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Last active March 1, 2018 15:21
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SKLearn's PCA sign ambiguity?
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{
"cells": [
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"import random\n",
"random.seed()\n",
"\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"import sklearn"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's generate an samples-by-dimensions vector, say 300 samples and 100 dimensions:"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [],
"source": [
"m = np.random.randn(300, 100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's consider sample number 0 as our _\"reference sample\"_.\n",
"\n",
"Now let's do 1000 rounds, each time we: \n",
"1. pick a random sample excluding the \"reference sample\" (i.e., among the remaining 299)\n",
"2. vary that random sample slightly, for example by adding gaussian noise with mu=0 and small sigma\n",
"3. reduce the dimensionality (via PCA) from 100 dimensions to 3, and save the results for our \"reference sample\""
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {},
"outputs": [],
"source": [
"data = []\n",
"\n",
"for i in range(0, 1000):\n",
" # pick a random row from the matrix\n",
" random_sample = random.randrange(1, 300)\n",
" \n",
" # vary that random sample slightly:\n",
" m[random_sample] = m[random_sample] + random.gauss(mu=0, sigma=0.3)\n",
" \n",
" # compute PCA:\n",
" pca = sklearn.decomposition.PCA(n_components=3, svd_solver='full') \n",
" m_low = pca.fit_transform(m)\n",
" \n",
" # save our reference sample:\n",
" data.append(m_low[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's plot the low-dimensionality values that our _reference sample_ had over the 1000 iterations:"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fb37301dc88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(16,8))\n",
"plt.plot(data)\n",
"plt.grid(b=True, axis='y')\n",
"plt.axhline(y=0, color='red')\n",
"plt.ylabel(\"Values\")\n",
"plt.xlabel(\"Iteration\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Many times, one of the dimensions *for all the samples* will change sign all of the sudden, while keeping the same absolute value. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I noticed that Sklearn's `PCA()` code already uses the trick implemented in `svd_flip()` ([code here](https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/utils/extmath.py#L499)) to make the results \"deterministic\" by removing SVD's sign ambiguity. Then... why is this still happening?"
]
}
],
"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": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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