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765 lines
325 KiB
765 lines
325 KiB
2 years ago
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"Simulating data points: 100%|██████████| 324/324 [00:11<00:00, 28.10it/s]\n"
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]
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},
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Decoding... done\n"
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]
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}
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],
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"source": [
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"# -*- coding: utf-8 -*-\n",
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"\n",
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"import numpy as np\n",
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"import pandas as pd\n",
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"\n",
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"import sys\n",
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"sys.path.insert(0, './Persistent_Homology')\n",
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"\n",
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"from gratings import grating_model\n",
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"from plotting import plot_data, plot_mean_against_index, show_feature\n",
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"from persistence import persistence\n",
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"from decoding import cohomological_parameterization, remove_feature\n",
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"from noisereduction import PCA_reduction, z_cutoff\n",
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"\n",
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"\n",
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"\n",
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"## Generate data\n",
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"data = grating_model(Nn=8, Np=(18,1,18,1), deltaT=55) #, random_neurons=True\n",
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"\n",
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"## Apply noise reduction\n",
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"# data = PCA_reduction(data, 5)\n",
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"# data = z_cutoff(data,2)\n",
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"\n",
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"## Analyze shape\n",
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"# persistence(data,homdim=2,coeff=2)\n",
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"# persistence(data,homdim=2,coeff=3)\n",
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"\n",
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"## Decode first parameter\n",
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"decoding1 = cohomological_parameterization(data, coeff=23)\n",
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"# show_feature(decoding1)\n",
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"# plot_data(data,transformation=\"PCA\", labels=decoding1,\n",
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"# colors=[\"Twilight\",\"Viridis\",\"Twilight\",\"Viridis\",\"Twilight\"])\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plot_mean_against_index(data,decoding1,\"orientation\")\n",
|
||
|
|
"plot_mean_against_index(data,decoding1,\"phase\")"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 3,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Decoding... done\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Decode second parameter\n",
|
||
|
|
"reduced_data = remove_feature(data, decoding1, cut_amplitude=0.5)\n",
|
||
|
|
"decoding2 = cohomological_parameterization(reduced_data, coeff=23)\n",
|
||
|
|
"# show_feature(decoding2)\n",
|
||
|
|
"plot_mean_against_index(data,decoding2,\"orientation\")\n",
|
||
|
|
"plot_mean_against_index(data,decoding2,\"phase\")\n",
|
||
|
|
"# plot_data(data,transformation=\"PCA\", labels=decoding2,\n",
|
||
|
|
" # colors=[\"Twilight\",\"Viridis\",\"Twilight\",\"Viridis\",\"Twilight\"])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 4,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# Klein bottle\n",
|
||
|
|
"R = 25\n",
|
||
|
|
"r = 12\n",
|
||
|
|
"N = 20\n",
|
||
|
|
"data_4D_klein_bottle = []\n",
|
||
|
|
"phase = np.linspace(0,2*np.pi, N)\n",
|
||
|
|
"orientation = np.linspace(0, np.pi, N)\n",
|
||
|
|
"for phi in phase:\n",
|
||
|
|
" for theta in orientation:\n",
|
||
|
|
" x1 = (R + r*np.cos(phi)) *np.cos(2*theta)\n",
|
||
|
|
" x2 = (R + r*np.cos(phi)) *np.sin(2*theta)\n",
|
||
|
|
" x3 = r*np.sin(phi)*np.cos(theta)\n",
|
||
|
|
" x4 = r*np.sin(phi)*np.sin(theta)\n",
|
||
|
|
" data_4D_klein_bottle.append([x1, x2, x3, x4])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 5,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# Klein bottle\n",
|
||
|
|
"R = 25\n",
|
||
|
|
"P = 8\n",
|
||
|
|
"N = 20\n",
|
||
|
|
"eps = 0.8\n",
|
||
|
|
"data_4D_klein_bottle = []\n",
|
||
|
|
"phis = np.linspace(0,2*np.pi, N)\n",
|
||
|
|
"vs = np.linspace(0, 2*np.pi, N)\n",
|
||
|
|
"param = []\n",
|
||
|
|
"for phi in phis:\n",
|
||
|
|
" for v in vs:\n",
|
||
|
|
" param.append([phi, v])\n",
|
||
|
|
" x1 = R * (np.cos(phi/2) * np.cos(v) - np.sin(phi/2)*np.sin(2*v))\n",
|
||
|
|
" x2 = R * (np.sin(phi/2) * np.cos(v) + np.cos(phi/2)*np.sin(2*v))\n",
|
||
|
|
" x3 = P*np.cos(phi)*(1 + eps * np.sin(v))\n",
|
||
|
|
" x4 = P*np.sin(phi)*(1 + eps * np.sin(v))\n",
|
||
|
|
" data_4D_klein_bottle.append([x1, x2, x3, x4])\n",
|
||
|
|
" \n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"$x_1 = (R + r\\cos(\\phi))\\cos(\\theta),\\\\\n",
|
||
|
|
" x_2 = (R + r\\cos(\\phi))\\sin(\\theta),\\\\\n",
|
||
|
|
" x_3 = r\\sin(\\phi)\\cos(\\theta/2)\\\\\n",
|
||
|
|
" x_4 = r\\sin(\\phi)\\sin(\\theta/2) $"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"4D non-intersecting parametrization\n",
|
||
|
|
"$ x1 = R(\\cos(\\phi/2) \\cos(v) - \\sin(\\phi/2) \\sin(2v)) \\\\\n",
|
||
|
|
"x2 = R(\\sin(\\phi/2) \\cos(v) + \\cos(\\phi/2) \\sin(2v)) \\\\\n",
|
||
|
|
"x3 = P\\cos(\\phi)(1+\\epsilon \\sin(v))\\\\\n",
|
||
|
|
"x4 = P\\sin(\\phi])(1+\\epsilon \\sin(v))\n",
|
||
|
|
"$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 6,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"data_4D_klein_bottle = pd.DataFrame(np.array(data_4D_klein_bottle))\n",
|
||
|
|
"param = np.array(param)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 7,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"(400, 4)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 7,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"data_4D_klein_bottle.shape"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 8,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"\n",
|
||
|
|
"## Apply noise reduction\n",
|
||
|
|
"# data = PCA_reduction(data, 5)\n",
|
||
|
|
"# data = z_cutoff(data,2)\n",
|
||
|
|
"\n",
|
||
|
|
"## Analyze shape\n",
|
||
|
|
"persistence(data_4D_klein_bottle,homdim=2,coeff=2)\n",
|
||
|
|
"persistence(data_4D_klein_bottle,homdim=2,coeff=3)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 9,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Decoding... done\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"## Decode first parameter\n",
|
||
|
|
"decoding1 = cohomological_parameterization(data_4D_klein_bottle, coeff=23)\n",
|
||
|
|
"# show_feature(decoding1)\n",
|
||
|
|
"# plot_mean_against_index(data_4D_klein_bottle,decoding1)\n",
|
||
|
|
"# plot_mean_against_index(data,decoding1,\"phase\")\n",
|
||
|
|
"# plot_data(data,transformation=\"PCA\", labels=decoding1,\n",
|
||
|
|
"# colors=[\"Twilight\",\"Viridis\",\"Twilight\",\"Viridis\",\"Twilight\"])\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 10,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import matplotlib.pyplot as plt"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.collections.PathCollection at 0x251304908e0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.scatter(param[:,1], decoding1['decoding'][:])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 12,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Decoding... done\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"\n",
|
||
|
|
"## Decode second parameter\n",
|
||
|
|
"reduced_data = remove_feature(data_4D_klein_bottle, decoding1, cut_amplitude=0.5)\n",
|
||
|
|
"decoding2 = cohomological_parameterization(reduced_data, coeff=23)\n",
|
||
|
|
"# show_feature(decoding2)\n",
|
||
|
|
"# plot_mean_against_index(data,decoding2,\"orientation\")\n",
|
||
|
|
"# plot_mean_against_index(data,decoding2,\"phase\")\n",
|
||
|
|
"# plot_data(data,transformation=\"PCA\", labels=decoding2,\n",
|
||
|
|
"# colors=[\"Twilight\",\"Viridis\",\"Twilight\",\"Viridis\",\"Twilight\"])\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.collections.PathCollection at 0x25130ef1dc0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.scatter(param[:,1], decoding2['decoding'])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 25,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"\n",
|
||
|
|
"N = 10\n",
|
||
|
|
"radius = 10\n",
|
||
|
|
"theta_range = np.linspace(0, 2* np.pi, 20)\n",
|
||
|
|
"data_circle = [[radius*np.cos(theta), radius*np.sin(theta)] for theta in theta_range]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 26,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"data_circle = pd.DataFrame(np.array(data_circle))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 27,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"persistence(data_circle, homdim=1, coeff=2)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 28,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Decoding... done\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"decoding1 = cohomological_parameterization(data_circle, coeff=25)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 22,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.collections.PathCollection at 0x1a8b5522850>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 22,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.scatter(theta_range, decoding1['decoding'])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Source manifold: coordinates to natural embedding\n",
|
||
|
|
"obser"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"source_manifold\n",
|
||
|
|
"open_cover\n",
|
||
|
|
"patch\n",
|
||
|
|
"set of patches\n",
|
||
|
|
"coordinate system for each patch\n",
|
||
|
|
"observed_embedding\n",
|
||
|
|
"homologies give us better candidates for meaningful coordinates"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def circle(theta):\n",
|
||
|
|
" \n",
|
||
|
|
"def torus(theta, phi):\n",
|
||
|
|
"\n",
|
||
|
|
"def klein_bottle(theta, phi):\n",
|
||
|
|
"\n",
|
||
|
|
"def sphere(theta, phi):\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# -*- coding: utf-8 -*-\n",
|
||
|
|
" \n",
|
||
|
|
"def hausdorff(data1, data2, homdim, coeff):\n",
|
||
|
|
" \"\"\"Hausdorff metric between two persistence diagrams\"\"\"\n",
|
||
|
|
" dgm1 = (ripser.ripser(data1,maxdim=homdim,coeff=coeff))['dgms']\n",
|
||
|
|
" dgm2 = (ripser.ripser(data2,maxdim=homdim,coeff=coeff))['dgms']\n",
|
||
|
|
" distance = directed_hausdorff(dgm1[homdim], dgm2[homdim])[0]\n",
|
||
|
|
" return distance\n",
|
||
|
|
"\n",
|
||
|
|
"@multi_input\n",
|
||
|
|
"def confidence(X, alpha=0.05, Nsubsamples=20, homdim=1, coeff=2):\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
" Compute the confidence interval of the persistence diagram of a dataset\n",
|
||
|
|
" \n",
|
||
|
|
" Computation done by subsampling as in arxiv:1303.7117\n",
|
||
|
|
" \n",
|
||
|
|
" Parameters\n",
|
||
|
|
" ----------\n",
|
||
|
|
" X: dataframe(n_datapoints, n_features):\n",
|
||
|
|
" Dataframe containing the data\n",
|
||
|
|
" alpha : float between 0 and 1, optional, default 0.05\n",
|
||
|
|
" 1-alpha is the confidence\n",
|
||
|
|
" Nsubsamples : int, optional, default 20\n",
|
||
|
|
" The number of subsamples\n",
|
||
|
|
" homdim : int, optional, default 1\n",
|
||
|
|
" The dimension of the homology\n",
|
||
|
|
" coeff : int prime, optional, default 2\n",
|
||
|
|
" The coefficient basis\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
" N = X.shape[0]\n",
|
||
|
|
" distances = np.zeros(Nsubsamples)\n",
|
||
|
|
" iterator = trange(0, Nsubsamples, position=0, leave=True)\n",
|
||
|
|
" iterator.set_description(\"Computing confidence interval\")\n",
|
||
|
|
" for i in iterator:\n",
|
||
|
|
" subsample = X.iloc[np.random.choice(N, N, replace=True)] # replace = False\n",
|
||
|
|
" distances[i] = hausdorff(X, subsample, homdim, coeff)\n",
|
||
|
|
" distances.sort()\n",
|
||
|
|
" confidence = np.sqrt(2) * 2 * distances[int(alpha*Nsubsamples)]\n",
|
||
|
|
" return confidence\n",
|
||
|
|
"\n",
|
||
|
|
"@multi_input\n",
|
||
|
|
"def persistence(X, homdim=1, coeff=2, threshold=float('inf'),\n",
|
||
|
|
" show_largest_homology=0, distance_matrix=False, Nsubsamples=0,\n",
|
||
|
|
" alpha=0.05, cycle=None, save_path=None):\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
" Plot the persistence diagram of a dataset using ripser\n",
|
||
|
|
"\n",
|
||
|
|
" Also prints the five largest homology components\n",
|
||
|
|
" \n",
|
||
|
|
" Parameters\n",
|
||
|
|
" ----------\n",
|
||
|
|
" X: dataframe(n_datapoints, n_features):\n",
|
||
|
|
" Dataframe containing the data\n",
|
||
|
|
" homdim : int, optional, default 1\n",
|
||
|
|
" The dimension of the homology\n",
|
||
|
|
" coeff : int prime, optional, default 2\n",
|
||
|
|
" The coefficient basis\n",
|
||
|
|
" threshold : float, optional, default infinity\n",
|
||
|
|
" The maximum distance in the filtration\n",
|
||
|
|
" show_largest_homology: int, optional, default 0\n",
|
||
|
|
" Print this many of the largest homology components\n",
|
||
|
|
" distance_matrix : bool, optional, default False\n",
|
||
|
|
" When true X will be interepreted as a distance matrix\n",
|
||
|
|
" Nsubsamples : int, optional, default 0\n",
|
||
|
|
" The number of subsamples used in computing the confidence interval\n",
|
||
|
|
" Does not compute the confidence interval when this is 0\n",
|
||
|
|
" alpha : float between 0 and 1, optional, default 0.05\n",
|
||
|
|
" 1-alpha is the confidence\n",
|
||
|
|
" cycle : int, optional, default None\n",
|
||
|
|
" If given highlight the homology component in the plot corresponding to\n",
|
||
|
|
" this cycle id\n",
|
||
|
|
" save_path : str, optional, default None\n",
|
||
|
|
" When given save the plot here\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
" result = ripser.ripser(X, maxdim=homdim, coeff=coeff, do_cocycles=True,\n",
|
||
|
|
" distance_matrix=distance_matrix, thresh=threshold)\n",
|
||
|
|
" diagrams = result['dgms']\n",
|
||
|
|
" plot_diagrams(diagrams, show=False)\n",
|
||
|
|
" if (Nsubsamples>0):\n",
|
||
|
|
" conf = confidence(X, alpha, Nsubsamples, homdim, 2)\n",
|
||
|
|
" line_length = 10000\n",
|
||
|
|
" plt.plot([0, line_length], [conf, line_length + conf], color='green',\n",
|
||
|
|
" linestyle='dashed',linewidth=2)\n",
|
||
|
|
" if cycle is not None:\n",
|
||
|
|
" dgm1 = diagrams[1]\n",
|
||
|
|
" plt.scatter(dgm1[cycle, 0], dgm1[cycle, 1], 20, 'k', 'x')\n",
|
||
|
|
" if save_path is not None:\n",
|
||
|
|
" path = save_path + 'Z' + str(coeff)\n",
|
||
|
|
" if (Nsubsamples>0):\n",
|
||
|
|
" path += '_confidence' + str(1-alpha)\n",
|
||
|
|
" path += '.png'\n",
|
||
|
|
" plt.savefig(path)\n",
|
||
|
|
" plt.show()\n",
|
||
|
|
" \n",
|
||
|
|
" if show_largest_homology != 0:\n",
|
||
|
|
" dgm = diagrams[homdim]\n",
|
||
|
|
" largest_indices = np.argsort(dgm[:, 0] - dgm[:, 1])\n",
|
||
|
|
" largest_components = dgm[largest_indices[:show_largest_homology]]\n",
|
||
|
|
" print(f\"Largest {homdim}-homology components:\")\n",
|
||
|
|
" print(largest_components)\n",
|
||
|
|
" return\n",
|
||
|
|
"\n",
|
||
|
|
"@multi_input\n",
|
||
|
|
"def persistence_witness(X, number_of_landmarks=100, max_alpha_square=0.0,\n",
|
||
|
|
" homdim=1):\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
" Plot the persistence diagram of a dataset using gudhi\n",
|
||
|
|
"\n",
|
||
|
|
" Uses a witness complex allowing it to be used on larger datasets\n",
|
||
|
|
" \n",
|
||
|
|
" Parameters\n",
|
||
|
|
" ----------\n",
|
||
|
|
" X: dataframe(n_datapoints, n_features):\n",
|
||
|
|
" Dataframe containing the data\n",
|
||
|
|
" number_of_landmarks : int, optional, default 100\n",
|
||
|
|
" The number of landmarks in the witness complex\n",
|
||
|
|
" max_alpha_square : double, optional, default 0.0\n",
|
||
|
|
" Maximal squared relaxation parameter\n",
|
||
|
|
" homdim : int, optional, default 1\n",
|
||
|
|
" The dimension of the homology\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
" print(\"Sampling landmarks...\", end=\" \")\n",
|
||
|
|
" \n",
|
||
|
|
" witnesses = X.to_numpy()\n",
|
||
|
|
" landmarks = gudhi.pick_n_random_points(\n",
|
||
|
|
" points=witnesses, nb_points=number_of_landmarks\n",
|
||
|
|
" )\n",
|
||
|
|
" print(\"done\")\n",
|
||
|
|
" message = (\n",
|
||
|
|
" \"EuclideanStrongWitnessComplex with max_edge_length=\"\n",
|
||
|
|
" + repr(max_alpha_square)\n",
|
||
|
|
" + \" - Number of landmarks=\"\n",
|
||
|
|
" + repr(number_of_landmarks)\n",
|
||
|
|
" )\n",
|
||
|
|
" print(message)\n",
|
||
|
|
" witness_complex = gudhi.EuclideanStrongWitnessComplex(\n",
|
||
|
|
" witnesses=witnesses, landmarks=landmarks\n",
|
||
|
|
" )\n",
|
||
|
|
" simplex_tree = witness_complex.create_simplex_tree(\n",
|
||
|
|
" max_alpha_square=max_alpha_square,\n",
|
||
|
|
" limit_dimension=homdim\n",
|
||
|
|
" )\n",
|
||
|
|
" message = \"Number of simplices=\" + repr(simplex_tree.num_simplices())\n",
|
||
|
|
" print(message)\n",
|
||
|
|
" diag = simplex_tree.persistence()\n",
|
||
|
|
" print(\"betti_numbers()=\")\n",
|
||
|
|
" print(simplex_tree.betti_numbers())\n",
|
||
|
|
" gudhi.plot_persistence_diagram(diag, band=0.0)\n",
|
||
|
|
" plt.show()\n",
|
||
|
|
" return\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.10.5 64-bit",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.5"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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