{ "cells": [ { "cell_type": "markdown", "id": "cell-0", "metadata": { "editable": false, "tags": [ "aufgabe" ] }, "source": [ "# DataScience 1 - Blatt 6\n", "\n" ] }, { "cell_type": "markdown", "id": "cell-1", "metadata": { "editable": false, "tags": [ "aufgabe" ] }, "source": [ "### Aufgabe (Z-Normalisierung)\n", "\n", "Den Datensatz mit den verschiedenen Sportbällen aus der Vorlesung finden\n", "Sie unter der URL [https://data.hsbo.de/baelle.csv](https://data.hsbo.de/baelle.csv).\n", "Diesen Datensatz sollen Sie im Folgenden betrachten und die enthaltenen Daten\n", "normalisieren.\n", "\n", " - Laden Sie die Daten zunächst in einen DataFrame. Ermitteln Sie Mittelwert und Standardabweichung für die Attribute *Umfang* und *Gewicht*. Schreiben Sie dazu die Funktionen `smean(s)` und `sdev(s)`, die für ein Series Objekt den Mittelwert bzw.\tdie Standardabweichung berechnen.\n", "\n", " - Definieren Sie eine Funktion `z_norm_series(s)`, die für ein Series Objekt `s` eine\n", "\tz-normalisierte Series zurückgibt (vgl. Foliensatz 6, Folie 27).\n", "\n", " - Schreiben Sie eine Funktion `z_norm_df(d)`, die für einen DataFrame `d` einen\n", "\tDataFrame zurückgibt, bei dem jede Spalte z-normalisiert ist.\n", "\n", "Überprüfen Sie ihre Funktionen, in dem Sie sich die Ausgabe von `data.describe()`\n", "anschauen (wenn Sie die Daten in den DataFrame `data` geladen haben), nachdem Sie\n", "die Daten mit Ihrer Funktion normalisiert haben.\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "cell-2", "metadata": {}, "outputs": [], "source": [ "# Hier ist Platz fuer ihre Loesung zu Aufgabe (Z-Normalisierung):\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "cell-3", "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import math" ] }, { "cell_type": "code", "execution_count": 12, "id": "f28c7637-4a91-4889-9fb8-11b991daf9ea", "metadata": {}, "outputs": [], "source": [ "df = pd.read_csv('https://data.hsbo.de/baelle.csv')" ] }, { "cell_type": "code", "execution_count": 2, "id": "85e0e2ac-d7ee-410a-b841-9e6efeaf0c5c", "metadata": {}, "outputs": [], "source": [ "# Testdaten:\n", "s1 = pd.Series([1,3,5,2,4,5])" ] }, { "cell_type": "code", "execution_count": 3, "id": "4bcd015a-f09c-4eb6-9d27-339b4c1096e7", "metadata": {}, "outputs": [], "source": [ "def smean(s):\n", " total = sum(s.values)\n", " return total / len(s.values)" ] }, { "cell_type": "code", "execution_count": 5, "id": "43c34a90-0b1b-4d35-a6af-c3106060b35b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(3.3333333333333335)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "smean(s1)" ] }, { "cell_type": "code", "execution_count": 6, "id": "c25995b8-6730-47ee-ae6c-5c42399ee369", "metadata": {}, "outputs": [], "source": [ "def sdev(s):\n", " mean = smean(s)\n", " \n", " total = 0\n", " for v in s.values:\n", " dev = (v - mean)**2\n", " total = total + dev\n", " \n", " return math.sqrt(total / (len(s.values) - 1))" ] }, { "cell_type": "code", "execution_count": 8, "id": "a6f44c49-f3ba-44d7-97a2-934befe7720b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.632993161855452" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sdev(s1)" ] }, { "cell_type": "code", "execution_count": 9, "id": "67f02d47-60f8-4182-b9b6-279b894e7933", "metadata": {}, "outputs": [], "source": [ "def z_norm_series(s):\n", " return (s - smean(s)) / sdev(s)" ] }, { "cell_type": "code", "execution_count": 10, "id": "6e3edc95-b404-42af-9ba3-3ba351ece357", "metadata": {}, "outputs": [], "source": [ "def z_norm_df(df):\n", " for c in df.columns:\n", " df[c] = z_norm_series(df[c])\n", " return df" ] }, { "cell_type": "code", "execution_count": 14, "id": "e125e52b-7f35-4d9a-8c2d-1e5677e7f484", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Gewicht Umfang Typ\n", "0 444.303723 70.291324 Fussball\n", "1 424.239800 69.348473 Fussball\n", "2 440.957231 68.281579 Fussball\n", "3 443.638611 69.298301 Fussball\n", "4 421.475816 70.179397 Fussball" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.head()" ] }, { "cell_type": "code", "execution_count": 16, "id": "2703568d-ef5e-40d7-b2bc-2ffa149045ad", "metadata": {}, "outputs": [], "source": [ "daten = df[['Gewicht','Umfang']]" ] }, { "cell_type": "code", "execution_count": 17, "id": "29bb9145-9b75-49d2-9d5b-005caa82fca6", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_1242/772145394.py:3: SettingWithCopyWarning: \n", "A value is trying to be set on a copy of a slice from a DataFrame.\n", "Try using .loc[row_indexer,col_indexer] = value instead\n", "\n", "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n", " df[c] = z_norm_series(df[c])\n" ] } ], "source": [ "normalisiert = z_norm_df(daten)" ] }, { "cell_type": "code", "execution_count": 19, "id": "a597247c-ba7d-460c-a003-ab683a58d315", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Gewicht Umfang\n", "0 -0.372036 0.267862\n", "1 -0.563240 0.170888\n", "2 -0.403927 0.061156\n", "3 -0.378374 0.165728\n", "4 -0.589581 0.256350" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normalisiert.head()" ] }, { "cell_type": "code", "execution_count": 20, "id": "9e5cd2fe-5236-463b-ad2d-ccd1e3b668a8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Gewicht Umfang\n", "count 1.500000e+02 1.500000e+02\n", "mean -1.533588e-15 1.657933e-15\n", "std 1.000000e+00 1.000000e+00\n", "min -1.598158e+00 -1.965362e+00\n", "25% -7.044373e-01 -9.143204e-01\n", "50% -3.870644e-01 2.147741e-01\n", "75% 1.059902e+00 8.261284e-01\n", "max 1.934487e+00 1.675627e+00" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normalisiert.describe()" ] }, { "cell_type": "markdown", "id": "cell-4", "metadata": { "editable": false, "tags": [ "aufgabe" ] }, "source": [ "### Aufgabe 2 (Klassifikation)\n", "\n", "Der Datensatz enthält Umfang und Gewicht für die verschiedenen Bälle. Im Folgenden\n", "sollen Sie ein Klassifikationsmodell trainieren und testen, wie gut das Modell die\n", "Bälle unterscheiden kann.\n", "\n", " - Trainieren Sie einen Entscheidungsbaum auf 80 Prozent der Daten und ermitteln Sie den Test-Fehler\n", " - Probieren Sie die Daten mit kNN zu klassifizieren.\n", " - Verbessert sich die kNN Vorhersage, wenn Sie die Daten zu allererst normalisieren?" ] }, { "cell_type": "code", "execution_count": null, "id": "cell-5", "metadata": {}, "outputs": [], "source": [ "# Hier ist Platz fuer ihre Loesung zu Aufgabe 2 (Klassifikation):\n" ] }, { "cell_type": "code", "execution_count": null, "id": "cell-6", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }