', degree=2)\n",
    "\n",
    "X = scaler.fit(X).transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:55:20.629940Z",
     "start_time": "2020-05-19T15:55:20.626950Z"
    }
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:55:20.809762Z",
     "start_time": "2020-05-19T15:55:20.805781Z"
    }
   },
   "outputs": [],
   "source": [
    "y_pred = svm.fit(X_train, y_train).predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-19T15:55:21.113405Z",
     "start_time": "2020-05-19T15:55:21.105950Z"
    }
   },
   "outputs": [],
   "source": [
    "print(f\"\"\" {\n",
    "\n",
    "classification_report(y_pred, y_test)}\n",
    "\n",
    "Confusion matrix:\n",
    "{confusion_matrix(y_pred, y_test)} \n",
    "\n",
    "Number of support vectors per class: {svm.n_support_}\n",
    "\n",
    "\"\"\")"
   ]
  }
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