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Created November 5, 2014 02:38
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PCA - Sorting high dimensional objects.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using PCA to sort high dimensional objects\n",
"\n",
"- Recall that PCA maximizes information retained when we project our data to lower dimensions. \n",
"\n",
"- Even when projecting our dataset down to 1 dimension, PCA will capture as much information as possible from the original dataset. \n",
"\n",
"- What's unique about 1 dimension data? Well it's an array, and it can be sorted!\n",
"\n",
"- So if we have objects that can be represented as a high-dimnesional vector, we have an oppurtunity to endow an \"order\" to them somehow (now you can't see it, but I am air-quoting \"order\"). This order has nothing to do with one object being \"better\", or \"larger\" (again air quotes) than another object, but instead has to do with an ordering that minimizes information lost. What does that mean?\n",
"\n",
"- Let's try this with colors! \n",
"\n",
"- Colors can exist in 3 dimensions, and the dimensions are R (red), G (green) and B (blue). \n",
"\n",
"- This example actually came from a problem I had. I wanted to sort my books my color, like:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![books](http://cdn.decoist.com/wp-content/uploads/2012/05/bookshelf-arranged-by-color.jpg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I took a photo of a subset of my book collection, sampled what color they were using Gimp, and recorded the colour in rgb. \n",
"\n",
"Sorting them was going to be inpractical: it would take time - plus it's actually really hard to decide on an order for colors. Example:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"figsize(12,8)\n",
"\n",
"colours = np.array([[111, 28, 21],\n",
" [ 27, 17, 20],\n",
" [ 79, 23, 17],\n",
" [185, 125, 50],\n",
" [155, 76, 32],\n",
" [ 82, 24, 17],\n",
" [127, 63, 33],\n",
" [193, 91, 63],\n",
" [176, 97, 36],\n",
" [ 79, 15, 19],\n",
" [176, 140, 47],\n",
" [203, 65, 46],\n",
" [174, 139, 87],\n",
" [138, 44, 34],\n",
" [144, 91, 36],\n",
" [ 86, 21, 16],\n",
" [123, 44, 32],\n",
" [109, 44, 30],\n",
" [ 84, 29, 27],\n",
" [121, 42, 65],\n",
" [ 70, 15, 11],\n",
" [107, 24, 17]])/255.0\n",
"\n",
"# I've normalized the colours between 0 and 1\n",
" "
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This a the color list of a subset of library that I pulled from a photo. There are 22 book colours here, and I've normalized the dimensions to be between 0 and 1. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def display_colours(colours):\n",
" figsize(13,2)\n",
" N = colours.shape[0]\n",
" for i,c in enumerate(colours):\n",
" ax = subplot(1,N,(i+1)%N, axisbg=c)\n",
" ax.get_xaxis().set_visible(False)\n",
" ax.get_yaxis().set_visible(False)\n",
" \n",
" plt.show()"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a little helper function that will display a list of colours passed in. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"display_colours(colours)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAuMAAAB+CAYAAACOGh8QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x109be6a10>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(22, 3)\n"
]
}
],
"prompt_number": 35
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can probably do a pretty good job of sorting these, though there are some odd ones: \n",
"\n",
" - where does that purple on go?\n",
" - and this orange one?\n",
" \n",
"But it is pretty time consuming even for only 22 colours here, and the process is very subjective. Likely your friend will have a very different ordering. We'd like something objective, and that scales to potentially hundreds or thousands of colors.\n",
"\n",
"Let's next visualize these colours in 3-space:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figsize(12,8)\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"\n",
"ax.scatter(colours[:,0], colours[:,1], colours[:,2],\n",
" c =colours, s=50 )\n",
"plt.xlim(0,1)\n",
"plt.ylim(0,1)\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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QI6pUVovoRpoviMrlMpYvXx7b9ycNktWQsLu9rhrsx1yv19vPqSSpfqOXaZRU\n8WLCMAylZs/qRqvVQq1Wkw5EFE9ESds/hHtk+YvscRKlg4ieoEtrsdxqcflhUi6Xcd1114X+PWmB\nZDWjsNv9/I9WJUn1S5SSGkUagGppGX5g24fPE7Z7D3tsmiYJSYqwuyVMZbWIIAkytzrs/lSpVKh0\nlQdIVkOCj6yqhCxCB8xF6QqFQkyt6k637Zi2SGovkqpKSS2WJ8wP/uKnqmXPJyEKQkRL1vIXifCI\nK5Wg2/GXBlh5g2Q1JFQRBoZdTiqAjiiWanRrVxolVVatoFAoJCqSKq4DMP+CSDzYs/QAsdyRnyhI\n0vY70Z2wymrJlhkUXgcZEdERdiqB7Lt4qM6qN0hWU063gVMsV1UVqXaCz2VUQVKDvCCxk9Qk1X2V\n7RMm2JZleRoVLB746bYwYUeYt36pv2SPIPuT7DPsmEiy6o1khGoSSNyRVVZ/s1qttkU1l8uhVCqh\nWCy2fzCqH4xlV72maaJWq6Fer7cFNp/Po1QqKVNb1C3sdn+1Wm2Lqq7rKBaLKJVKiRBVJtrVarVj\nnxQKhY6+1gtMXnVdh67ryOVy7ces9Jisr7BR6Ow/0zTbj1VM0yGCgb/gkfUZuyiY2GdM06Q+45M0\nRZX99ieGZVl45513sGHDBvzO7/wOPvOZz8CyLBw9ehSVSqXn9o2NjeHWW2/F1q1b8fDDD897/Ykn\nnsB73/te3H777Xj/+9+Pp59+2vVnVUFrOfzyLly4EGVbEg/fYev1OprNJvL5PPL5fGRt8FqCqtls\nol6vI5fLKTs17MzMDACgUCjMy4HM5/OxCWqr1cLs7CwAoL+/3/NnZZFhdru/l/WJsu+JM2fJotuy\n9jCpFZcF2Ncsdku3KKyMqCNqQa1rUmCix072qhFEnxEfA9nbzzxZXnd2UcP3o5/85Ce4++67pe9f\nu3YtNmzYgA0bNuDGG2/Ehz70IdfHbtM0sW3bNoyOjmJoaAg7duzAI488gpGRkfZ7pqensWDBAgDA\niRMncO+992J8fNzVZ6NmyZIl0ucpDSAkoo6sprVOKg9fXitOSZXBpyh0e1/c6QtBIJs5S5V9QoNz\nCK+46TN+B+AQ2UM8/+dyOdx222147rnncPLkSZw8eRL/9E//hL6+Prz88suYmJjAxMQEvve972HB\nggW2UitjfHwc69atw9q1awEAu3fvxuHDhzuEk4kqAFy6dAlLly51/VlVIFkNiahktVdJjTtdwQkm\ndTyqCBH6UlX7AAAgAElEQVTg7WTEbi3yEcWkSqo4KYFK+8SOIAfnkMBmgyD7DMvZpvzp7CCmQei6\njtWrV2P16tX4wAc+gH//93/H448/jmaziV/84hc4ceIETpw4gXq97inAdObMGaxevbr97+HhYYyP\nj8973+OPP47PfvazOHv2LL797W97+qwKkKwmlDRHUsVby4xisZiIHE4R2a1yVtA/KScsu0kJ3Myc\npfIFUZgRtaTs27ho1qZx6fwvcfHNn8PI92Hx8A1YsHQNNF3t3zgN6CJ6pdFowDDm9MswDIyMjGBk\nZMRTRJXhts/s2rULu3btwjPPPINPfOIT+MlPfuL5u+KEZDUkwjpBBy2pKomETFINw4Bpmkq0TwYr\nsSRLA5CtTxRRyKCrFCR9UgKvUBQ2fKxGDZMnnsLF0y+2n3v79aNYu3knlqzZFGPL/GHXZ/hybIBa\nZbWI+CiXyxgcHAxkWUNDQ5icnGz/e3JyEsPDw7bv3759O5rNJi5cuIDh4WFPn42TdJ5tFCBoCXQ7\nuj+JWJaFWq2GWq3WFjvDMNDX14dCoZC4A7VsffL5PPr6+lxFIlWASers7Gzq+ptf3FQkELEbXS6+\nnjVmy292iCrj9Mmn0aj2PjpaNVi/cVPFAkBHn6EqFukjyAkBtmzZglOnTmFiYgL1eh2jo6PYuXNn\nx3teffXVdp954YUXAABLly519VlVoMiq4oR9uz/OyKos/1F2a1ml6K8TbtdHZdJQ7zVK/EZh+feJ\nuW1ZiMLWZsrS55v1GTRr08iX0jsNZZCRe34ZWeg3aSHIyKphGDh48CD27NkD0zSxd+9ejIyM4NCh\nQwCAAwcO4LHHHsM3v/lN5PN5LFiwAF/96lcdP6siVLoqQPir5F7KGgFy8Qnj9muv7fSDV6mr1Wow\nTROFQqGd56MK1WoVlmVB1/V56QtxSWqj0WjnRLmdQldWpSAoSZW1R5aTnPZSN7xseLnwSsMtYbF0\nVeWtUzj10/857326UcDIe/eh0L84hlYGTxB9OqyyWmHCIsMAMnuR67Tvn376aTz77LN44IEH4mia\n0lDpqgiwK1/ktqwREJ2kyvDSTj/YSaphGI7rpmpklT8g8wfmuPM5vWyvtJTSSgK8QPAnMkaWBub0\nLVqFBUuGMX3hdMfzq667LTWiGhQ0CDB9lMtlDAyk9+5BGJCshoTXg0BckhrFwcqvpKqKbNCRruvt\ngv5JwU1B/yBwK89Og9XSjJOM+LklnIQorFHox9pb7sKFyZO4MHkCOaOA5evejcGV18bdtMCQDbQL\nijAHAYbRXqKTSqVCU616hGQ1RNycfOOMpHpppx9UWLcgkUkqI0nirXJBf2IOu8iXGxlJSjSt0L8Y\nK6/fjuXr3gXoOeg6nY56xU9ZLYrCRs/U1BTWrVsXdzMSBR0dYiJtIseTtvJaToOOms1mxz5UmaQW\n9Ccuk8YorG6oOc1zWghjQJcK/SbJVCqVwAZYZQWS1RDhI5YMFSVV1k4/pK0mp5uR8bIoa9yIct9L\nQX9CfbIQhSWCJ8x+QzgTZOmqrECyGgFsII5qkhoUYUtq1JFVp5Hx4sjOuKO+TrRaLdTrdSUvHuik\nFj5BRWEppzFbBBm9By5PNSsuM810Ox9QZNU7JKshwn6YzWazIz9QFWFg+BWuNEZS0zAynj9x8AX9\nk7pfiOCgnEbCD36jsOy5LF/8yNZtamoKixdT1QsvkKyGBJtthD0G0iMMUY+GDzt6mSZJVbGgv8rR\nZ4KmlyX8Y3fxI9ZQ5qGLn7nIKpWu8gbJasCYpjlv0I2maUpPUelWJlSVIb/w6Rl+yzepIGIy2WaU\nSqWYWkUknSCjsPzrWStNljXYACy2n9l5j1JQLmOapnIT3KgOba0AYSWBGOwHy+aDTippk1Rgfo1R\nIHkj45ls1+v1joiwYRhoNBqJWQ8iOfiNwvLwF4ayv0Q6oRQUohdIVgNE1/X2AJx8Pj9PJFTFLjqo\niqQGGb1MS41Rp4L+LE1DVZhk84JNJJtuIiK7LUwiQlBZLcItJKsBw+dtOuXtqIyTpCZ13na7WbR6\nLd8UdRqAG9lW9eKISbRMpNldCPY+IvnIfldup5cVnyeBzRZJL8fmdCFOxzd/kKwGTFLKGvGwdjKh\nazabXUs2xdE+P9sxLEmNGi8F/VXrd/yJhYkqL6f8exhsPSlSkj7c3A72EkmzWyaRPoIsqxVX35mZ\nmUF/f38k35UmSFaJ9o+Yr2CgaVo7SpzEE4BdIfwkTYsKJLugPz+AjcH6Fetr/InETdkbtgzZXyK5\npLEiAaW5REMvUVjx+SgGdNGEAP4gWQ0R1SJcIvwocobqJZu6jSSWldUKs2RYWPs46vUIGtkANmCu\nOgEfVeVPDry86rqeSEEhgiXoSBpF6aNBBVFXNYJfLpdpQgAfkKyGiKqy2q3UkWoHcTftSbrcMWT5\nwklaD7u0i2azOU8W7GDvC2rUMAlKukh6PiMRH2FG8MXHdtDsVf4gWQ0Yu8hft4hgFMgkVSx1FHcb\nvWI3GCysCQrCIqzKC1H1O9nFAktXYOvWC72cZEhQsgFFYQm/uInCunmOLcNpsOjU1BTJqg9IVkNE\nlQOcnaTyIiSLsqoEOwAw+QpL7vy0C/AfPZftm17XI8p+5yaiHWa/CkpQSGDTCUVhCb/0GoVlmKaJ\nr3/965icnMSGDRtw8eJFLFy4MLB2jo2N4aGHHoJpmrj33ntx3333dbz+6KOP4vOf/zxarRYWLlyI\nv/3bv8XGjRsBAJs3b8bAwED7mD02NhZYu4KGZDVkRMmKkm6SqmqaghO8pAYld3HABh+JBf1Vzhfm\nUTldwY+gqDZimAgXisISfnFzfBH7yLe//W38+Mc/bv87n8/jW9/6FjZs2IANGzZg48aN2LhxI664\n4gpPbTFNEw888ABGR0cxNDSEHTt2YOfOnRgZGWm/56qrrsLjjz+OwcFBjI2N4f7778eTTz7ZXofH\nHnsMS5Ys8fS9cUCymkLsRIiNhu82QEnlg22tVms/TpLc8TgV9Fd9PcKIBEcFRWEJJ4KOwjrdCibS\nB99/xNJ7H//4x7Ft2zacOHECx44dw5tvvonnn38ezz//fMcyvvjFL+IjH/mI6+8cHx/HunXrsHbt\nWgDA7t27cfjw4Q5Z3bZtW/vx1q1bcfr06Y5lJKV/kqyGDB9ZDRsmqV6nEVX5ZMvkSJQFVeTOS3Q6\njtmzgrr46CUSLNtGce83RtAjhinClj56uchhmKbpe0AOkVzYMeGuu+7CXXfdBQD4m7/5G7zvfe9D\nf38/jh8/3v7v5MmTuO666zwt/8yZM1i9enX738PDwxgfH7d9/9e+9jXceeedHe27++67kcvlsH//\nfuzfv9/jGkYHyWoK8CupPHGmK8iQyREwd6u5UCgo0Ua3eCnoHxR8ZKdXkhwJ9gMN5iK6EfRFjt0y\nk0hSInVxUalUMDw8jBtvvBHbt29vP+9nxksvfeWHP/whvv71r+N73/te+7nDhw9j1apVOH/+PHbv\n3o3169d3tEklSFZDJuy8UFk9yyTOdc8jkyNgbhsmSZCSXNAfiEeyVSboNAL2fBa3ZRoRL3KobnBy\n290L3c71dnVW/eT6Dw0NYXJysv3vyclJDA8Pz3vf8ePHcf/99+PRRx/F4sWL28+vWrUKALBs2TLs\n2rUL4+Pjyspqcmr7JJSwZNU0TVSrVdRqtbbU5fN59PX1+ZIhFQZb2a1TqVSKfdCOG/iTTr1eR7Va\nbYtqLpdDqVRKRFSYbz8TVcMwfPetNMNu8+m6Dl3Xkcvl2o/tZn8TI3CmacI0zbbcRJU2RESDmz4i\ny5Nld5csy+roI3w/IdRG9vsvl8uBzWC1ZcsWnDp1ChMTE6jX6xgdHcXOnTs73vPGG29g3759+NKX\nvoRrrrmm/fzMzAwqlQoAYHp6Gk899RQ2bNgQSLvCgCKrIRBmtCSNkVQ3ETwVZFqGGCVTdYS8G9yU\noSK64yaNQNaPKY0gXfC53SK9lkVKYxQ2K8zMzGDBggWBLMswDBw8eBB79uyBaZrYu3cvRkZGcOjQ\nIQDAgQMH8LnPfQ4XL17Epz/9aQBol6g6d+4c9u3bBwBoNpu45557cMcddwTSrjDQWg5n/wsXLkTZ\nltTAXyk3Gg00Gg0YhoFCoeB7mbLBOUHeUq7VajBNE4VCAYYRzTWM3WxHsnWq1+toNpvI5/PI5/OR\ntM8tMzMz856Le4R8tVqFZVkoFotd2yCT7CAnVmi1WpidnQUA9Pf3A5i76BInCmCRJADKVxboFXG0\nsJeR40mUE7a+dtHmNBLUOnfLhbUjrn6Spd+xjG7r/+EPfxiPP/541M1KDHZltCiyGhF+I4JehC4p\n+FknFSOr7BYuT9yS6oWoylBRjqY9TFa9lEuiagTZgqKwBEGyGjp+DwZRS2oUMpiW28x2lQqSlI6R\ntRH+ScPvYC5KI8gOVJGAyBIkqyHjVQLTGEkNUlLjjqzKJI+1KQmiJ6aTkKQmh6DkhMQkvVAUNn6c\ncpVN00zEXTcVIVlVBDtJNQwjkqhjGJHVIAccxX2gdCroz6oXxC3SPOL+pDJU6cSPnFB0LXsEVXaN\nLYPSTfxRqVQwMDAQdzMSCclqyHSTQJlEJPHWOI/dgJ2k5HLyJD3SzcpQJbXWK+GPoGvCksCmD7t9\n2mu6iVgfm7jMxYsXpTVWie6QrIaMnazKCsbHKalBRFaZpDabzcAH7EQ9wEqWupAkyWPbKalltIjg\nCTrHkaJr6SSoCx2W20/95DKVSoVk1SckqyFgN+KZnQxUktQgkI0q1zStXfooSQcoP/m1KlUqYP2L\nT1cIsgyVX1huL1UDUItechwpjSA7hBWFlS0zzUxNTQU2IUDWIFkNGf6HWK/Xlb3d70e47CQ1jAE7\nYQthkPm1cSDbF8DcOhSLxRhbRiSRoNMIiHQi6yf8OY4fgMpIe7Te6RxFkVX/kKyGDN9x2Y84SRIk\nI0pJDZswUxeiQlahgOWOqdrHktRHiDl6SSNgiH1UXDaRfJigaprWcfzJWhRW1tYgp1rNGiSrISG7\nnazC7Vg73EYu467PGVRkVSbcfiU1rjQApwoF4pS8KsEGrdFAjOTjJo1A9rtIm5iIqJASpBphDfoT\nH6tMuVzG6tWr425GIiFZDQEmQSJJjqaKkgpEW/ooqO9gSf98Qf+kRYWTXIZKbDcgP7E71Sok1IcX\nCvabA+YuCLNWjSCJbY4KN9F6N8/JlqXidq9UKhRZ9QnJagiwHwmL1Kkc5WI4VS2wi97FdTDwO0gn\n7qhwr3ipUKDaoC/WDj4Vhu0HWRvF3wvdNk4H4n4E/NeEpf6gJr1eaPYy6E98XjWBnZqaopxVn5Cs\nhoCu6yiVSu0oKpMLFcTBDUwuVKov2st3hi3cNPhLDp9qwWCpMEBnWS3W5+y2YdpvG2cZv7eHqT9k\nizREYSln1T8kqyHBS4RKUS47nKoWJKm+KE8aCvrL8mpVzXtmyFItGEywZZFT9llgTsbTEEkh/NHL\nYK605DcS3VEtCtvtHE+y6h+S1ZDwe6s6Lnh5YHIX5XSvbmD5b922rZfb5SpiV22hUCgoX6FAjGKz\nVAuxpJYb7E4aXm8bk8CmAz9iolpkjYiGoC52ZMty21fsqgFQGoA/SFYjQOXIatKqFjghW5cobpcH\nuX+DyquNus91G/TFlwbrFa+3jUlY0k1Yo8ypP6QLFaKwjUajnQZFeINkNaPIxI6hei6kSFJzOnmS\nOsJflSg2CQvBE3RkjdII0kuQfUV8j93AV8I7yTiTJxyVIqtMLmZnZ9uCIQ4IUxVxO7J1qVarbVHV\ndR3FYhHFYlH59QHmJLVWq6FarXakX/T19SmdtiDrR7lcDqVSCYVCQYl2M8nQdR26riOXy7Uf200D\nzE5MlmXBsiyYptl+7DQAjFAf1h9Yn8jlch19QlapAEBHf6A+kQ389hUey7Lwxhtv4E/+5E/wyCOP\n4Ec/+hEMI7j44NjYGG699VZs3boVDz/88LzXH330Ubz3ve/Fb/zGb2Dnzp04fvy468+qCEVWI0AF\nWZVFH8Ui+Cq00w38uvADj1gkNWpR8rPdVIlIesVu0FdSZvwKOu+RIm7JJ4yovOrH0LBI+3p36yvi\n+h85cgTf+MY3Op7bvHkzNm3ahI0bN2Ljxo3YtGkT1q1b5ym4YpomHnjgAYyOjmJoaAg7duzAzp07\nMTIy0n7PVVddhccffxyDg4MYGxvD/fffjyeffNLVZ1WEZDXlOMlFHGIXBEme5jWqlIUwLjxk+bQs\nt7nbtlf9QojKJxE8QZZJsiwrkxc1WVtPTdPa0XZ2Ibtx40b89V//NU6cOIHjx4/j+PHjeP311/H6\n66/j8OHD7WXcdttteOKJJ1x/5/j4ONatW4e1a9cCAHbv3o3Dhw93COe2bdvaj7du3YrTp0+7/qyK\nkKxGQBwnarsR5U5ip7JQsFtvwOVcoKRJalIjkrJ8WlaZIAnb3i+UB0vw9DJAhy5qsoemabjqqqvw\nx3/8xwCAc+fO4cEHH8SDDz6IY8eO4fjx4+2/1157radlnzlzpmPa1uHhYYyPj9u+/2tf+xruvPNO\nX59VBZLVCIlCAv1IqsrICvqzvFRV1sVJ8lm+mzi9q9uIZJzIUhWSMOgrTIIejMH3CSKZyPoEf2En\nSwugi5rsMTU1hcWLF2NkZAQjIyP43d/93fZrsunZnfDSN374wx/i61//Or73ve95/qxKkKyGBD8S\nMIrOwaSol7JHKkVWZdE8dtBPinQndXpXWapCEvJp48JvxI09JwpLFm8Zpw12rGIDdBh+c6Nlf4lk\n4TQhQD6f97SsoaEhTE5Otv89OTmJ4eHhee87fvw47r//fjz66KNYvHixp8+qhvrDpVNGGCJomiZq\ntRpqtVpbjPL5PEqlUuKiYK1WC/V6XTo6XvXb5Qw2wj/O/eF30Fez2eyorhDWCH9ZVNkuWplUnKoR\n2EEjz9ONU59wqkZAFSqST7lcxsDAQCDL2rJlC06dOoWJiQnU63WMjo5i586dHe954403sG/fPnzp\nS1/CNddc4+mzKkKR1QgIS07EyB3Q223aOCOrslvO4sAjlSK/PHy76vV6Ikf4i6kKScmnTRpiP3CK\nujk9T9G29BBUaolsOdQvosXp3DQ1NRXYVKuGYeDgwYPYs2cPTNPE3r17MTIygkOHDgEADhw4gM99\n7nO4ePEiPv3pTwOYc4OxsTHbz6qO1nLYuhcuXIiyLamDPxHNzs6i1WoFUs80rALyzWYT9XoduVwO\nxWKxpza6xcvo+EajgUajAcMwlJoFxLIsVKvVjufinpSAtUnTNPT19Tm+TzY9atCpCkzi8/l8+5YX\nL8cM1qdVz+ftlW7r2U1WZKgqsOxiCEBmLn74UeFBHgPcpJaIRNkvsriveZx+11/72tewYMEC/P7v\n/34cTUsMS5YskT5PkdWIYDlMvUQFZZIaZOQuysglk1R+Gs5u0TzVIqtRlaEKg6TOmJUV/OTBOuU8\nUrQtHVCFiuRSqVQSkRuqKiSrCSBsSY2SNNR9la0DQ6XZmwD5iSuJkxEQc/iVFRq0k16CrFDR64UN\nVbewZ2pqCoODg3E3I7GQrEaE3wEv3fI4426jW+xKOPm55RxXZNVpHer1eixtckuSo8CEM2HlPJJw\nJBeqCase5XKZZLUHSFYVJGpJDZugSjjFeZDsltupsqzKpqZldV6JdEJpBIQMSiOID6fSVUR3SFZD\nRFZr1SkqGHf0K+jIqqygf9LyIt3mdvI5yaqtGxNpTUvGZAREeFAaASHiJjLv5jkeVY+FYdLtvEmy\n2hskqxHhJIIySY27dFAvB5qwcmyjHgCW1NxOdpHAE/f0qKoNjiMuE3a0jfIYk4ffNAIe/i6U7G+a\nka3jpUuXsHDhwhhakw5IVmPEz4j4MOn1IJJkwWPEHd3uBdn2BxBIuTQiWwSZB+ulzBKhNt0ubOyC\nMfxf2XKScn7oFToO+4dkNSL4KINsNHmSb9FGlWMb9gAwWXTbbW5nEKXJ/CJru2EY7f2hYn9iM/Aw\nVGwj0UkvebAMdrcl7XmwWYom88LJ15cVj9du86NlfwmCZDUi2I+OFWvvdUR8WHjJvUxyFJLhVEpL\n9aLWrO38LX9++4sRVhVotebP8sUQBUiF3wPRHb/RNhKV9MGf12gwFxEkJKsRwKSCPQbUk1QvqJC+\nEITMBFWlIGpkJbRk21+lQV+snXwes9172GPTNOlElVBk0TZgrp+SqGSXsMqsiY9Vw7IspduXBEhW\nQ0YUIkDtEfFOt7PjTl8IavmyKgW9DkCKagBR0gSb9Rk+ksrSK5rNZsc+8HuiUnG9ifmwaFvQokL7\nP9n0kl6iUnTeKfWDBlf1DslqiNTrdWkkic2NrjLigSGogv5xkuQpRpPYdtmFmq7rKBaLtpERMafR\n7YmKBCaZBC0qSYm0Ed1JUxrB1NQUBgYGIv/eNEGyGiLsR8Gkrlqtxtyi7og/ZNUieX5ubSe5SkES\n2y4T61wu176t76bdTlE4vwKj6vYi5uNXVFSKtBHBE1QaAVtGVBc3VGO1d0hWQ4QNduEjRIDag0f4\ngWC1Wi1RkTyRKAeABZ0GEETbnVI6wsBJrE3TnHeXQfxddCNIgaEIXPJIU6SNCA4/0Xn276gubmiq\n1d4hWQ2RJEZ12I9X1UieGwGzG+GfhClGk9j2OKtCUAQu24Q1YIf2f/JR6eKGIqu9Q7IaIX5uYUcF\ni4oFPetUlNiJXhLKUAHylAuVa++6rUoQNSQw2YbyYOMhqjs4veDm2ODmObYMt/2BIqu9Q7IaAyr9\nqGW3boG5yFihUIipVd0Rt2HcubW9pAGI1Qnizgt2Q7c2q9THAbnAkMBmC4rCR0eStkmQaQT8a5Zl\ntS/aK5UKVq5cGWi7swbJaoSodBK3u3WraZqSxeQZ4kFQVoYqKbm1rVZrXsWIINsedB4tW1a3Njdr\ndZw++XOc+P7TuHTubdx453uxZvMG5AcXKNP/geAicCQvySWsKDyRfPxc3LDnWq0W9u3bh9deew2b\nNm1Cf38/pqence7cOaxYsaKndo2NjeGhhx6CaZq49957cd9993W8/vLLL+NTn/oUjh49ioceegif\n+tSn2q9t3rwZAwMD7TStsbGxntoSJVrL4exx4cKFKNuSSvicPTZgqVAowDDiuU7odqu82WyiXq8j\nl8uhWCzG0kYn2DbM5/OwLEuZAWCNRgONRgOGYXSNSDsNRAqy7UH2N9nFjazNrVYLr/x/P8P//Mz/\nBXCHluveuw07/o+PobRoAKVSCQDmlbUCLk8aoFrqg5uTlIjTLWRV17NXWpaFxpnXcOmlI2iWL2DB\n9TehuPZaaP0D0DRN2bxrNwTdB9IGiyYCSETaVZDw687YunUrTp8+Pe+9K1euxMaNG3HTTTdh06ZN\n+MAHPuA6n9U0TWzbtg2jo6MYGhrCjh078Mgjj2BkZKT9nvPnz+P111/HE088gUWLFnXI6i233IKn\nnnoKS5Ys8bmm4WPXNoqsZgSZpMpyIsOIxoVBN2mKGjfbLc6BSH6R9RunNk+/fQFj//dXO0QVAF75\n4U+xZc9dGL7p8kE1SSfusCoRpI3qqy/ijf/3fwDWnIxPjf8QCze9B8t/+w+g9S2IuXW9QWkEhB38\nPmTn0x/96Ed46aWXcOzYMXznO99BuVzGK6+8grNnz+Ls2bP4j//4DwDAj3/8Y9eyOj4+jnXr1mHt\n2rUAgN27d+Pw4cMdsrps2TIsW7YM3//+96XLUP3cbgfJasjwg6niEEHZIJgk5ESKMNETa3eqLHqM\npA78Mk1zXr9hM33ZMVu+hPLZt6SvTZ9P152aIOSFn4Yx6fJizU7j3BPfbIsqo3L0Z1j8nttRvHrE\n5pPJRbbP+OllZalflEqSDfr6+nDLLbfglltuwQ9+8AN8+ctfxvLlyzExMYFjx47h6NGjOHnyJK69\n9lrXyzxz5gxWr17d/vfw8DDGx8ddf17TNNx9993I5XLYv38/9u/f72md4oRkNUKillU/g45Ui6zK\nRA+AsmkKInEO/PK7L8Wi/l7aXFy4AAuuWILpt+eLaf+S7qNhVa6Y4YYsVyKwZi6hfm5S+lrjwvlU\nyqoMXlDZhXRW+kBW6XaMrVQqWLRoEXRdx9VXX42rr74av/3bv+35e3rtA4cPH8aqVatw/vx57N69\nG+vXr8f27dt7WmZUqB2SInzBCvrXarW2JOXzeZRKpUQMPAIuR1Kr1Wo7uqdpWjuqp9o6iGKYxH3A\nBk9Vq9W2qHpt88Dypbjjvj+c9/zad23C0qvXBN7mJMBu/bOcTT4ybZcWwITGsqx2bjZ77DQKOU60\nYgnGgPx2prEw22V7ZH0gl8tB1/X2bWOxH8j6AOsH7DUV+0HWkf2ea7VaO1e/F4aGhjA5efmCcHJy\nEsPDw64/v2rVKgBzqQK7du3yFJWNG5LVCAk7askEiZcNwzDQ19fnOqdThciqaZqo1WodklooFFAq\nlaSRCpWQCZ/XfRA1bMDX7Oxse9BXLpfz1WZN03Ddr78Hv/c//iuu/Y33YNWN1+HOT/8xfuv//N9R\nHFwY1iokll7lRSWBzS1chGW/uWfe88UVwyisujKGFqkPL7CsHzj1AQAdfUDFfkCEx5YtW3Dq1ClM\nTEygXq9jdHQUO3fulL5X7AczMzOoVCoAgOnpaTz11FPYsGFD6G0OCkoDiIGgDyZhjS6P+lasbE55\ncYS/irIHdN7G44VP5Zxau1zaXmfLKvSVcPV7NmPtuzbBMk0YhQJarRaq1SqdSLvgNQ/WLjc2rlHo\nCza8C6uLfXj7h4dhTpcxePOtGNi8HdpCmr3HLX5zocXno04j4PN0iXAwDAMHDx7Enj17YJom9u7d\ni5GRERw6dAgAcODAAZw9exY7duxApVKBruv48pe/jGeeeQbnz5/Hvn37AMzNUHnPPffgjjvuiHFt\nvEGlq0KGP2mwiKGu64HcEpBJahCCNDMzA2AuQTyKA49MUu1kW7XSWkz46vV6+zlVpket1+toNpvS\nctwRsMUAACAASURBVFpRz5ZlWRaq1So0TUNfXx8AzBswx97HLpLi3n5h0mvpKr9llGR/w6DVqKPV\nbEDvW5CZfcqIqoRTtzxYGWH2gaztZ55u+/zuu+/Gd7/73aiblUiodJUCBHWLPYklkGT4iQirkKbA\nEIWPUSwWlYguyNrgJnpNqI/q0TctX4CWdz8DntWsolm/BC2Xh1EYpL7oArvIeZIi8VmgXq/HVlc9\nTdAWTBBRlUAKe0R20mVbNtUom1DBLs8sbsJKFSHUIamVCGanJjBz8ZewrLm+Wey7AguXrYdu9IX6\nvWkliJJqsuXQccIepxSIcrmMwcFsDzAMApLVkOGFz29UUCapYd+2DYMgZDvOyCobPCWLSgJzt7VV\niPiKWJaF2dnZ9r+TdGFA9EZQ0bdexMXpRF6fOY9L77zC3oiW1UBt+i1Az2FwxSbX30E4o3okPs2U\ny2XXRf8Je0hWY8JN1JLlwURd0J+PrAaB3XokRbbdRCVVk1Q+h4r9TcJEBEQ0hDGQy8/vuD5zHgBg\nzl5E9cIkzGoZmlFAY8mV6F90NYwiVZAIC7v95vdCRrVjoCpMTU1RZDUASFYjxMvBPM5i8kGS5PVI\narqCmKYAoD3zVFzbnE5o6hPk7WO3/azVMmFWK7h0+gRav0oDgNnA9JsvobbyZhgrk1Nah5H0UfF+\nL2T4f5umSVHYX8EmBCB6g2Q1Yrrlg6owACYIsQhrPaKQnl7TFaIu+cWQbXNgru2qJfizyG/ST+xp\nJyiBFd/HlpcvLUbj0vnLovor8v1LMX32FPqXXQ8tlw9gTYheoDQC/0xNTWFgYCDuZiQetc5gGcZL\n+SaViXIgTxhS6DcSHOc+kkWA2UVBo9FQrv+wUl+yiJyXUkxEPPgZyCV7XtM0GKXlyBcHUeXepxtF\n9C1YBas6BatZQ45kVUnEfsBPz2yXSpZFga1UKli8eHHczUg8JKsRI/6IVRyl7Sd6KVuPMG6Zh7VN\nVIhoe0UWAea3OdsXqolfrVaTPi+2k24lJgfZQC62P8XSboxWqwVNz2HBkvWw6k1YZhWabsDQizCr\n0ygsXA49TxUBkgaT1SyV0+pWDeCaa66Jukmpg2Q1YlhnZtPkhS13veBGcpKa18kI8mIh7JJfPGJ0\nUpamoMrBnW1jHrZ9+e1OkZh0Ie4XNphS3KfFpWsxc+7naJk1wDTRxAyg6egf3gCrBWjcXQ7Zcgn1\nyXI5LSpdFQwkqxHAywv78aksd24OAEGUoeqlfb1KYVIlW4wAqzxgTbaNgcszo/GRU2BuXfg8Vl3X\nSWBTiLiPCguWYOmNH0D17VdRu3gGRt8gSsvWIT+wCkA6Im/EfLKSB0ulq4KBZDUimNzxt8RULyVk\nF1kVo3oqC5OInWSrMD2qE7IIsMppCrLIr3g7WDzxiOLhdCsxDScx4jL5/sXI92/BwJVb2s8FUYmA\n9nmy8JMPrfpvnyKrwUCyGjJMjsSC8bquKzMtp4hdm2QzNyVFUgG5ZLOSTkFgN6igF+wGT6k68M6p\nj7CJCSzLarc9l8u1t5mYyy1GzrtFYpJ2EiOcyfKtY+IydhcfScmDLZfLNMAqAEhWI4CJhqZp0HUd\npmkqXQxfNkBCpcFHXqUwiZIdRATYz0A5v3iJ/NZqtY7IKUsJ4NvJ7xvxJORFYGWfF58jmUkOaYy8\npYE4BnGqcjHTbd3L5TKVrgoAktWQYWKkaXPzx5umOe/ErCqt1tz0oipVKvCCapLtFln5rCAjwEHi\nJvLL1oP1f/Y5u98Au5CTpQHYCSgJbHZxE3kjgY2OOLdb3Hmwsve1Wi0lj91Jg2Q1AlSXIzuYiABq\nDT7qFjGURfmikOxeI5kyuY575iknZHmpYuSXDZhiB2x221/M3+axLKtD1GX/MeyEhASWoH1OABSN\nTwskqxET5a1Zr8iiZEkYfMSQtV8lybYjLrn2i5u0CvaabFCVKKriLX/ZfzwyeeX3b5QCy7dHXBah\nHmHsc3F5hPoEmQfLIx5jiOBQ9wyeUlSUVSZ51Wp1XpmhUqmknOiJ21DWfjaArVgsKtd+BpPU2dnZ\njgh2qVRCoVDo+aAXdF9jaSHVarUtm/l8HqVSqX33gEVFW61Wh5DyFxLseb4ahq7r0HUduVyuLeos\nZYO9zq8PX6e40Wi001X4FBu2PP4/cZvaSQjfHvZYFBR+GWy9WZoPH1Em1KbXfc72O9/32XKJZOGn\nL/BYloVf/vKXePDBB/GNb3wDR44cCez8MzY2hltvvRVbt27Fww8/PO/1l19+Gb/5m7+JoaEhfOEL\nX/D02SRAkdWMYze9aL1ej7ll7vA7PWoYuJVDu8FTqpYx85KXKotmspM5g50Euu0f2cnBKfIqSysQ\n81/FE4csettrBFa2HezWh1CTXnIfGXzVC4q8J5d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MDQ21XwOAZcuWYdeuXRgfH0+krKp3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\nhBBCCCGSRcEqIYQQQgiRrP8PqxW8nlVVxqcAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x109bc15d0>"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What we'd like to do \n",
"\n",
"1. Find a 1-dimensional representation of each book's color, that way it can be sorted.\n",
"2. Determine some ordering. Consider the following made-up example: An ordering that sorts based on the amount of blue in a set of books that are only mostly green and red book would be very poor, as the human eye would have difficult time seeing the amount of blue vary over the ordering. Instead, what we want is colors that are distant in 3-D to be very distant in 1-D too, similarly for close colours: colours close in 3-space, and appear visally similar, should be close in 1 space too . Thus, I would like an ordering that maximizes the amount of variation when we project to 1-D.\n",
"\n",
"This is exactly what PCA does. So let's do that: "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sklearn.decomposition import PCA\n",
"pca = PCA(n_components=1) \n",
"# I'm setting n_components to 1 as we are projecting down to only 1 dimension"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 36
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"one_d_colours = pca.fit_transform(colours)[:,0]\n",
"print one_d_colours.shape\n",
"print one_d_colours"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(22,)\n",
"[-0.1251 -0.3963 -0.2339 0.356 0.1311 -0.2228 0.019 0.3082 0.2474\n",
" -0.2516 0.3639 0.2567 0.3946 0.0051 0.14 -0.2195 -0.0403 -0.0827\n",
" -0.1949 -0.0188 -0.2855 -0.1504]\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ix = np.argsort(one_d_colours)\n",
"#what I want is the sorted order of elements in 1-dimension, and I'll use that in\n",
"# ordering the colours."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 38
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"display_colours(colours[ix])\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAuMAAAB+CAYAAACOGh8QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10c077a90>"
]
}
],
"prompt_number": 39
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Let's try (sorta) random colors\n",
"\n",
"So that worked well, but let's try some more diverse colors.\n",
"Below I'll generate 60 random colours from a subset of the unit cube. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = 60\n",
"colours = np.random.uniform([0.15,0.1,0.5], [.9,0.5,0.7], size=(N,3))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 40
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#here are the colours, unsorted\n",
"display_colours(colours)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAuMAAAB+CAYAAACOGh8QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text": [
"<matplotlib.figure.Figure at 0x109bddf50>"
]
}
],
"prompt_number": 41
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figsize(12,8)\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(colours[:,0], colours[:,1], colours[:,2],\n",
" c =colours, s=50 )\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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whz/ED3/4w5pz/eM//iMeffRRx9eenZ3Fli1bsHHjRgDAoUOHcOzYMVuxevToURw6dKhm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\nsvU/DwNaowMR6AkAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x108bee4d0>"
]
}
],
"prompt_number": 42
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"one_d_colours = pca.fit_transform(colours)[:,0]\n",
"\n",
"ix = np.argsort(one_d_colours)\n",
"\n",
"display_colours(colours[ix])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAuMAAAB+CAYAAACOGh8QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text": [
"<matplotlib.figure.Figure at 0x109ba9110>"
]
}
],
"prompt_number": 43
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This looks pretty good to me, I'd grade it an 80%. There are some oddities, but considering what is means to \"sort colors\", I'd say it did a pretty decent job. \n",
"\n",
"\n",
"## Conclusion\n",
"\n",
"Recall that this method of sorting is completely unsupervised: there is no \"better\" or \"larger\" colour. PCA is finding the line in 3-space that maximizes the data variance in 1-space. This line also happens to be what we wanted: we wanted different colors in 3-space to be maximally different in 1-space too. \n",
"\n",
"I chose rgb space. Though this way arbitrary. You could also use other color schemes: HSV, HSL, or CMYK. HSV might even produce better results, as it was designed to be more intuitive and perceptually relevant than RGB. Interestingly, CMYK colors would live in 4 dimensions originally, not 3 like RGB. \n",
"\n",
"\n",
"On sorting colors: There is acutally a better way to sort colours using the travelling salesman problem, but I'll explain that in another lecture. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 43
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 43
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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