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@aphearin
Created June 28, 2021 20:04
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Calculate the change-of-basis matrix defined by the covariance of a dataset
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{
"cells": [
{
"cell_type": "markdown",
"id": "forced-cheat",
"metadata": {},
"source": [
"# Rotating to and from the eigenbasis of a covariance matrix\n",
"\n",
"These notes demonstrate how to rotate back and forth between the eigencoordinates associated with a covariance matrix."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "vocal-transaction",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"id": "minimal-shoulder",
"metadata": {},
"source": [
"### Define the example covariance matrix and some associated data"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "informed-bidding",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"cov = np.array([[0.00138731, 0.00074807], [0.00074807, 0.00150738]])\n",
"\n",
"n_sample = int(1e4)\n",
"mu = np.zeros(cov.shape[0])\n",
"X = np.random.multivariate_normal(mu, cov, size=n_sample)\n",
"\n",
"fig, ax = plt.subplots(1, 1)\n",
"__=ax.scatter(X[:, 0], X[:, 1], s=1)"
]
},
{
"cell_type": "markdown",
"id": "charming-prophet",
"metadata": {},
"source": [
"### Diagonalize the covariance matrix"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "digital-surgeon",
"metadata": {},
"outputs": [],
"source": [
"evals, V = np.linalg.eig(cov)"
]
},
{
"cell_type": "markdown",
"id": "intimate-least",
"metadata": {},
"source": [
"### Define the rotation and scaling matrices"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "centered-niagara",
"metadata": {},
"outputs": [],
"source": [
"R, S = V, np.sqrt(np.diag(evals))"
]
},
{
"cell_type": "markdown",
"id": "chief-transportation",
"metadata": {},
"source": [
"### Define the matrix that transforms original ==> eigencoords"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "christian-documentary",
"metadata": {},
"outputs": [],
"source": [
"T = R.dot(S).T\n",
"Tinv = np.linalg.inv(T)"
]
},
{
"cell_type": "markdown",
"id": "auburn-polymer",
"metadata": {},
"source": [
"### Transform original data to eigencoordinates"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "imported-segment",
"metadata": {},
"outputs": [],
"source": [
"X_espace = X.dot(Tinv)"
]
},
{
"cell_type": "markdown",
"id": "desperate-lawyer",
"metadata": {},
"source": [
"### Transform eigendata into original coords"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "refined-sigma",
"metadata": {},
"outputs": [],
"source": [
"X_orig = X_espace.dot(T)"
]
},
{
"cell_type": "markdown",
"id": "compact-search",
"metadata": {},
"source": [
"### Verify that we recover our original result"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "prescription-validation",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.allclose(X, X_orig)"
]
},
{
"cell_type": "markdown",
"id": "mathematical-threshold",
"metadata": {},
"source": [
"### Generate some uncorrelated random Gaussian data"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "fabulous-measure",
"metadata": {},
"outputs": [],
"source": [
"std_X_espace = np.std(X_espace, axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "departmental-opposition",
"metadata": {},
"outputs": [],
"source": [
"U_espace = np.random.normal(loc=0, scale=1, size=np.prod(X.shape)).reshape(X.shape)\n",
"U_espace[:, 0] *= std_X_espace[0]\n",
"U_espace[:, 1] *= std_X_espace[1]"
]
},
{
"cell_type": "markdown",
"id": "wrong-darkness",
"metadata": {},
"source": [
"### Transform synthetic data from eigencoords into original coords"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "hybrid-details",
"metadata": {},
"outputs": [],
"source": [
"W = U_espace.dot(T)"
]
},
{
"cell_type": "markdown",
"id": "boolean-hostel",
"metadata": {},
"source": [
"### Verify that our synthetic data looks like the original"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "according-shirt",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"__=ax.scatter(X[:, 0], X[:, 1], s=1)\n",
"__=ax.scatter(W[:, 0], W[:, 1], s=1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "stuck-crossing",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "proprietary-provider",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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