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@danlooo
Created August 30, 2017 20:05
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 35,
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},
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Visualisierung hochdimensionaler Daten @Daniel2\n",
"\n",
"![](https://media.makeameme.org/created/artificial-intelligence.jpg)\n",
"\n",
"\n",
"# Datensatz\n",
"Verwendet wird der berühmte Iris-Datenatz von [Ronald Fisher](https://en.wikipedia.org/wiki/Ronald_Fisher). Es handelt sich um den einzigen von EGST authorisierten Datensatz zur Verwendung in ML-Analysen.\n",
"Es gibt insg. 4 Dimensionen: Die Längen und Breiten der äußeren (sepalen) und inneren (petalen) Blütenblätter von drei verschiedenen Iris-Arten. \n",
"![](https://s14-eu5.ixquick.com/cgi-bin/serveimage?url=https:%2F%2Fs3.amazonaws.com%2Fassets.datacamp.com%2Fblog_assets%2Firis-machinelearning.png&sp=01362f4bd525443968175bdd000e7a03)\n",
"Ich bitte um Ignoranz der nicht kursiv geschriebenen Artennamen."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
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"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
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"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
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"\n",
" .dataframe tbody tr th {\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>sepal_length</th>\n",
" <th>sepal_width</th>\n",
" <th>petal_length</th>\n",
" <th>petal_width</th>\n",
" <th>species</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>5.1</td>\n",
" <td>3.5</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4.9</td>\n",
" <td>3.0</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>4.7</td>\n",
" <td>3.2</td>\n",
" <td>1.3</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4.6</td>\n",
" <td>3.1</td>\n",
" <td>1.5</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5.0</td>\n",
" <td>3.6</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" sepal_length sepal_width petal_length petal_width species\n",
"0 5.1 3.5 1.4 0.2 setosa\n",
"1 4.9 3.0 1.4 0.2 setosa\n",
"2 4.7 3.2 1.3 0.2 setosa\n",
"3 4.6 3.1 1.5 0.2 setosa\n",
"4 5.0 3.6 1.4 0.2 setosa"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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rK73/vuWWW/Dmm2/i9ddfx4YNGwKux+l0Bn1frMPh8PlvuJcrZ9lsc+SX7XA4kJCQENQy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OxAt7UPpgvJHgBwrO9jwbY0vfj3rqUYUtKQt2oVkuprYe/tgS4nB6llFTgz2oeevg/dCSUA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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1a08060160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import seaborn as sns # matplotlib in fancy + stats\n",
"\n",
"%matplotlib inline\n",
"sns.set_style(\"whitegrid\")\n",
"\n",
"data = sns.load_dataset(\"iris\")\n",
"sns.pairplot(data, hue=\"species\")\n",
"data[:5]"
]
},
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 5,
"height": 23,
"hidden": false,
"row": 35,
"width": null
},
"report_default": {
"hidden": false
}
}
}
}
},
"source": [
"# Principal Component Analysis (PCA)\n",
"*3D Objekte von der Seite fotographieren, so dass sie möglichst formatfüllend abgebildet werden*\n",
"![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Faktorenanalyse.svg/226px-Faktorenanalyse.svg.png)\n",
"- Der Datensatz umfasst 4 Dimensionen, wir können aber lediglich 2 sinnvoll darstellen\n",
"- Die PCA ist das simpleteste Verfahren, um möglichst viel von den Daten in z.B. 2D zu sehen\n",
"- hierbei wird die *Varianz* maximiert, nicht aber die eigentliche *Ähnlichkeit* der Datenpunkte zueinander\n",
"- Es ist eine *lineare* Projektion der Daten mit $\\mathbb{R}^n \\rightarrow \\mathbb{R}^n$. Demnach findet keine *Reduzierung* der Dimension im engeren Sinne statt.\n",
"\n",
"## Vorteile\n",
"- schnell und einfach zu berechnen\n",
"- Man kann neue Punkte ganz einfach in den PCA transformierten Raum einbetten\n",
"\n",
"## Nachteile\n",
"- Varianz ist nicht mit Ähnlichkeit gleichzusetzen\n",
"- Die Daten müssen vorher normalisiert werden\n",
"- Transformation ist nur *linear*. Nichtlineare Daten lassen sich mit der PCA nicht gut darstellen."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 12,
"hidden": false,
"row": 53,
"width": 4
},
"report_default": {
"hidden": false
}
}
}
}
},
"outputs": [
{
"data": {
"text/plain": [
"<seaborn.axisgrid.FacetGrid at 0x7f19cd8edda0>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Os7IspOcUwf95F4SG+EBqZ2vusIhEoVIqkXfuPBTpGXD094Nnm9awkeq/21WscYjMgUkU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\n/OMftWLFCrVr186j9WPHjtW4ceMubygAAIBLCPgzUREREXr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TRUWFNm7cqC1btmjAgAGS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\nALDg/wOY7bFqNY7mhgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f19cd887cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.lmplot(\"sepal_length\", \"sepal_width\", hue=\"species\", data=data, fit_reg=False)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"hidden": true
},
"report_default": {
"hidden": false
}
}
}
}
},
"outputs": [
{
"data": {
"text/html": [
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"\n",
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"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>sepal_length</th>\n",
" <th>sepal_width</th>\n",
" <th>petal_length</th>\n",
" <th>petal_width</th>\n",
" <th>species</th>\n",
" <th>PC1</th>\n",
" <th>PC2</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>5.1</td>\n",
" <td>3.5</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" <td>-2.264703</td>\n",
" <td>0.480027</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4.9</td>\n",
" <td>3.0</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" <td>-2.080961</td>\n",
" <td>-0.674134</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>4.7</td>\n",
" <td>3.2</td>\n",
" <td>1.3</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" <td>-2.364229</td>\n",
" <td>-0.341908</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4.6</td>\n",
" <td>3.1</td>\n",
" <td>1.5</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" <td>-2.299384</td>\n",
" <td>-0.597395</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5.0</td>\n",
" <td>3.6</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" <td>-2.389842</td>\n",
" <td>0.646835</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" sepal_length sepal_width petal_length petal_width species PC1 \\\n",
"0 5.1 3.5 1.4 0.2 setosa -2.264703 \n",
"1 4.9 3.0 1.4 0.2 setosa -2.080961 \n",
"2 4.7 3.2 1.3 0.2 setosa -2.364229 \n",
"3 4.6 3.1 1.5 0.2 setosa -2.299384 \n",
"4 5.0 3.6 1.4 0.2 setosa -2.389842 \n",
"\n",
" PC2 \n",
"0 0.480027 \n",
"1 -0.674134 \n",
"2 -0.341908 \n",
"3 -0.597395 \n",
"4 0.646835 "
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# split dataset into features X and targets Y\n",
"features = [\"sepal_length\", \"sepal_width\", \"petal_length\", \"petal_width\"]\n",
"X = data[features]\n",
"Y = data[\"species\"]\n",
"\n",
"# do not forget scaling in PCA!\n",
"from sklearn.preprocessing import StandardScaler\n",
"X = StandardScaler().fit_transform(X)\n",
"\n",
"from sklearn import decomposition\n",
"pca = decomposition.PCA()\n",
"Xpca = pca.fit_transform(X)\n",
"\n",
"data[\"PC1\"] = Xpca.T[0]\n",
"data[\"PC2\"] = Xpca.T[1]\n",
"\n",
"data[:5]"
]
},
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 4,
"height": 4,
"hidden": false,
"row": 58,
"width": null
},
"report_default": {
"hidden": false
}
}
}
}
},
"source": [
"Nun schauen wir aus einer anderen Richtung auf den Datensatz und können die Unterschiede zwischen den Arten viel besser erkennen. Dargestellt sind die ersten beien der insgesamt $n=4$ Hauptachsen."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 4,
"height": 12,
"hidden": false,
"row": 62,
"width": 4
},
"report_default": {
"hidden": false
}
}
}
}
},
"outputs": [
{
"data": {
"text/plain": [
"<seaborn.axisgrid.FacetGrid at 0x7f19d15b8400>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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xzDPPoLW1FcuWLcN///tfiKKI4cOH44UXXkBMTAxqamrw1FNPoaSkBCaTCYMH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\n4f8A4BpB/hocuKsAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f19d15b59b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.lmplot(\"PC1\", \"PC2\", data=data, hue=\"species\", fit_reg=False)"
]
},
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 5,
"hidden": false,
"row": 74,
"width": 12
},
"report_default": {
"hidden": false
}
}
}
}
},
"source": [
"## Anteil der erklärten Varianz nach Hauptkomponente\n",
"Im PCA-Objekt ist unter `pca.explained_variance_ratio_` zu finden, wie viel der Varianz die einzelnen Hauptachsen abdecken konnten. Die erste Hauptachse ist natürlich am wichtigsten: Sie erklärt über 70% der Gesamtvarianz.\n",
"\n",
"Eine einfache Summation zeigt: Unser PCA Plot konnte insg. 95.8% der Gesamtvarianz darstellen, obwohl er nur 2 anstatt 4 Dimensionen hat!"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false,
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 8,
"height": 10,
"hidden": false,
"row": 62,
"width": 4
},
"report_default": {
"hidden": false
}
}
}
}
},
"outputs": [
{
"data": {
"text/plain": [
"0.95813207200001638"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f19d18edc88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.barplot(pca.explained_variance_ratio_, [\"PC%s\" % x for x in range(1, len(features)+1)])\n",
"plt.xlabel(\"Explained variance\")\n",
"sum(pca.explained_variance_ratio_[:2]) # cummulative explained variance of the first 2 axes"
]
},
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 5,
"hidden": false,
"row": 79,
"width": 12
},
"report_default": {
"hidden": false
}
}
}
}
},
"source": [
"## Factor Loadings\n",
"Jeder Punkt auf einer Hauptachse ist immer eine Linarkombination aller Features. Die Gewichte heirbei heißen *factor loadings*. Der Wert ist analog zum Korrelationscoeffizient zwischen dem Feature und der Hauptachse. Streut ein Feature gar nicht, ist der Wert 0. Streut nur ein Feature in einem Datensatz, ist ihr Loading 1; alle anderen (konstanten) Features haben dann den Wert 0."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 10,
"hidden": false,
"row": 84,
"width": 4
},
"report_default": {
"hidden": false
}
}
}
}
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f19cdab21d0>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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9vn37qm/fvoW6TAAA4HqcVgMAALAgHAEAAFgQjgAAACwIRwAAABaEIwAAAAvC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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f19cda30d68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.barplot(pca.components_[0], features)\n",
"plt.title(\"Factor loadings for first principal component\")"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 4,
"height": 10,
"hidden": false,
"row": 84,
"width": 4
},
"report_default": {
"hidden": false
}
}
}
}
},
"outputs": [
{
"data": {
"text/plain": [
"<seaborn.axisgrid.FacetGrid at 0x7f19c406ab70>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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5EggWlXe4o+vVhiO8A5YzokJ7Iq3JgQMH7OWSkpIKs06L1JcSXSIiIi3M2rVr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\nbLf4hBDd1+nTp4OPNeZAQsvv8eP3nLk/0JgC+6uqqnC5XB0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erzfcIQghhAiR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\n6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"text/plain": [
"<matplotlib.figure.Figure at 0x7f19c406af98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p = sns.factorplot(col=\"species\", data=data[features + [\"species\"]], kind=\"violin\")\n",
"p.set_ylabels(\"Distance (cm)\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
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"source": [
"## Kernel PCA\n",
"Die Standard PCA ist eine PCA mit *linearem* Kernel. Ist man damit nicht zuftrieden und hat nicht linear separierbare Daten, so kann man die PCA mit einem Kernel ausführen, der Nichtlinearitäten erlaubt.\n",
"\n",
"- Deine Daten sind nicht linear, du willst aber linear separierbare Daten im transformierten Raum? Dann ist die Kernel PCA genau das Richtige für dich!\n",
"- Mehr Infos siehe [BogotoBogo-Blog](http://www.bogotobogo.com/python/scikit-learn/scikit_machine_learning_Data_Compresssion_via_Dimensionality_Reduction_3-nonlinear-mappings-via-kernel-principal-component-analysis.php)\n",
"\n",
"Originaldaten:\n",
"![](http://www.bogotobogo.com/python/scikit-learn/images/CompressData-3-DimensionalityReduction-KernelPCA/KCPA-Circles-Plot1.png)\n",
"Normale PCA kann Nichts zur besseren Separierbarkeit beitragen:\n",
"![](http://www.bogotobogo.com/python/scikit-learn/images/CompressData-3-DimensionalityReduction-KernelPCA/KCPA-Circles-Plot2.png)\n",
"Die Kernel PCA dagegen schon:\n",
"![](http://www.bogotobogo.com/python/scikit-learn/images/CompressData-3-DimensionalityReduction-KernelPCA/KCPA-Circles-Plot4.png)\n",
"\n",
"Hier wird der Radial basis function kernel (RBF) verwendet, der einfach eine Gaußfunktion abbildet. Die Kernelfunktion kann man oft im transformierten Raum erkennen :). In unserem Falle ist die Kernel-PCA aber eher sinnlos:"
]
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"outputs": [
{
"data": {
"text/plain": [
"<seaborn.axisgrid.FacetGrid at 0x7f19d165e550>"
]
},
"execution_count": 8,
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R2eLMExF5zdXLU73adfV2SW5n1uuhPnAQumIlpHGxCE9NgVAisc44HS45hmqDDoAO1QYt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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f19d165ef98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"kernelPCA = decomposition.KernelPCA(kernel=\"rbf\")\n",
"XkernelPca = kernelPCA.fit_transform(X)\n",
"data[\"kernelPC1\"] = XkernelPca.T[0]\n",
"data[\"kernelPC2\"] = XkernelPca.T[1]\n",
"sns.lmplot(\"kernelPC1\", \"kernelPC2\", data=data, hue=\"species\", fit_reg=False)"
]
},
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 12,
"hidden": false,
"row": 156,
"width": 12
},
"report_default": {
"hidden": false
}
}
}
}
},
"source": [
"# Multidimensionale Skalierung (MDS)\n",
"*PCA in fancy*\n",
"\n",
"Bei der MDS platziert man die Punkte so auf die Ebene, dass ihre Abstände im n-dimensionalen Raum möglichst gut erhalten bleiben. Meist wird eine euklidische Metrik verwendet.\n",
"\n",
"## Vorteile\n",
"- Man kann die Anzahl der Achsen im transformierten Raum selbst wählen (z.B. 2 für 2D-Plot)\n",
"- Der Begriff *Abstand* ist näher an *Ähnlichkeit* als der Begriff *Varianz*\n",
"\n",
"## Nachteile\n",
"- sehr rechenaufwendig\n",
"- bei neuen Daten muss alles neu berechnet werden\n",
"- das Ganze ist ein iterativer Prozess; irgendwann wird abgebrochen"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 21,
"hidden": false,
"row": 168,
"width": 4
},
"report_default": {
"hidden": false
}
}
}
}
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f19cd8d0128>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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REUlbeT87rb5MxMXF4fz581iwYAGAx+dOVERycrIJUxEREdETVl8mdu/ejczMTHTr1g3A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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f19d1786b38>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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e/ssu5MSdtsldvc05WlPdM1Q5uQbfs+LvmVIuhzjAX+PntrqAnuofp/OIyGKV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\nikI7cAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f19d15e7f98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.manifold import MDS\n",
"mds1 = MDS(n_components=1) # 1 dimensional MDS\n",
"data[\"1D-MDS1\"] = mds1.fit_transform(X)\n",
"\n",
"mds2 = MDS(n_components=2)\n",
"data[\"2D-MDS1\"] = mds2.fit_transform(X).T[0]\n",
"data[\"2D-MDS2\"] = mds2.fit_transform(X).T[1]\n",
"\n",
"\n",
"sns.stripplot(x=\"species\",y=\"1D-MDS1\", data=data)\n",
"plt.title(\"1 dimensional MDS\")\n",
"sns.lmplot(\"2D-MDS1\", \"2D-MDS2\", data=data, hue=\"species\", fit_reg=False)\n",
"plt.title(\"2 dimensional MDS\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 4,
"hidden": false,
"row": 189,
"width": 12
},
"report_default": {
"hidden": false
}
}
}
}
},
"source": [
"# Isomap\n",
"\n",
"Isomap erweitert die MDS um Gewichte. Somit kann 1cm sepale Breite stärker gewichtet werden als 1cm sepaler Länge. Dies bietet mehr Flexibilität als bei der reinen MDS.\n",
"Im Iris-Datensatz gibt es nun viel weniger Überlappung von *versicolor* und *verginica* als bei PCA oder MDS :)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 4,
"height": 12,
"hidden": false,
"row": 144,
"width": 4
},
"report_default": {
"hidden": false
}
}
}
}
},
"outputs": [
{
"data": {
"text/plain": [
"<seaborn.axisgrid.FacetGrid at 0x7f19cd85c978>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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OjB07FgqFAkqlEq+++io2btyI6667DkuXLsWxY8cglUqxYsUKAA1XrmbNmoWZ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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f19cd85ccf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.manifold import Isomap\n",
"iso = Isomap().fit_transform(X).T\n",
"data[\"ISO1\"] = iso[0]\n",
"data[\"ISO2\"] = iso[1]\n",
"sns.lmplot(\"ISO1\", \"ISO2\", data=data, hue=\"species\", fit_reg=False)"
]
},
{
"cell_type": "markdown",
"metadata": {
"extensions": {
"jupyter_dashboards": {
"version": 1,
"views": {
"grid_default": {
"col": 0,
"height": 4,
"hidden": false,
"row": 69,
"width": 4
},
"report_default": {
"hidden": false
}
}
}
}
},
"source": [
"# Weitere Methoden\n",
"\n",
"- Selbstorganisierende Karten (SOM)\n",
"- Autoassoziative Neuronale Netze\n",
"- ...\n"
]
}
],
"metadata": {
"extensions": {
"jupyter_dashboards": {
"activeView": "report_default",
"version": 1,
"views": {
"grid_default": {
"cellMargin": 10,
"defaultCellHeight": 20,
"maxColumns": 12,
"name": "grid",
"type": "grid"
},
"report_default": {
"name": "report",
"type": "report"
}
}
}
},
"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": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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