{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import pearsonr\n",
"from numpy.random import poisson, lognormal\n",
"from skbio.stats.composition import closure, clr\n",
"from deicode.preprocessing import rclr\n",
"from deicode.optspace import OptSpace\n",
"from IPython.core.display import HTML\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#fix font-size\n",
"HTML(\"\"\"\"\"\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Robust Aitchison and Subcompositional Coherence \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We skip over the use of matrix completion here, but for a primer on the methodology see [here](https://github.com/asberk/matrix-completion-whirlwind/blob/master/matrix_completion_master.ipynb). The exact method used here, OptSpace can be found [here](https://arxiv.org/pdf/0906.2027.pdf)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example from [\"A Concise Guide to Compositional Data Analysis\"](http://www.leg.ufpr.br/lib/exe/fetch.php/pessoais:abtmartins:a_concise_guide_to_compositional_data_analysis.pdf) by John Aitchison\n",
"(page 21-22)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider the simple data set with $[x_1, x_2, x_3, x_4]$ features and three samples\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[100, 200, 100, 600],\n",
" [200, 100, 100, 600],\n",
" [300, 300, 200, 200]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X = np.array([[100, 200, 100, 600],\n",
" [200, 100, 100, 600],\n",
" [300, 300, 200, 200]])\n",
"X"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The full composition A is demonstrated below with $corr(x_1,x_2)=0.5$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.1, 0.2, 0.1, 0.6],\n",
" [ 0.2, 0.1, 0.1, 0.6],\n",
" [ 0.3, 0.3, 0.2, 0.2]])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = closure(X)\n",
"A"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.49999999999999983"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pearsonr(A[:,0],A[:,1])[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's consider the subcompositon of x with $x_4$ missing so define B = $[x_1, x_2, x_3]$. We now get $corr(x_1,x_2)=-1.0$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.25 , 0.5 , 0.25 ],\n",
" [ 0.5 , 0.25 , 0.25 ],\n",
" [ 0.375, 0.375, 0.25 ]])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B = closure(X[:,:-1])\n",
"B"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-1.0"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pearsonr(B[:,0],B[:,1])[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is thus incoherence of the product-moment correlation between raw components as a measure of dependence."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note, however, that the log ratio of two components remains unchanged when we move from full composition to subcomposition. For example"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-0.69314718, 0.69314718, 0. ])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(X[:,0])-np.log(X[:,1])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-0.69314718, 0.69314718, 0. ])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(X[:,:-1][:,0])-np.log(X[:,:-1][:,1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This can be further shown by the clr transform on a slightly larger dataset. We we will construct a dataset with three features all sampled in time. The first feature is lowly abundant but exponentially increasing in time. The second feature is highly abundant and constant in time. Finally, the third feature highly abundant and is stochastic in time. \n",
"\n",
"\n",
"clr transformation is given by:\n",
"\n",
"$clr(\\vec{x}) = [log(\\frac{x_i}{g(\\vec{x})}) , ... , log(\\frac{x_D}{g(\\vec{x})})] = log(\\vec{x}) - \\bar{log(\\vec{x})}$\n",
"\n",
"where $g(\\vec{x})$ is the geometric mean of all the features.\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(100, 3)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 100\n",
"t = np.linspace(1, 10, n)\n",
"x1 = np.exp(t) * 0.001\n",
"x2 = np.random.normal(size=n) + 100\n",
"x3 = np.random.normal(size=n) * 10 + 100\n",
"X = np.vstack((x1, x2, x3)).T\n",
"X.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To visualize this we will plot counts by time colored by feature. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
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