{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Online Robust PCA\n", "\n", "### Tom Furnival ([tjof2@cam.ac.uk](mailto:tjof2@cam.ac.uk))\n", "\n", "*14th July 2016*\n", "\n", "A key assumption of using Principal Component Analysis (PCA) for denoising and dimensionality reduction is that the underlying data is corrupted by a small amount of Gaussian noise. As a result, PCA is very sensitive to large errors, such as X-ray spikes, dead pixels or even missing data.\n", "\n", "Robust PCA (RPCA) was introduced to overcome this problem [1]. It decomposes a corrupted dataset **Y** into a low-rank component **X** and a sparse error component **E**, i.e. **Y** = **X** + **E**.\n", "\n", "This notebook is a demonstration of the Online Robust PCA (ORPCA) algorithm [2], as implemented in HyperSpy, which is able to recover the low-rank component of a corrupted matrix in a memory-efficient manner that is suitable for \"big data\". In particular, the algorithm updates the low-rank estimate as each observation arrives, avoiding the expensive re-calculation associated with batch methods.\n", "\n", "\n", "[1] E. J. Candes et al, *Robust Principal Component Analysis?*,\n", "(2009).
URL: [https://statweb.stanford.edu/~candes/papers/RobustPCA.pdf](https://statweb.stanford.edu/~candes/papers/RobustPCA.pdf)\n", "\n", "[2] J. Feng, H. Xu and S. Yan, *\"Online Robust PCA via Stochastic Optimization\"*, (2013).
\n", "URL: [https://papers.nips.cc/paper/5131-online-robust-pca-via-stochastic-optimization](https://papers.nips.cc/paper/5131-online-robust-pca-via-stochastic-optimization)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#Download the data (1MB)\n", "from urllib.request import urlretrieve, urlopen\n", "from zipfile import ZipFile\n", "files = urlretrieve(\"https://www.dropbox.com/s/ecdlgwxjq04m5mx/HyperSpy_demos_EDS_TEM_files.zip?raw=1\", \"./HyperSpy_demos_EDX_TEM_files.zip\")\n", "with ZipFile(\"HyperSpy_demos_EDX_TEM_files.zip\") as z:\n", " z.extractall()\n", "\n", "# Set up HyperSpy\n", "import hyperspy.api as hs\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Let's go with inline plots\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Normal PCA+ICA\n", "\n", "In the first instance, we follow the routine described in [this HyperSpy tutorial](https://github.com/hyperspy/hyperspy-demos/blob/master/electron_microscopy/EDS/TEM_EDS_Tutorial_HyperSpy_CoreShellNanoparticles.ipynb), which carries out the standard PCA decomposition to reduce noise, followed by BSS with a known number of components (3)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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qZNOtV2V7rk+5irruNWeRPRdfdJVF3fvy8pe/vO1y17eXLcsnpq9ZsyZtmzNn\nTtqWxd9dfNG9l646Z3auu3PWVUB258rWrVvTtuz9dO+liw+764q7RmTRV9fvXf9119Isyu7OFXed\nGksn0AhG15AiAQAAXcdHJAAA1IwRDAAAgA4wggEAQM0YwQAAAOhAz0Yw3CzrSZMmpW3Z7OF169al\n60yePDltc2mWbFa0m1m+evXqUW9Pymexu/VcMsIVF3L7nxV3cjO63fbcPrqCRdkMd5eacMWi3Ez7\nKoWkXAEv17ddEiObre5muD/33HNpmys+5Wb1Z+kI1wfcOetSXFnCxB0nV2jOHSt3TmTruePk9sP9\ntrlgwYK2y10hsU2bNqVtWcpMkp544om07fDhw22Xu/PBFTbsdl90z+XaXF/M+psrhFel8GIvMIIB\nAADQAeZgAABQM0YwAAAAOsAIBgAANWMEAwAAoAOMYAAAULN+HMHo2Q2Gi7y5CFIWAXTRJBcPdfGp\nmTNntl2exbskaWhoKG17+umn0zYXv8yeb3BwMF2naiGmLHLqomsuQueeyx3HLBrmIrGuAJKLoWUF\nkKQ8vuhel+OeK3vPqkaOXdTTnWPTpk1ru9wVkVqyZEna5s6/GTNmtF3uYsVue67YmbvmZBHn7373\nu+k67vguXrw4bbvvvvvaLnd91L1frviiuw5s27at7XIXy3SF69w1osp1wBUZcwXZ3GvOCsq5vuGe\nC8eHEQwAAGrWjyMYzMEAAABdxwgGAAA1YwQDAACgA4xgAABQM0YwAAAAOtCzEYysaqdULUZ5xhln\npOu4eKir9pnFnTZu3Jiu4+J1rtqgs2fPnrbLs5iZ5F+X28eDBw92vmNNWfTrWPtR5Xi4vuFifuee\ne27a5n4zyCpcusqtLkbp4nBZPNAdX8e9z1UqVbr3cuvWrWnbnDlz0rasImkWX5X8vrvriov7Ztt0\nFU5dleY777wzbcveT9dv3PXNxbNd38626WLn7px1MVVXeTarprphw4Z0HVeh110HMu5rAtx5NJYY\nwQAAAOgAczAAAKgZIxgAAAAdYAQDAICaMYIBAADQAUYwAACoWT+OYNRSTTWrYCnl0TAXrapSLVPK\n41OOq27p4lOuYl/WsRYsWJCu4+J1WexVyuNa7v1yETR3Uriqjdl+uEjeokWL0rb58+enbW4fsyqh\n7vi6yr4u6plFLF3M2sX13Oty+5j1D3fsXWTTRZ+z88XFXl1U2UVR3Taz/XCRWHcebdmyJW1bunRp\n2+XuPHLM0iCAAAAgAElEQVSRdHfNcbLj4a577jW7OGdWmdqt56K57rlc5DSLArvY+ebNm9O2sdSP\nNxh8RAIAALqOj0gAAKgZIxgAAAAdYAQDAICaMYIBAADQgZ6NYLiZ4CeffHLals3orXp352ZMZ8/l\nZsy72eNutreb+ZzNwnfJE/dcLgGRrefSNrNmzUrbduzYUWk/slndblb/1KlT0zZXBGvatGlpW/a+\nuAJkLt3jUg7ZsXLvpSs+dfjw4bTNzcLP3peJEyem67jj6xJILpWQceff3r170zZ37LP+7fbdXXPc\nPmZ92PVft+8uYeL2MStO5o5hlcKA7rmk/Hrvrs2uv7lradaH3f9H7vowlhjBAAAA6ABzMAAAqBkj\nGAAAAB1gBAMAgJoxggEAANABRjAAAKhZP45g9OwGo2qkKSuQ5QoFue2tX78+bcu4qOScOXPSNhcb\nrBIpdMXT9u/fn7a5GHAWy3P756K5TpV9dEXLLr300rTNvS+u8Ff2XruiZS6a6+J12X6447t8+fK0\nzRVCe+qpp9K2rDig6/euT7kIYNbfXN92++EillXeZxc3ddcVtx/Zeu41V+X2MTunXYTZHQ+3njse\nWf9w8WxXnMydL9nxcNci938Ljg8jGAAA1KwfRzCYgwEAALqOEQwAAGrGCAYAAEAHuMEAAKBmpZSe\n/jlaREyOiGciYm9E7I+IrzeXfz0inm0u3xsRH2pZ5/aIOBgRByLig8d6TXxEAgDAOFNK2R0Ri0sp\nwxFxiqRtEfFLzeZ/LqW8vfXxEfGjkq6WNFnSFZK+HhE3FvPZTs9uMFx1wIhI27I4kaug56KBrhpl\nVnnPxadWrVqVtmXxv2PJomGuEuUZZ5yRtrnIWHasXCVNdwzdc82cOTNtmzFjRtvlLnrpIqwuZusi\nb4sWLWq73FVTdXG9rEKvJD3++ONtl7t9nzt3btr29NNPp23u2Gf76M7ZLD4u+fMlq2LqKou6PuXi\nhq4tqwg8NDSUruNe19atW9O2wcHBtstd9NlFJV381sXwsz7soqiuL7rj6659WUS4SiVYyV+rsv1w\nMevFixenbWOpjjkYpZTh5o9T1PhEY2Qn2v0n/R5Jd5ZSDki6OyJ2SrpW0qey7fMRCQAA41BEnBwR\neyVtlfRIKeUvm01viYh9EfG9iFjYXDZP0uqW1YclLXPb5yMSAABq1u0RjDvuuEOPPvrosZ7zsKTT\nI2K+pMci4hpJ10laUUopEXGXpK9KOr/KPnCDAQBAn3n961+v17/+9Uf+/d73vjd9bCllQ0Q8JOnd\nR829+ICkrzV/3ihpaUvbdEkr3D7wEQkAADWrIUVy3sjHHxExIOlySQ9GxMUtD3u/pJGJSjdJel1E\nTIqI10iaKukW95oYwQAAYPx5qaRPxw9SF3eVUm6IiFURMa+5bIekN0lSKeW2iPimpO1qTAa93iVI\nJG4wAACo3VinSEopfyfpBfGwUsrZZp03j+Y5enaDUTX2mFUcdOu4SJNryyJ0rhKsi2q5OJmTRdRc\nNNdF+bpdHdC9Lhc3dFHPTZs2tV0+b968tsslHxt0MUpn586dbZe76qxZv5F8dDSLh7pzZc2aNWmb\n64uu72TnhIvzukqgLrKZVdLMopySjyO7c9NFEbPj6K4PAwMDaZuL2mcRcvd+uUi6q1brzpesv7mY\ntTse7vzLquZKeb9yr9ltz/WBgwcPtl1+1llnpeu4foPjwwgGAAA1oxYJAABABxjBAACgZoxgAAAA\ndIARDAAAataPIxg9u8GoWkQo44p7uTfGzabPZnVnxXkkadq0aWnbtm3bKq2XHQ83c9+lalyiIpuB\nnaUpJJ9ycMkDt81LLrmk7XL3PrvtuT7gEjdZASrXB4aHh9O2hQsXpm1PPfVU2+VbtmxJ13HFpxy3\nj1lKY+PGjek6LslQ5cLoitqtW7cubcuK00n+NWfnmEsruD7gZKkadx65hInbD7delo5w54NLkbjk\njNtmVlzNneuXXnpp2nb22WmKMu3bbv/cNQzHp6MbjOa3fM2TtE/SmlJK/r8bAAAYlXE1ghERUyX9\nJ0nvlDRB0hZJp0maHRH3SLqplHLHmOwlAAB4UXEjGF+QdKuk15RSdrQ2RMQrJP1CRCwtpdzcyx0E\nAKDfjasRjFLKD5u2ByU92JM9AgAAL3qdzsF4maQlrY9vfo85AAA4TuNqBGNERHxK0sskLZc0Mrmz\nSOIGAwAAtNXJCMZVpZQLR7thF0V1xWqymJS7u3NFc1w8KYtJuajWjh070rYDBw6kbS5qlh2PKgWr\npLyQmJS/L+79cq/ZxfzcPmbFp1atWpWuc+WVV6ZtrpiRe21ZQTb3utz74qKe2TZdsSXXb9w+unjr\nihUr2i53UVR3zrr1pkyZ0na5Oy9dpHv9+vVpW5XItCtc546vk71mVwhv5syZaZuLpLuCgtn74q6l\nWbEwyb9nrg9n74uL02fHUKp2zXEF9Nx1eyz14whGJ9/k+e2IGPUNBgAAGL86GcG4VY2bjEFJBySF\npFJKeVlP9wwAgHGiH0cwOrnBuFnSL0h6TD+YgwEAAJDq5AZjSynlSz3fEwAAxqnxOoLxcET8jaTb\n1PiIRBIxVQAAkOvkBmOiGjcWP9KyjJgqAABdMi5HMEop11basIkoVomwDg4Opuu4KoUu4pW1uSp/\nLtLkXrPbj2eeeabtchcZcxEvV2Exi1i6GKKrYppVSpT88cgqiLq+sXz58rTN9Y/t27enbVl8rWo1\nYHfss2q7rkql629Zv5GkZ599dtRtrk+57bmoZFbh1FUKdhdaF2F1++j6acZdV1xkMztvXb9x76WL\ngLq+kx1H10fda64aZZ87d27b5VWj5a4PZMf+iSeeSNeZMWNG2obj08kXbc2U9Ct64Td5/nLvdgsA\ngPFjXI5gSPpHSXdJ+j+S8m/vAQAAaOrkBuP0UsoHer4nAACMU/04gtHJN3n+U0S8ted7AgDAOFVK\n6emfOnRyg/E+NW4y9kXErojYHRH5F/gDAIBxr5MUyeinXwMAgI7140ck6Q1GRCwppawx7SFpfiml\nbXlDF4VykcgsduViS1Xbsn10kaupU6embS6WWSU6WjV252JtWTzQxd3mzJmTtlWpjCvlkUj3ulyM\n0lUPXbhwYdqWxVFd9NK9LldZNOuLLqLojoe7ILnjke2/q0pctbJo9lyuv7mYuDsn3Guuco65Srau\n2mcWSXeveWBgIG1z5/PmzZvTtuy1udfs9sNVg3XnWBYDdfvhjpWL/Gex6CoxZRw/N4LxiYg4SY0U\nyYOStkg6TdI5kl4v6Y2SPiIpr58MAACOaVyNYJRSfrpZpv3nJP2ypLmS9kp6QtKXJX20lJL/Wg4A\nAMYtOwejlPK4pA+N0b4AADAu9eMIRicpEgAAgFHp5Iu2AABADzGCAQAA0IFOip29StJ3Sil7IuLn\nJV0m6X+VUvLM0jG42NWsWbPaLq8SQZN8BDCLw7kYlItPudiV20cXbcy4ao7uWGX776KX7rlcpNDF\nfTPu+GbVSCUfA3bR4uxYuffERXNdLDqLFLpj736rySJ5ku9v2fs5e/bsdB0XYXX7kZ3rLgbs3i/H\nVZ7NIs5V4/Ru/3ftav89hNOnT0/X2bp1a6Xncte3bP9dpDSrciz5/uEqFlf5zdzFZVesWJG2ZfFh\nd0138fexNF5HMP5U0t6IeLmk35S0StKtPd0rAADwotbJDcazpXFr9XZJf1xK+RNJfGsJAABd0o+1\nSDqZ5Lk7In5L0s9Lurr55VvVvtYPAACMC52MYPyspAOS/n0pZVDSAkmf6OleAQAwjozLEYzmTcUf\ntPx7rZiDAQAADFfs7O5SyqsjYrek1tufkFRKKXm1n2Nws3bXr29f2sTNwHZ3Z65I08yZM9sud7PH\ns8I9kvTkk0+mbW5mfLb/boa7S4q4GdPZ8Th48OCo15GkiRMnVlpv0qRJbZe79MPOnTvTNnd83XpZ\nWsQlI9xzVUkluLSNS1xVTS2deeaZbZdnhfCk/P2SqvVFlxZyRcbcc7lrRJaCWbBgwajXkfyxz5JE\n7vi6c8Wdmy7tlCUqNm7cmK5z1llnpW2rV69O21xBxPvvv7/tcpdKcf0j679SfhzXrl2brnPeeeel\nbWOpH1MkrhbJq5t/M6ETAACMyjHnYETEm9os+8Xe7A4AAONPP87B6GSS5/UR8acRMSkiZkfEbZKu\n6fWOAQCAF69ObjBeq8aXa31H0t2S/qaU8lM93SsAAMaRsR7BiIjJEfFMROyNiP0R8fXm8iURsTUi\nDjb/Xtiyzu3N5Qci4oPHek2d3GAMSLpSjZuMA5IWh5uBAwAATmillN2SFpdSTlfjyzOviIhfkvRZ\nSfeWUiZIuk/S5yUpIq6RdHXzsW+UdMOx7gU6ucG4R9LtpZQ3S7pC0jxJ/7fSKwIAAC9QxxyMUspI\nXG6KGvcDRdKlkt7fXP4BNeqPSdJ1ku4spRwopdwtaaeka91r6uSbPN/U/O4LlVL2Sfr1iLj6WCu5\naJWbcJLFpFzBLVcsysW4sriTK1jlnqtq3GlwcLDtchcNdFFaF1PNCobNnz8/XccdexflcxHLLDrq\nIpuu6JOLNk6bNi1ty+Ko7rkcV7Qqu9l377OLAbtCVy5GWWUdF3t1sfPsOlA13uyini6+uHjx4rbL\nXYE0V8DL/eKWnRPuvHTXHPea3TazNlegcNOmTWnb3Llz0zbXd7LCZe65Fi1alLa59yVbL4vsSj6S\n3u8i4mRJuyVNlPTtUspfRsQtpZTlklRKeSwiRk7IeZLuall9WNIyt/1OvmhrbUQMSDpXUn4WAACA\nSrqd9LjvvvvsdzM1n/OwpNMjYr6kxyLix7q5D52Ua3+3pPep8RXh35F0laRvS3pDN3cEAAB0x5VX\nXqkrr7zyyL8/9rGPpY8tpWyIiIckvVvSoYi4qJSyPCIuljQyXL5R0tKW1aZLWuH2oZM5GO9TY+7F\n06WU16vx+Uw+jg0AAEalhhTJeSMJkeanFJdLekDSw/pBvbEbJT3U/PkmSa9rfmXFayRNlXSLe02d\nzMHYX0rZHxGKiFNLKd+LCPu5CwAAOKG9VNKnW5Igd5VSboiIT0u6PyIOStol6RWSVEq5LSK+KWm7\nGpNBry/H+FynkxuM9RFxpqR/kPTViNgu6elqrwcAABxtrL9ts5Tyd5JeMEO7lLJajY8/2q3z5tE8\nRyeTPH+i+ePvRMQdagyL3D6aJwEAAONLJyMYR5RSvtHpY138y0VHs8ibW8fFELOKqVJeSdFVG3RV\nA12lR1fRc926daPe3uTJeQ06F//K4nWbN29O13FRVFdd1kVHs/1w0Va3Hy5K66KjWUTUxe7cfrj4\nYhYtdpFYt+9Vo7TZa3PH0MVK3bmeVcx0sVcXo3zlK1+ZtrkoYvY+u0jshRdemLbdc889aVvWB1yf\ncm3ufXax+Sq/EbuYeBanl3wl2+x65OLZ9957b9rmzrGHH3647XJ3LXXH6T3veU/a1m111QvppU4m\neQIAAIzKqEYwAABA943LEYyIeG8zwgIAANCRTkYwZqsRWXlI0qck/euxoikAAKBz/fjf6jFHMEop\nH1bja8JvlvRLkp6MiN+PiLN7vG8AAOBFqqNJns0Ri8Hmn2fVKOH+hYj4eA/3DQCAcaGOaqq91kkt\nkvdJ+neStkr635L+SynlUEScJOlJ/aCs6/O4WJuLVg0NDbVdvnDhwnQdF5Fycc6pU6eOarnkKwqu\nXbs2bXMVALOop4tsusiYixu6CGDGHQ8Xa3Pvc7YfrkKoqzjpYswuDpfF19yxd9FGF2HN1nMROncM\nXUXdLVu2pG3uXMq44+v2MXvP3PF11Vnd+ef6dlbp+KmnnkrXccdw3rx5aVsWSXfvl/sPwF1Ls4i7\nlB9HV4G16vtcJbrtIthZvFny+58dR3dN3L9/f9qG49PJHIxpkn6ylPK8b+8spTwXEW/rzW4BADB+\n9OMcjE6+yfMjpu2J7u4OAADoB3wPBgAANevHEQy+yRMAAHQdIxgAANSsH0cwenaD4QqQVZlpPzw8\nnK5zwQUXpG2u2NmZZ57ZdvnSpUvTdVxSJNue5GfuZ7Op3Qxxl95wqYlsxrSb1V81EVRl1rzb3sGD\nB9M2lyBw+5FxBeNc8Sk3wz0rCuZmsVc9Hi4NkO2jm7nvEjyu72TruWTSy172srTt/PPPT9vcObZi\nxYq2y12/cdtbvnx52pYloVyRLnc+u/VcW9avXGE19166vui2mZ1/bt/dtc/tR7b/7vi6VBiODyMY\nAADUrB9HMJiDAQAAuo4RDAAAasYIBgAAQAcYwQAAoGaMYAAAAHSgZyMYLorqYo8nndT+nscVLVu8\neHHalhUSk6RZs2a1Xe72/Zxzzknbnngi/+b0rACSlMe1XIGeqgW3Mi5m5gqQOS7ylsWO3fu1e/fu\ntM3F0FzxrOx1z58/v9JzuUhsFq9z8VBXcMtFUd1vQ9k+Vtl3yUdYs7j6okWL0nWWLFmStrn30kWL\ns1jshg0b0nXWr1+ftrn3JeP6rzuGLsbsop7ZsXLb27Vr16i3dyxZX3RF/tzxcLLz2V0vXex8LPXj\nCAYfkQAAULN+vMHgIxIAANB1jGAAAFAzRjAAAAA6wAgGAAA1YwQDAACgAz0bwagau8qqG7ropYuH\nzpkzJ23bt29f2+Vnn312us6UKVPSNhdtzOK3kvTUU0+1Xe5iYVllzqrc3bOLKA4MDKRtLs6ZbdNF\nW90+upitq8Q7ffr0tsuzCreSr1brIm9ZpND1bVed1b1m15b1HRd7dTFx109XrVrVdrmLV7r44qtf\n/eq0zV1zsuPoKtK6Y+9ij1nU2j2Xuz644+H2I+sDLv7uuD5VpdLxtm3bRr2O5P//yK4R7rx015yx\nxAgGAABAB5iDAQBAzRjBAAAA6AAjGAAA1IwRDAAAgA4wggEAQM36cQSjlmqqLvaYRahcHMvF67Zv\n3562ZRUdXVXJ++67L23LKkdK0po1a9K2rMqii665WJiLUWaRtyyyK/kqkO6kcDG/LFI4NDSUrnPm\nmWd29bmk/Bi753IRVhfZnDdvXtvlrgpolXNF8nHqLLLnoqPuGLr+sXDhwrbLq0ZzXT9114HBwcFR\nr+Oi4C6Cne2jq0rsKky7iKU7jtl75q4P7nx2/c1dq7I297pcLNr106wvuuPkrqU4PoxgAABQs34c\nwWAOBgAA6DpGMAAAqBkjGAAAAB1gBAMAgJr14whGz24wXAEZ15YVz3Kztp988sm07cILL0zbstne\nbhb77Nmz0zbXQaoU1HGzzt2sfpecydZzM7NdOsbNwnczy7PX5oocuQTB1KlT0zY3gzxLfbiZ5e65\n3HHM+rCb1e8KO7mkSJWCUC454xIV7pzI9sOlbVxxr5UrV6ZtWUpHyvvAunXr0nV27tyZtlVJn8yd\nOzddx/XRXbt2VVovu465omUu2VE1zZL1e9dvXFLLXVey98X1X5eCwvFhBAMAgJr14wgGczAAAEDX\ncYMBAEDNSik9/XO0iLg8IrZFxP7mn79tLv96RDwbEXubfz7Uss7tEXEwIg5ExAeP9Zq4wQAAYPw5\nIOnXSimnSVos6e0R8ZZm2z+XUk5v/vmoJEXEj0q6WtJkSW+UdEO4SWdiDgYAALUb6zkYpZTHJD3W\n/HkoIoYlXdRsbnfj8B5Jd5ZSDki6OyJ2SrpW0qey52AEAwCAcSwiXi1ppqS/ai56S0Tsi4jvRcRI\nQaF5kla3rDYsaZnbbs9GMIaHh9O2s846K23LImquGJCLLz700ENp2+bNm9suf+CBB9J1XITVFTRz\n62WRTRefckWwXOwxi1+66Je7sx7LQkGuAJLjIsJZ1NNFhF1E0a2XHWMXQ3SRWBejdH0gixS6goKO\nK1CXxaJnzpyZruOio+5cd1H2VatWtV1eNb7oYpnZeu48ctdLd266EeqsOFnVuKk7Vi42n8Wfq8Zl\nXQw/+5oDF9vO1hlrdaVIImK2pH+VdGNzJOM6SStKKSUi7pL0VUnnV9k2H5EAANBnHn/8cXuzLkkR\ncaqk70q6vZTyIUkqpXyv5SEfkPS15s8bJS1taZsuaYXbPjcYAADUrNsjGBdccIEuuOCCI//+9Kc/\n3e5hj0taW0p5x8iCiLi4OT9Dkt4vaWSI8iZJn4uISZIukzRV0i1uH7jBAABgnImIX1VjRGJ/RIx8\nnvZRSb8cESNfi7tD0pskqZRyW0R8U9J2SUXS9eUYd0XcYAAAULMaUiSflPTJNk0fNeu8eTTPQYoE\nAAB0HSMYAADUrB9rkfTsBmPx4sVpm4tkuShUxkVYXTw0i6m6+JTbPxfxcrI4WdVqqi7CmkX53Pac\nQ4cOVVovi19u27YtXcdVy3RxPRfzy+Jrrt+47bkKp9k2XezVcVFU10+z/u2ifO4cc7KLpus369ev\nT9sefvjhtM1VK83eMxdFdZHYKtxzuSrC7nx2bRkXLXfxUBeLrnL9cP8PuHi2q8Sb9Xu3varXMBwb\nIxgAANSsH0cwmIMBAAC6jhEMAABqxgg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evHnU++GK5Ln3zPX77HrkkjguJecSSNn+u/7r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\nYAAAdQYGAFD3AXPvTWXWCkZuAAAAAElFTkSuQmCC\n", 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6x4Ld6SefmgAAZAb64SpPpVKooaGCxsPbB7A8R+098NX7sHlf876iIcdCKU/3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Load data\n", "cs = hs.load('core_shell.hdf5')\n", "cs.change_dtype('float')\n", "cs.plot()\n", "\n", "# Apply PCA\n", "cs.decomposition()\n", "cs.plot_explained_variance_ratio()\n", "\n", "# Apply ICA\n", "cs.blind_source_separation(3)\n", "axes = hs.plot.plot_images(cs.get_bss_loadings(), axes_decor=None, cmap='RdBu', colorbar=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Normal PCA+ICA on corrupted data\n", "\n", "Now we corrupt the data with sparse errors to simulate e.g. hot pixels or X-ray spikes. We apply the corruption by masking 5% of the datapoints with the value 1000." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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xUkTsjIjGiPhDRIyNiO4R8WJE7M//e1LJ7y/Pxxsj4oaS8csi4vW8trFkvGNE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\nxowZZa3HunXraI1tK7WdVGRu/PjxZa3HCSecUDi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CW3+LiPHANcDXcttPgF9FxARgb+AMSZPze1OAt0bEZOA/gCkRMZr0R3sXgIj4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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Corrupt the data with sparse errors\n", "sparse = 0.05 # Fraction of corrupted data\n", "\n", "cserror = cs.copy()\n", "E = 1000 * np.random.binomial(1, sparse, cs.data.shape)\n", "cserror.data = cserror.data + E\n", "\n", "cserror.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As discussed above, PCA is known to be sensitive to outliers, so first we try the same PCA+ICA analysis. Notice how the scree plot is dominated by the sparse errors and so is tricky to interpret. The BSS results are essentially noise." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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44Dd8c49ofmWNbjop0bLOnVPGVdorY/jaF3kg4iwA0qKFP12SFUAFos1Ofmo5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y8HaiyYsI5u2sGFf5Ou88jkUBxt6MZlAxN71NK12+2otnjQ5WI/N1hdmBNGWMUekQ5jO+tM+fVm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\nkRfW0z1e147MCB20j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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Apply PCA\n", "cserror.decomposition()\n", "cserror.plot_explained_variance_ratio()\n", "\n", "# Apply ICA\n", "cserror.blind_source_separation(3)\n", "axes = hs.plot.plot_images(cserror.get_bss_loadings(), axes_decor=None, cmap='RdBu', colorbar=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Online Robust PCA+ICA on corrupted data\n", "\n", "Now we try the ORPCA algorithm on the same corrupted data, followed by ICA. \n", "\n", "- `output_dimension` is an initial estimate of the rank of the data\n", "- `init` is the initialization method, which can be
- `rand` (random), or
- `qr` (QR-decomposition based) - **default**\n", "- `lambda1` is the nuclear norm regularization parameter\n", "- `lambda2` is the sparse error regularization parameter\n", "\n", "Here we set `normalize_poissonian_noise=False`, although this option may depend on your data.\n", "\n", "Interpreting the scree plot is much more straightforward, and the results of the BSS match the originals seen above." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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cwjIz6xz1vg+rNPjt1og4JK3bFhGTmhDriDlhmZl1jnp7Ce6U9MLcweYBOxoVnJmZWS1q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\nMysEJywzMysEJyw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0Cw4zWyNDGHPywA5gG5XJ8+k2Mj6ai14AP+PDoy/iRTePaT3j0XGfjgwzrraA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\ntMVUXHjv9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Try online robust PCA\n", "cserror.decomposition(normalize_poissonian_noise=False,\n", " algorithm='ORPCA',\n", " output_dimension=10, \n", " init='rand', \n", " lambda1=0.005,\n", " lambda2=0.005)\n", "cserror.plot_explained_variance_ratio()\n", "\n", "# Apply ICA\n", "cserror.blind_source_separation(3)\n", "axes = hs.plot.plot_images(cserror.get_bss_loadings(), axes_decor=None, cmap='RdBu', colorbar=None)" ] } ], "metadata": { "kernelspec": { "display_name": "Anaconda 3 (root)", "language": "python", "name": "root" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.0" }, "widgets": { "state": {}, "version": "1.1.2" } }, "nbformat": 4, "nbformat_minor": 1 }