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Last active April 23, 2020 23:49
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**ANALYZING THE VARIANCE RETAINED**\n",
"\n",
"By retrieving the information on the explained variance ratio from each of our implementations and examine the amount of variance retained after implementing the two PCA models."
]
},
{
"cell_type": "code",
"execution_count": 406,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.49683495, 0.06809232, 0.0484369 , 0.03703542, 0.03144589,\n",
" 0.02775687, 0.02379556, 0.0224499 , 0.02057392, 0.01920976,\n",
" 0.01707584, 0.0164477 , 0.01477331, 0.01401689, 0.0125533 ,\n",
" 0.01186567, 0.01170221, 0.01020539, 0.00898293, 0.00869672,\n",
" 0.00761753, 0.00683836, 0.00642722, 0.00601069, 0.00579448])"
]
},
"execution_count": 406,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pca.explained_variance_ratio_"
]
},
{
"cell_type": "code",
"execution_count": 397,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.49683495, 0.06809232, 0.04843689, 0.03703532, 0.03144585,\n",
" 0.02775618, 0.02379536, 0.02244964, 0.02057338, 0.01920622])"
]
},
"execution_count": 397,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pca2.explained_variance_ratio_"
]
},
{
"cell_type": "code",
"execution_count": 368,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pca = PCA().fit(scaled_x)\n",
"plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
"plt.xlabel('number of components')\n",
"plt.ylabel('cumulative explained variance');"
]
}
],
"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": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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