{ "cells": [ { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "## Iskanje strukture v podatkih\n", "\n", "Podatkovno rudarjenje, naloga, 13. april 2025\n", "**Gašper Dobrovoljc**" ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "Z modeliranjem skušamo poiskati strukturo v podatkih. Z metodami nenadzorovanga modeliranja skušamo poiskati skupine podobnih podatkov oz. skupine primerov.\n", "\n", "V nalogi boste uporabili modeliranje verjetnostnih porazdelitev za iskanje osamelcev ter metode za iskanje skupin podobnih primerov (gručenje)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Podatki\n", "\n", "Opis podatkovne zbirke MovieLens ostaja enak prvi nalogi." ] }, { "metadata": { "ExecuteTime": { "end_time": "2025-04-13T19:29:49.004377Z", "start_time": "2025-04-13T19:29:48.481942Z" } }, "cell_type": "code", "source": [ "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "ratings = pd.read_csv('./podatki/ml-latest-small/ratings.csv')\n", "movies = pd.read_csv('./podatki/ml-latest-small/movies.csv')\n", "\n", "ratings['timestamp'] = pd.to_datetime(ratings['timestamp'], unit='s')" ], "outputs": [], "execution_count": 1 }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "### Vprašanja\n", "\n", "Z uporabo principov, ki ste jih spoznali na vajah in predavanjih, odgovorite na\n", "spodnja vprašanja. Pri vsakem vprašanju dobro premislite, na kakšen način boste\n", "najbolje podali, prikazali oz. utemeljili odgovor. Bistven del so odgovori na\n", "vprašanja in ne toliko implementacija vaše rešitve." ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 1. Iskanje osamelcev (50%) \n", "O ocenah katerih filmov so si uporabniki najmanj enotni? Povedano drugače, za katere filme so pripadajoče ocene najbolj razpršene?\n", "\n", "Formuliraj problem kot modeliranje verjetnostne porazdelitve. Premisli o naslednjih vprašanjih, naredi ustrezne poizkuse in odgovori." ] }, { "metadata": { "ExecuteTime": { "end_time": "2025-04-13T19:29:49.021962Z", "start_time": "2025-04-13T19:29:49.009148Z" } }, "cell_type": "code", "source": [ "ratings_agg = ratings.groupby('movieId')['rating'].agg(['count', 'var'])\n", "ratings_agg = ratings_agg[ratings_agg['count'] >= 5]\n", "\n", "ratings_agg.merge(movies, on='movieId').sort_values(by='var', ascending=False)" ], "outputs": [ { "data": { "text/plain": [ " movieId count var \\\n", "2042 3973 5 4.550000 \n", "1305 2365 5 4.200000 \n", "1428 2570 5 3.500000 \n", "2515 6535 6 3.366667 \n", "1993 3813 6 3.366667 \n", "... ... ... ... \n", "2167 4356 6 0.041667 \n", "239 346 6 0.000000 \n", "1348 2417 5 0.000000 \n", "1510 2749 5 0.000000 \n", "483 829 7 0.000000 \n", "\n", " title \\\n", "2042 Book of Shadows: Blair Witch 2 (2000) \n", "1305 King Kong vs. Godzilla (Kingukongu tai Gojira)... \n", "1428 Walk on the Moon, A (1999) \n", "2515 Legally Blonde 2: Red, White & Blonde (2003) \n", "1993 Interiors (1978) \n", "... ... \n", "2167 Gentlemen Prefer Blondes (1953) \n", "239 Backbeat (1993) \n", "1348 Heartburn (1986) \n", "1510 Morning After, The (1986) \n", "483 Joe's Apartment (1996) \n", "\n", " genres \n", "2042 Crime|Horror|Mystery|Thriller \n", "1305 Action|Sci-Fi \n", "1428 Drama|Romance \n", "2515 Comedy \n", "1993 Drama \n", "... ... \n", "2167 Comedy|Musical|Romance \n", "239 Drama|Musical \n", "1348 Comedy|Drama \n", "1510 Drama|Mystery \n", "483 Comedy|Fantasy|Musical \n", "\n", "[3496 rows x 5 columns]" ], "text/html": [ "
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movieIdcountvartitlegenres
2042397354.550000Book of Shadows: Blair Witch 2 (2000)Crime|Horror|Mystery|Thriller
1305236554.200000King Kong vs. Godzilla (Kingukongu tai Gojira)...Action|Sci-Fi
1428257053.500000Walk on the Moon, A (1999)Drama|Romance
2515653563.366667Legally Blonde 2: Red, White & Blonde (2003)Comedy
1993381363.366667Interiors (1978)Drama
..................
2167435660.041667Gentlemen Prefer Blondes (1953)Comedy|Musical|Romance
23934660.000000Backbeat (1993)Drama|Musical
1348241750.000000Heartburn (1986)Comedy|Drama
1510274950.000000Morning After, The (1986)Drama|Mystery
48382970.000000Joe's Apartment (1996)Comedy|Fantasy|Musical
\n", "

3496 rows × 5 columns

\n", "
" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "execution_count": 2 }, { "metadata": { "lang": "sl" }, "cell_type": "markdown", "source": [ "\n", "Odgovor: **Za izračun razpršenosti ocen za določen film lahko uporabimo varianco.**" ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 1.1. vprašanje:\n", "\n", "Katera je ustrezna naključna spremenljivka (količina) v podatkih, ki odgovarja na vprašanje?" ] }, { "metadata": { "lang": "sl" }, "cell_type": "markdown", "source": "Odgovor: **Ustrezna naključna spremenljivka je varianca ocen filma.**" }, { "metadata": { "lang": "sl" }, "cell_type": "markdown", "source": [ "#### 1.2. vprašanje:\n", "Nariši njeno porazdelitev, npr., s pomočjo histograma." ] }, { "metadata": { "ExecuteTime": { "end_time": "2025-04-13T19:29:49.178991Z", "start_time": "2025-04-13T19:29:49.097436Z" } }, "cell_type": "code", "source": [ "ratings_agg['var'].plot.hist(bins=50)\n", "plt.title('Porazdelitev varianc ocen')\n", "plt.xlabel('Varianca ocen')\n", "plt.ylabel('Število filmov')\n", "plt.show()" ], "outputs": [ { "data": { "text/plain": [ "
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" }, "metadata": {}, "output_type": "display_data" } ], "execution_count": 3 }, { "metadata": { "lang": "sl" }, "cell_type": "markdown", "source": [ "#### 1.3. vprašanje:\n", "\n", "Ali porazdelitev spominja na kakšno znano porazdelitev? Ali je porazdelitev morda normalna ali katera druga?" ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": "Odgovor: **Porazdelitev ni normalna, spominja na beta porazdelitev.**" }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 1.4. vprašanje:\n", "\n", "Oceni parametre te porazdelitve s pomočjo postopkov, ki smo jih spoznali na vajah. Izmed porazdelitev, ki smo jih spoznali na vajah, izberi tisto, ki se podatkom najbolj prilega. " ] }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2025-04-13T19:29:49.841898Z", "start_time": "2025-04-13T19:29:49.230253Z" } }, "source": [ "from scipy.stats import beta, norm, t\n", "epsilon = 1e-4\n", "\n", "normalized = np.clip(ratings_agg['var'] / 5.0, epsilon, 1 - epsilon)\n", "interval = np.linspace(0, 1, 100)\n", "\n", "a, b, loc, scale = beta.fit(normalized, floc=0, fscale=1)\n", "beta_pdf = beta.pdf(interval, a, b, loc=loc, scale=scale)\n", "plt.plot(interval, beta_pdf, label='Beta porazdelitev')\n", "print(f\"beta: a = {a:.4f}, b = {b:.4f}\")\n", "\n", "mean, std_dev = norm.fit(normalized)\n", "norm_pdf = norm.pdf(interval, mean, std_dev)\n", "plt.plot(interval, norm_pdf, label='Normalna porazdelitev')\n", "\n", "df, loc, scale = t.fit(normalized)\n", "t_pdf = t.pdf(interval, df, loc=loc, scale=scale)\n", "plt.plot(interval, t_pdf, label='Studentova porazdelitev')\n", "\n", "normalized.plot.hist(bins=50, density=True, label='')\n", "plt.xlabel('Variance ocen')\n", "plt.ylabel('Gostota verjetnosti')\n", "plt.legend()\n", "plt.show()" ], "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "beta: a = 2.9284, b = 12.9440\n" ] }, { "data": { "text/plain": [ "
" ], "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "execution_count": 4 }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": "Odgovor: **Od porazdelitev, ki smo jih spoznali na vajah, se najbolj prilega beta porazdelitev.**" }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 1.5. vprašanje:\n", "\n", "Izpiši filme z vrednostjo naključne spremenljivke, ki spada v zgornjih 5% statistično značilnih primerov. " ] }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2025-04-13T19:29:49.866278Z", "start_time": "2025-04-13T19:29:49.859062Z" } }, "source": [ "threshold = ratings_agg['var'].quantile(0.95)\n", "\n", "ratings_agg[ratings_agg['var'] >= threshold].sort_values('var', ascending=False).merge(movies, on='movieId')" ], "outputs": [ { "data": { "text/plain": [ " movieId count var \\\n", "0 3973 5 4.550000 \n", "1 2365 5 4.200000 \n", "2 2570 5 3.500000 \n", "3 3813 6 3.366667 \n", "4 6535 6 3.366667 \n", ".. ... ... ... \n", "172 1241 11 1.800000 \n", "173 5530 6 1.800000 \n", "174 3678 5 1.800000 \n", "175 32596 5 1.800000 \n", "176 5108 5 1.800000 \n", "\n", " title \\\n", "0 Book of Shadows: Blair Witch 2 (2000) \n", "1 King Kong vs. Godzilla (Kingukongu tai Gojira)... \n", "2 Walk on the Moon, A (1999) \n", "3 Interiors (1978) \n", "4 Legally Blonde 2: Red, White & Blonde (2003) \n", ".. ... \n", "172 Dead Alive (Braindead) (1992) \n", "173 Simone (S1m0ne) (2002) \n", "174 Man with the Golden Arm, The (1955) \n", "175 Sahara (2005) \n", "176 John Q (2002) \n", "\n", " genres \n", "0 Crime|Horror|Mystery|Thriller \n", "1 Action|Sci-Fi \n", "2 Drama|Romance \n", "3 Drama \n", "4 Comedy \n", ".. ... \n", "172 Comedy|Fantasy|Horror \n", "173 Comedy|Drama|Fantasy|Sci-Fi \n", "174 Drama \n", "175 Action|Adventure|Comedy \n", "176 Crime|Drama|Thriller \n", "\n", "[177 rows x 5 columns]" ], "text/html": [ "
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movieIdcountvartitlegenres
0397354.550000Book of Shadows: Blair Witch 2 (2000)Crime|Horror|Mystery|Thriller
1236554.200000King Kong vs. Godzilla (Kingukongu tai Gojira)...Action|Sci-Fi
2257053.500000Walk on the Moon, A (1999)Drama|Romance
3381363.366667Interiors (1978)Drama
4653563.366667Legally Blonde 2: Red, White & Blonde (2003)Comedy
..................
1721241111.800000Dead Alive (Braindead) (1992)Comedy|Fantasy|Horror
173553061.800000Simone (S1m0ne) (2002)Comedy|Drama|Fantasy|Sci-Fi
174367851.800000Man with the Golden Arm, The (1955)Drama
1753259651.800000Sahara (2005)Action|Adventure|Comedy
176510851.800000John Q (2002)Crime|Drama|Thriller
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177 rows × 5 columns

\n", "
" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "execution_count": 5 }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": "Odgovor: **Filme, ki so v zgornjih 5% značilnih primerov lahko najdemo z izračunom standardnega odklona ocene za vsak film. Nato izračunamo 95% mejo in filtriramo filme po njej.**" }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 2. Gručenje filmov (50%)\n", "\n", "Priporočilni sistemi pogosto odkrivajo skupine predmetov (v našem primeru filme), za katere velja visoka medsebojna podobnost.\n", "\n", "Poiščite 100 najbolj gledanih filmov. Ali med njimi obstajajo skupine?\n", "Uporabite ustrezen algoritem za gručenje. Na film lahko gledamo kot vektor, kjer je \n", "število komponent enako številu uporabnikov. \n", "\n", "Vektorji vsebujejo tudi *neznane vrednosti*.\n", "Primer vektorjev za deset filmov prikazuje spodnja tabela.\n", "\n", "Algoritme gručenja lahko izvajamo v izvornem prostoru (koordinatni sistem filmi-uporabniki) ali pa filme primerjamo z merami podobnosti, ki smo jih spoznali na vajah. \n", "Premisli, kateri način je primernejši glede na obliko podatkov." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "| x |Movie | $u_0$ |$u_1$ | $u_2$ | $\\cdots$ |\n", "|------------|-------------------------------------------|:-----:|:----:|:------|:--------:|\n", "|$\\vec{x_0}$ | Fight Club (1999) | ? | ? | ? | $\\cdots$ |\n", "|$\\vec{x_1}$ | Twelve Monkeys (a.k.a. 12 Monkeys) (1995) | ? | ? | 2.5 | $\\cdots$ |\n", "|$\\vec{x_2}$ | Independence Day (a.k.a. ID4) (1996) | ? | ? | ? | $\\cdots$ |\n", "|$\\vec{x_3}$ | Dances with Wolves (1990) | 4.0 | ? | ? | $\\cdots$ |\n", "|$\\vec{x_4}$ | Fargo (1996) | ? | ? | ? | $\\cdots$ |\n", "|$\\vec{x_5}$ | Speed (1994) | ? | ? | ? | $\\cdots$ |\n", "|$\\vec{x_6}$ | Apollo 13 (1995) | ? | 2.0 | ? | $\\cdots$ |\n", "|$\\vec{x_7}$ | Seven (a.k.a. Se7en) (1995) | ? | ? | ? | $\\cdots$ |\n", "|$\\vec{x_8}$ | Sixth Sense, The (1999) | 3.0 | ? | 4.0 | $\\cdots$ |\n", "|$\\vec{x_9}$ | Aladdin (1992) | ? | ? | ? | $\\cdots$ |\n", "|$\\cdots$ | $\\cdots$ | $\\cdots$ | $\\cdots$ | $\\cdots$ | $\\cdots$ |" ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "Pri tem odgovori na naslednja vprašanja." ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 2.1. vprašanje:\n", "\n", "Utemelji izbiro algoritma in mere podobnosti." ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": "Odgovor: **Za gručenje bi bil najbolj primeren algoritem hierarhično gručenje. Zaradi mankajočih podatkov se za mero podrobnosti uporabi Jaccardov index.**" }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 2.2. vprašanje:\n", "\n", "Koliko skupin filmov je med izbranimi? Ali poznamo kvantitativne ocene za različne možnosti razvrščanja v skupine?" ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": "Odgovor: **Med izbranimi filmi je 14 skupin. Poznamo koeficient silhuete in mero skupne deljene informacije.**" }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 2.3. vprašanje:\n", "\n", "Prikaži rezultate z uporabo ustrezne vizualizacije." ] }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2025-04-13T19:29:50.446389Z", "start_time": "2025-04-13T19:29:49.900462Z" } }, "source": [ "import scipy.cluster.hierarchy as hr\n", "\n", "top_100 = ratings.groupby(['movieId'])[\"rating\"].size().sort_values(ascending=False).head(100)\n", "\n", "matrix = ratings.pivot(index='movieId', columns='userId', values='rating')\n", "\n", "linkage = hr.linkage(matrix.loc[top_100.index].notna().astype(bool), method='average', metric='jaccard')\n", "\n", "labels = movies.loc[movies['movieId'].isin(top_100.index), 'title'].tolist()\n", "plt.figure(figsize=(25, 50))\n", "plt.axvline(x=0.57, color='k', linestyle='--')\n", "hr.dendrogram(linkage, labels=labels, leaf_font_size=22, orientation='right')\n", "plt.show()" ], "outputs": [ { "data": { "text/plain": [ "
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}, "metadata": {}, "output_type": "display_data" } ], "execution_count": 6 }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": [ "#### 2.4. vprašanje:\n", "\n", "Komentiraj smiselnost dobljenih rezultatov." ] }, { "cell_type": "markdown", "metadata": { "lang": "sl" }, "source": "Odgovor: **Dobljeni rezultati niso smiselni. Kažejo, da podatki o ogledih filmov niso podobni za podobne filme (pričakovali bi, da se filmi grupirajo recimo po žanrih)**" } ], "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" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "nbTranslate": { "displayLangs": [ "sl" ], "hotkey": "alt-t", "langInMainMenu": true, "sourceLang": "sl", "targetLang": "en", "useGoogleTranslate": true } }, "nbformat": 4, "nbformat_minor": 2 }