SU1-2021-05-LDM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sveučilište u Zagrebu  \n",
    "Fakultet elektrotehnike i računarstva  \n",
    "  \n",
    "## Strojno učenje 1 2021/2022  \n",
    "http://www.fer.unizg.hr/predmet/struce1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------------------------\n",
    "\n",
    "### Linearni diskriminativni modeli\n",
    "\n",
    "*Verzija: 1.1 (ispravljena greška u tekstu prvog zadatka)  \n",
    "Zadnji put ažurirano: 1. 10. 2021.*\n",
    "\n",
    "(c) 2015-2021 Jan Šnajder, Domagoj Alagić  \n",
    "\n",
    "Rok za predaju: **31. listopada 2021. u 23:59h**\n",
    "\n",
    "------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Upute\n",
    "\n",
    "Ova laboratorijska vježba sastoji se od dva zadatka. U nastavku slijedite upute navedene u ćelijama s tekstom. Rješavanje vježbe svodi se na **dopunjavanje ove bilježnice**: umetanja ćelije ili više njih **ispod** teksta zadatka, pisanja odgovarajućeg kôda te evaluiranja ćelija. \n",
    "\n",
    "Osigurajte da u potpunosti **razumijete** kôd koji ste napisali. Kod predaje vježbe, morate biti u stanju na zahtjev asistenta (ili demonstratora) preinačiti i ponovno evaluirati Vaš kôd. Nadalje, morate razumjeti teorijske osnove onoga što radite, u okvirima onoga što smo obradili na predavanju. Ispod nekih zadataka možete naći i pitanja koja služe kao smjernice za bolje razumijevanje gradiva (**nemojte pisati** odgovore na pitanja u bilježnicu). Stoga se nemojte ograničiti samo na to da riješite zadatak, nego slobodno eksperimentirajte. To upravo i jest svrha ovih vježbi.\n",
    "\n",
    "Vježbe trebate raditi **samostalno**. Možete se konzultirati s drugima o načelnom načinu rješavanja, ali u konačnici morate sami odraditi vježbu. U protivnome vježba nema smisla."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "# Učitaj osnovne biblioteke...\n",
    "import sklearn\n",
    "import matplotlib.pyplot as plt\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_2d_clf_problem(X, y, h=None):\n",
    "    '''\n",
    "    Plots a two-dimensional labeled dataset (X,y) and, if function h(x) is given, \n",
    "    the decision surfaces.\n",
    "    '''\n",
    "    assert X.shape[1] == 2, \"Dataset is not two-dimensional\"\n",
    "    if h!=None : \n",
    "        # Create a mesh to plot in\n",
    "        r = 0.04  # mesh resolution\n",
    "        x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "        y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "        xx, yy = np.meshgrid(np.arange(x_min, x_max, r),\n",
    "                             np.arange(y_min, y_max, r))\n",
    "        XX=np.c_[xx.ravel(), yy.ravel()]\n",
    "        try:\n",
    "            Z_test = h(XX)\n",
    "            if Z_test.shape == ():\n",
    "                # h returns a scalar when applied to a matrix; map explicitly\n",
    "                Z = np.array(list(map(h,XX)))\n",
    "            else :\n",
    "                Z = Z_test\n",
    "        except ValueError:\n",
    "            # can't apply to a matrix; map explicitly\n",
    "            Z = np.array(list(map(h,XX)))\n",
    "        # Put the result into a color plot\n",
    "        Z = Z.reshape(xx.shape)\n",
    "        plt.contourf(xx, yy, Z, cmap=plt.cm.Pastel1)\n",
    "\n",
    "    # Plot the dataset\n",
    "    plt.scatter(X[:,0],X[:,1], c=y, cmap=plt.cm.tab20b, marker='o', s=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Linearna regresija kao klasifikator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "U prethodnoj laboratorijskoj vježbi koristili smo model linearne regresije za, naravno, regresiju. Međutim, model linearne regresije može se koristiti i za **klasifikaciju**. Iako zvuči pomalo kontraintuitivno, zapravo je dosta jednostavno. Naime, cilj je naučiti funkciju $f(\\mathbf{x})$ koja za pozitivne primjere predviđa vrijednost $1$, dok za negativne primjere predviđa vrijednost $0$. U tom slučaju, funkcija $f(\\mathbf{x})=0.5$ predstavlja granicu između klasa, tj. primjeri za koje vrijedi $h(\\mathbf{x})\\geq 0.5$ klasificiraju se kao pozitivni, dok se ostali klasificiraju kao negativni.\n",
    "\n",
    "Klasifikacija pomoću linearne regresije implementirana je u razredu [`RidgeClassifier`](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.RidgeClassifier.html). U sljedećim podzadatcima **istrenirajte** taj model na danim podatcima i **prikažite** dobivenu granicu između klasa. Pritom isključite regularizaciju ($\\alpha = 0$, odnosno `alpha=0`). Također i ispišite **točnost** vašeg klasifikacijskog modela (smijete koristiti funkciju [`metrics.accuracy_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.accuracy_score.html)). Skupove podataka vizualizirajte korištenjem pomoćne funkcije ``plot_clf_problem(X, y, h=None)`` koja je dana na početku ove bilježnice. `X` i `y` predstavljaju ulazne primjere i oznake, dok `h` predstavlja funkciju predikcije modela (npr. `model.predict`). \n",
    "\n",
    "U ovom zadatku cilj je razmotriti kako se klasifikacijski model linearne regresije ponaša na linearno odvojim i neodvojivim podatcima."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression, RidgeClassifier\n",
    "from sklearn.metrics import accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a)\n",
    "\n",
    "Prvo, isprobajte *ugrađeni* model na linearno odvojivom skupu podataka `seven` ($N=7$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "seven_X = np.array([[2,1], [2,3], [1,2], [3,2], [5,2], [5,4], [6,3]])\n",
    "seven_y = np.array([1, 1, 1, 1, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted: [1 1 1 1 0 0 0]\n",
      "accuracy: 1.0\n",
      "score: 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "classifier = RidgeClassifier(alpha=0).fit(seven_X, seven_y)\n",
    "\n",
    "# model predict\n",
    "predicted = classifier.predict(seven_X)\n",
    "print(f\"predicted: {predicted}\")\n",
    "\n",
    "# score\n",
    "accuracy = accuracy_score(y_true=seven_y, y_pred=predicted)\n",
    "print(f\"accuracy: {accuracy}\")\n",
    "\n",
    "score = classifier.score(seven_X, seven_y)\n",
    "print(f\"score: {score}\")\n",
    "\n",
    "assert(accuracy == score)\n",
    "\n",
    "# show plot\n",
    "plot_2d_clf_problem(seven_X, seven_y, classifier.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kako bi se uvjerili da se u isprobanoj implementaciji ne radi o ničemu doli o običnoj linearnoj regresiji, napišite kôd koji dolazi do jednakog rješenja korištenjem isključivo razreda [`LinearRegression`](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html). Funkciju za predikciju, koju predajete kao treći argument `h` funkciji `plot_2d_clf_problem`, možete definirati lambda-izrazom: `lambda x : model.predict(x) >= 0.5`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted lin reg: [ 1.   0.9  1.2  0.7  0.2  0.1 -0.1]\n",
      "predicted override: [ True  True  True  True False False False]\n",
      "accuracy: 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg = LinearRegression().fit(seven_X, seven_y)\n",
    "\n",
    "# model predict\n",
    "predicted_reg = reg.predict(seven_X)\n",
    "print(f\"predicted lin reg: {predicted_reg}\")\n",
    "\n",
    "# override model predict\n",
    "def predict_override(X):\n",
    "    return reg.predict(X) >= 0.5\n",
    "\n",
    "predicted_override = predict_override(seven_X)\n",
    "print(f\"predicted override: {predicted_override}\")\n",
    "\n",
    "# score\n",
    "accuracy = accuracy_score(y_true=seven_y, y_pred=predicted_override)\n",
    "print(f\"accuracy: {accuracy}\")\n",
    "\n",
    "assert(accuracy == 1.0)\n",
    "\n",
    "# show plot\n",
    "plot_2d_clf_problem(seven_X, seven_y, predict_override)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q:** Kako bi bila definirana granica između klasa ako bismo koristili oznake klasa $-1$ i $1$ umjesto $0$ i $1$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b)  \n",
    "\n",
    "Probajte isto na linearno odvojivom skupu podataka `outlier` ($N=8$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [],
   "source": [
    "outlier_X = np.append(seven_X, [[12,8]], axis=0)\n",
    "outlier_y = np.append(seven_y, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted: [1 1 1 1 0 1 0 0]\n",
      "accuracy: 0.875\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "classifier = RidgeClassifier(alpha=0).fit(outlier_X, outlier_y)\n",
    "\n",
    "# model predict\n",
    "predicted = classifier.predict(outlier_X)\n",
    "print(f\"predicted: {predicted}\")\n",
    "\n",
    "# score\n",
    "accuracy = accuracy_score(y_true=outlier_y, y_pred=predicted)\n",
    "print(f\"accuracy: {accuracy}\")\n",
    "\n",
    "# show plot\n",
    "plot_2d_clf_problem(outlier_X, outlier_y, classifier.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q:** Zašto model ne ostvaruje potpunu točnost iako su podatci linearno odvojivi?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c)  \n",
    "\n",
    "Završno, probajte isto na linearno neodvojivom skupu podataka `unsep` ($N=8$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "unsep_X = np.append(seven_X, [[2,2]], axis=0)\n",
    "unsep_y = np.append(seven_y, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted: [1 1 1 1 0 0 0 1]\n",
      "accuracy: 0.875\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "classifier = RidgeClassifier(alpha=0).fit(unsep_X, unsep_y)\n",
    "\n",
    "# model predict\n",
    "predicted = classifier.predict(unsep_X)\n",
    "print(f\"predicted: {predicted}\")\n",
    "\n",
    "# score\n",
    "accuracy = accuracy_score(y_true=unsep_y, y_pred=predicted)\n",
    "print(f\"accuracy: {accuracy}\")\n",
    "\n",
    "# show plot\n",
    "plot_2d_clf_problem(unsep_X, unsep_y, classifier.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q:** Očito je zašto model nije u mogućnosti postići potpunu točnost na ovom skupu podataka. Međutim, smatrate li da je problem u modelu ili u podacima? Argumentirajte svoj stav."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Višeklasna klasifikacija"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Postoji više načina kako se binarni klasifikatori mogu se upotrijebiti za višeklasnu klasifikaciju. Najčešće se koristi shema tzv. **jedan-naspram-ostali** (engl. *one-vs-rest*, OVR), u kojoj se trenira po jedan klasifikator $h_j$ za svaku od $K$ klasa. Svaki klasifikator $h_j$ trenira se da razdvaja primjere klase $j$ od primjera svih drugih klasa, a primjer se klasificira u klasu $j$ za koju je $h_j(\\mathbf{x})$ maksimalan.\n",
    "\n",
    "Pomoću funkcije [`datasets.make_classification`](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_classification.html) generirajte slučajan dvodimenzijski skup podataka od tri klase i prikažite ga koristeći funkciju `plot_2d_clf_problem`. Radi jednostavnosti, pretpostavite da nema redundantnih značajki te da je svaka od klasa \"zbijena\" upravo u jednu grupu."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_classification\n",
    "\n",
    "X, y = make_classification(n_samples=30, n_features=2, n_redundant=0, n_repeated=0, n_classes=3, n_clusters_per_class=1)\n",
    "plot_2d_clf_problem(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trenirajte tri binarna klasifikatora, $h_1$, $h_2$ i $h_3$ te prikažite granice između klasa (tri grafikona). Zatim definirajte $h(\\mathbf{x})=\\mathrm{argmax}_j h_j(\\mathbf{x})$  (napišite svoju funkciju `predict` koja to radi) i prikažite granice između klasa za taj model. Zatim se uvjerite da biste identičan rezultat dobili izravno primjenom modela `RidgeClassifier`, budući da taj model za višeklasan problem zapravo interno implementira shemu jedan-naspram-ostali.\n",
    "\n",
    "**Q:** Alternativna shema jest ona zvana **jedan-naspram-jedan** (engl, *one-vs-one*, OVO). Koja je prednost sheme OVR nad shemom OVO? A obratno?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# h1\n",
    "y1 = [1 if i == 0 else 0 for i in y]\n",
    "\n",
    "reg1 = LinearRegression().fit(X, y1)\n",
    "def predict1(X):\n",
    "    return reg1.predict(X) >= 0.5\n",
    "    \n",
    "plot_2d_clf_problem(X, y1, predict1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# h2\n",
    "y2 = [1 if i == 1 else 0 for i in y]\n",
    "\n",
    "reg2 = LinearRegression().fit(X, y2)\n",
    "def predict2(X):\n",
    "    return reg2.predict(X) >= 0.5\n",
    "\n",
    "plot_2d_clf_problem(X, y2, predict2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# h3\n",
    "y3 = [1 if i == 2 else 0 for i in y]\n",
    "\n",
    "reg3 = LinearRegression().fit(X, y3)\n",
    "def predict3(X):\n",
    "    return reg3.predict(X) >= 0.5\n",
    "\n",
    "plot_2d_clf_problem(X, y3, predict3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_argmax(X):\n",
    "    predicted = list()\n",
    "    for r in [reg1, reg2, reg3]:\n",
    "        predicted.append(r.predict(X.reshape(1, -1)))\n",
    "    return np.argmax(predicted)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_2d_clf_problem(X, y, predict_argmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "classifier = RidgeClassifier(alpha=0).fit(X, y)\n",
    "plot_2d_clf_problem(X, y, classifier.predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}