data-science-ipython-notebooks/scikit-learn/scikit-learn-pca.ipynb
2015-05-31 10:06:35 -04:00

283 lines
84 KiB
Python

{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# scikit-learn-pca"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Credits: Forked from [PyCon 2015 Scikit-learn Tutorial](https://github.com/jakevdp/sklearn_pycon2015) by Jake VanderPlas"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Dimensionality Reduction: PCA"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Reduced dataset shape:', (150, 2))\n",
"Meaning of the 2 components:\n",
"0.362 x sepal length (cm) + -0.082 x sepal width (cm) + 0.857 x petal length (cm) + 0.359 x petal width (cm)\n",
"-0.657 x sepal length (cm) + -0.730 x sepal width (cm) + 0.176 x petal length (cm) + 0.075 x petal width (cm)\n"
]
},
{
"data": {
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Yu5+jX3/Lsb17aXcxGxeTSkK/Njz/xXzc3NzsEb2wgp49rVOp62fHju1i0mTL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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c246f90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn; \n",
"from sklearn import neighbors, datasets\n",
"\n",
"import pylab as pl\n",
"\n",
"seaborn.set()\n",
"\n",
"iris = datasets.load_iris()\n",
"\n",
"X, y = iris.data, iris.target\n",
"from sklearn.decomposition import PCA\n",
"pca = PCA(n_components=2)\n",
"pca.fit(X)\n",
"X_reduced = pca.transform(X)\n",
"print(\"Reduced dataset shape:\", X_reduced.shape)\n",
"\n",
"import pylab as pl\n",
"pl.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y,\n",
" cmap='RdYlBu')\n",
"\n",
"print(\"Meaning of the 2 components:\")\n",
"for component in pca.components_:\n",
" print(\" + \".join(\"%.3f x %s\" % (value, name)\n",
" for value, name in zip(component,\n",
" iris.feature_names)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Dimensionality Reduction: Principal Component Analysis in-depth\n",
"\n",
"Here we'll explore **Principal Component Analysis**, which is an extremely useful linear dimensionality reduction technique. Principal Component Analysis is a very powerful unsupervised method for *dimensionality reduction* in data. Look for directions in the data with the most variance.\n",
"\n",
"Useful to explore data, visualize data and relationships.\n",
"\n",
"It's easiest to visualize by looking at a two-dimensional dataset:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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poLX2t9UPl49VcM2m4qzlDIwxd6tfGjW16HnLvF3Semvt6yT9qaS7PLen1owx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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c39ddd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(1)\n",
"X = np.dot(np.random.random(size=(2, 2)), np.random.normal(size=(2, 200))).T\n",
"plt.plot(X[:, 0], X[:, 1], 'o')\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that there is a definite trend in the data. What PCA seeks to do is to find the **Principal Axes** in the data, and explain how important those axes are in describing the data distribution:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 0.75871884 0.01838551]\n",
"[[ 0.94446029 0.32862557]\n",
" [ 0.32862557 -0.94446029]]\n"
]
}
],
"source": [
"from sklearn.decomposition import PCA\n",
"pca = PCA(n_components=2)\n",
"pca.fit(X)\n",
"print(pca.explained_variance_)\n",
"print(pca.components_)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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4g1og+3xerFjSij/5D+9nHG+xObB41cNYfu8ObHhgC0ZDKcTiKYwFYwhFEwhF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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c47f490>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X[:, 0], X[:, 1], 'o', alpha=0.5)\n",
"for length, vector in zip(pca.explained_variance_ratio_, pca.components_):\n",
" v = vector * 3 * np.sqrt(length)\n",
" plt.plot([0, v[0]], [0, v[1]], '-k', lw=3)\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that one vector is longer than the other. In a sense, this tells us that that direction in the data is somehow more \"important\" than the other direction.\n",
"The explained variance quantifies this measure of \"importance\" in direction.\n",
"\n",
"Another way to think of it is that the second principal component could be **completely ignored** without much loss of information! Let's see what our data look like if we only keep 95% of the variance:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(200, 2)\n",
"(200, 1)\n"
]
}
],
"source": [
"clf = PCA(0.95) # keep 95% of variance\n",
"X_trans = clf.fit_transform(X)\n",
"print(X.shape)\n",
"print(X_trans.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Isomap: manifold learning, good when PCA doesn't work like in a loop. Large number of datasets, can use randomized PCA."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By specifying that we want to throw away 5% of the variance, the data is now compressed by a factor of 50%! Let's see what the data look like after this compression:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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oI5VQUbE9VOpWhLlBAMfzuzqJiGg3YAATVS2VHczmyxAC0FUZ2QEdiiIhm26c\n14x6s9Hq6bVKFE7nSvjuyTksLtmYWbChKoB58Qg+ec8E7v9GGksFBUEQDjHrumh57F90pN/QkIuF\nvAYRhCuXE6kAv/nu87jsUgWDA0PIL4Upvnc0vDmIeqfzizY0TcaRvZlam23XRzqh4dJ9Qw1z2M0W\nmTWrwvXsy8bwr49NA354LRRFqt2UtBqGjmP/NVE/YQATYXmBkaErqNgeHM9HfsnBpQcGUa54SCUa\ne3Jj1V7mej3fR0/mUCy5+NM/2I+HvjWEclFFEDRfwew4red3FQV4761n8Q9fHoEsBXj1r57HvgNh\n2BqqggN79gAAMqnlG4aTF4qYni/D9X0EAtCEjMUlFxcdDPfsNlsQtd4is2YrmEcyRu0owJHM8tz4\nXL4CPwi/qZUBy7N2iRjARACWFxgd2ZvB48/kEfgC6aSKwpKD6y7fs7r+8kXr9+ze/e4EvvG1S1Fa\n0tp6/+hUIknCqiCW5fDPnb+Xw4//uIr//NIcAMD1ZOQKElRJbrpoCgiDzRcBZFnCUEqHqsjwRICZ\nhXJDUDe7FvXqF1atDOxMSq+tgo7kCw6SSbU2SrAyYHnWLhEDmKiBpiqY3D+IXMFGvuBgqezhXx49\nD0kCEpqK0cG197hOTRn40l8rWJgf6OjQA1kOA1iWAdcN/37ZpIc9Ez7e/s7F6rm6eu1mQFMV7B9d\nHYj1/EBgJJNofMwXmF+0gX0bb2MzzYamhzLGqgInDFiiRgxg2vWmcyXMLVYaKlVpsgxIAgNJFYEQ\nyC85CPwKliouBAQu3rNc5WZqysBnPqM1VKbaKFkGEgmBa64JkK5WdDxxwsbkZLQiezn0Vw4DrzeX\nmtSVhqLtQBiQwyu2UdXr5BzclW1a62jEbt6DaKdhANO21c4inlbPieYiR7IGLuSC2hYjzxPIpHQI\nEe7bdasriBcKNlRVggQJH/vICD77l3pX5R8lCUilBRIGMDkZ4M4760O3ufp521ZzqQcvymIuV2ro\nne4bS68bdJ2cg7tyLrlVwPKsXSIGMG1TzYLn4R/MIp1QoakKErpSe7z+OWcuLEFA1OZc64tqDGUN\nLCyGJ/tI1eHTfNHBzHzYm7vzPVfj/DPJ3pypKwGKImBeaeMDtxbwoud11vNrNZe6b3wAp4cSmF0I\n7xLGhhJrrtiuv1HptlxkOwHLkpS02zGAqW9sZFvKyuDJ5SuouD4qroeJ4RTKjocLuTKGsgb0ugVC\nF+ZLcIM6MPYvAAAUi0lEQVSgtlXGdj1cyAW150XFMfJLDmYXy7jpZVdB9PiQzYFMgENHbLzvdwo4\nfCS8QThzwe9qBfDcYgVOtZeuawomhpav3f7xAejVgiHNgq7ZzYw7H3S9IrlVwLIkJe12DGDqC91u\nS7HdAPmigyAIEAQCuqbAF8HyYQd1z5PrXk7XFNiOj4VFG4oqwXF9/NefuQTFpd5vhUmlA3zgg3M4\nes0CFEluWglro4GU0BWcmV2CXXdD4nuiVggDaB10m7UimQFLtD4GMPWFjYbAyjnGqL5yNh3O29qO\nj6Wyi7TRuA1IUSQMZ5a334xmE5ieL2GhYOM9b74MT59sfZhAO3Q9gOPIkBWB1/zaWfzcL5Rrve4L\nOblWCatbEyMpnDq/fDScKi8H+8x8GQf2Nd+e1I65xbX38RJR9xjA1FK/ViyKSjwamgxZljCSbtxu\nM5Q2ENRN2KqyjEMTmYbgvuO2QTz6nXFY39Nq88KdiKpUDQwEeOfxC3j2cwqQpfATp84VcG5OhuP4\nyKYMHLoo09MVwMNZI9xWBHQU7M0WTOWXHKQSypr7eImoewxgWtdWVSzayLaUszNLKDsehjM6cgUb\nbhAgbajhgQLVJIx6gkEgoMrhHHDU5mhx0LFXjuOZMypcV+o4fBUFyGQDHLnEwxvfPo09eyuYX7Th\nejpURcJS2cHYUBLlioelsoeJ0TRcLxwml+XltnYzVJtN6dBWFMLYSKA33cc7wH28RJuNAUzr2qqK\nRRvZllKyw6BeLLkIqkOkFc9DQlNqYTuUNcIQGg1Dd2rKwEMPKThzRoIQaQSBwOKiDF1Hx+GbHhD4\nb7ecw403+tBUBefmKhAC8EWAQtHBcNZAxfEgSxJGsgmosgxdlRu+R6D7FcC92NKz0X28RNQ9BjBt\niXaGsTeyLWVusdKw8Cipq1gquji8PwVdlRtCaGrKwIMPhuFbKoW9TtsOe722vbHv4xd+eRbHbpqv\n9bDPzZaQKwATwynklxw4no+lchi69cUuVLlx3ldXe7tAqdstPRvdx0tE3WMA07p68Yu43WHsdlfN\npgy1tuWmvk37JwZQWHLwyXsuwje+lkSpJCGdDnvI+/eLWvgCy/WW6w+9b7a/V5bDed0PfGgel1yZ\ngxCNYVq2XZRtH/N5G4WyA0NTMJjS4QUBcosVqIqMwZTRsOJ5M4Ks1yuOWSiDaPMxgGldvfhF3Oth\n7H3jA1Ck8FCBqE1ve8PB2nwuAOjVxczFogTbBkql8LShaLGULK8duLIMfPrTZdxwQ9ju6PufW1Tg\ne6IWprl8BemUBl1XkFuswNAUlCoe9o2H31Ox7GLPUHJVT3i7BBkLZRBtLgYwtdSPv4j3jqVwbraE\nN73uYpx6avXWoXIZ0DRAVcPQrVTCBVOqCgghkEg2zv1qqsDlVwTQjQBve0ceh494mM6FQ+XR9z8x\nlILjLd9MeIHAxHAKrudjYSkcy94zkkSx7GI0m8BFoymkdLUvr187uI+XaHMxgKmljfwibjbXuxnz\niRfvyeC/vHwcZ55e+0fYdcPA1XXAcYBEdZdSIICLD3pIJARSqbAbfPM78xgeL2FwIAxzgcah8uj7\nP32hgHPVBUpRD1pTFewdTdfmpAcS4fxw9D0yyIioGQYw9cx6c73ufNDxMHa0ghkArr3Wxyc/GT5+\n9hm1rRXMqgocPeojWc37iuMjlRK4+Z35WilIALgwv/5Q+XSuBD8Q2DO8PAT9/acXkDRUqIqMpZKL\noQGjtgJbU+XaauJ+2j9NRP2BAUw9s95cbyfDsFNTBr78ZRXFooRUSuDAAYEHH1Tw0pcCt9wit/x6\nTRNQVOD66wPce2+59vjKGwUgvCkYyaxfxKLZ9+f4Ppyij5FsAqmkCkWWoMoSBMSW7J8mou2LAUxb\nop1h2LfcrOCRh8MfSdeRkE7JKBbDVVOlkoQnn5Swb1+ACxeA48cNHDoU4PHHZQRB44IqWQbMy12c\nO6fgyCUeTpxoDNu1FpY9+tQcZvJhUEfnAquyDAGBU+cLODdXhK7KGBkMx7JtN0A2pWOp4kJRJIxn\nEtDUcC9yVMKxHgtZEFE9BvA21Y/lITuZ642Gl089DUAAE3urK49PK1DUcKFUtV4FPA84e1bG0aPh\nx/ffX8IVV6QxPx+GtBDhcPNH7prDC15o196/WeA1O9Q+ndRQLHvwgvBc4LmFCvaMJGthqmkyKo5f\nO2UJAAxdwd7RFDSVvVoi2hgG8Da0VeUhN6rdLUtR6H7vezI8L1yt7DjhkPHpp1VMTIQh7HuA7y8H\ncGTPHuCWW8KAvfvuCn7jNxJYWpIwabr4wAfna/O664X/yh55dDNTOxMYQGZAx7m5Um3ONzq4YS5f\nwcxCGboW9obrwzd6z4WC3fJmpB9vooho6zCAt6GtKg/ZiVZzvfVVqaIqVNEQsuNIUIXA9LSCZFKg\nXJZgJARkSYLnhb3bq67y8bd/q2JmJgz5G27w8f3vFwGgJ4Uj6s8EbkoI5Is2ggC4eM8A5hYq8PwA\nIxkDSV2rvWerm5F+vYkioq3TeiUL0QZEPcsDewaaBkm0mrlYXH5MiOU/XrWQxsReH8mkwL59Afbt\nC5BKCVx/vY8771y7duT4cLj1p5MtTgl9dVtVWcbe0cZe6XzBQSap48CeASiKhIShIpe3MZe3V73n\neu1Z7yaKiHYHBvA2tFZY9EuRh6kpA1demcahQwO48so0pqaary6uH1qW5WqVKgmYmPAxOhrgb/6m\ngoMXAwcOCNx3Xxn33lvG5OTa+44WCjb8QMAPBBYKGyvyPDGSqh2OACz3WC/ek6k9PrdYwexCeEZu\nqeyGz1MkDA7o0BR51Q1Hq5sRItrdOAS9DfVrnd5o21C0KErXw1KQn/+8hscek3HnnTauvdbHgw+G\nQ8xAOOwMAKomYBgChw47GByUcOutDiYnpYbtQ+vpxZDuWsPn48NJfO/kPHxPYChjIAgCOJ6P+UUb\nmbQOQ5cbyk22g4cdEBEDeJvqh/KG9QUyKhXAMMLAjYpj2Ha4wMrzgEcfVXD8uIF77y3j2LEkXE/g\n1CkFhiwgy+ECrE98eg7XX6dXA1Na+42b6MW8+FpbpQxNwVAmPB9XUSWcmy0iCAT8IECx7OKSvaO1\nldTtLqrq15soIto6DOBtKu7yhtFiqsipU3K1zvLyc4QIy0EaKzqHJ07YOH7cgJFwIQSQSgm8412L\neOHz+r/3N5pNoGx7tSFuWQb8QODRp3IQEBjNhnuE2+mB98NNFBHFhwFMHYl6vvW8um1D9SUio9XL\nJ06EoTU5GVamsl2/ZwG02UO69a8/MZyEpoalJ/eOpiAgYDs+BASm50sYyRjQVKVlDzzumygiihcD\nuEvcyxlKpcLzdqMDD6JVzokEcP31ftO53E4D6OzMEs6eL4SvX73mmz2kW//6mqpg/+gA/GEBgcaK\nV74vkCvYmBjenT8HRNQ+roLuQrTwR1T/i4YdbXf1fOR20O7qZSA8FKHegQPhyULRtqFsVmB4WOCa\na5Z7vr0wnSuhVGl+zbvZhtSO9V7f0Fb/U+KiKiJaDwO4CztpL+fUlIH77lNrtZej1cs/+7NJPP74\n6h+T22+3MTa23PsbGwu3Ch04EB6a8JWvlPHYY0Xcd9/6W4dWms6VcOp8AafOFzCdK636/HrXfLO3\n/ax8/frtYCODYd1oRZEwkjFqPXBuPyKitTCACUA4p1sqNa48rl+93MyJE2EIj40JnDhh1+Z2W+3X\nXct2G1FYuXd4bCiB/aMDSOoae75E1BLngLuwlXs5+3GuOQrclTptaztbifqtCEnDSuZRlpEkovax\nB9yFtaon9fqX8Fb0DK+9Njykvt7K1cv90NaJkRRUdfOvebtY7YqIOsUA7tJmL/wBtmau+fbbbfzQ\nDwVQq2MiqhquXt7oHG6ztl6YL+HhH8yuOa8babd3e9FoatOvORHRZmMAd6nfekBTUwZuvDGFG29M\nrbuKuZkTJ2xcdVXYE95oz3ctuXwFFddvq0fc7ohCQlf76poTEXWCAbwNtNszjKpTRScLPfiggmPH\nmq9ibmZyMsB994Wrl//4U3PQM/mWvdZWbbXdoLYyOLJe730rRhSIiPoBA3gbqO8Z3nHbIG46No7X\nv3oPjt/SuLipWXWq2VlpzVXMa+lmHndlL1ZRJEwMpxoOrV9Pv40oEBFtFgbwNjE+nMRHPjiER7+j\nQ1Hkjnq47ep2zrm+F7vyPF2ABSqIiAAG8LZhaAoe/14CuqZAlpb369b3cFdWpwJQ26O7lep7sfXn\n6QLxr1omIuoXDOA+080iqmbVqTopitHrvbac1yUiWo0B3Efe9Casu4iqnR7uyupUnej1/mbO6xIR\nrSYJIVo/q3tiZqawFe+zrb30pRm4TRY6RT1ZADh2LInZWWnV47228qjAfgrO8fEM+PPUHl6r9vA6\ntY/Xqj3j4xmp1XPYA95metHDbQd7rUREm4u1oPvI9dcDDzzQ+NjKoF2r/jIREW0vDOBNMjVl1Pbl\nXnutj9tvb91b/fjHgRtuEFsyxNyufjwEgohoJ+AQ9CbopiLVVg0xt2O7HQ9IRLSdsAe8CdarSNWq\nR9tPQ8ztHA9IRESdYQ+YiIgoBgzgTdAvFam61euCHEREtIwBvAl6VZEqbr0uyEFERMt2ZQBP50o4\ndb6w4aP2NqIXi6m2op2tsIwkEdHm2HWLsKKVvZFoZW+vqz11u5hqq9rZSlSQg4iIemvX9YC7PWpv\nq2yXdhIRUWd2XQ84csdtg3j0uzoA4KqrHbznt1nblIiIts6u6wEndAV33DaI735HrxXKePQ7Ot7x\n1rGeH2zfDa5AJiLa2foncbbIxEgK/17t+QKABEDXFOTm5NrB9v2AK5CJiHa2XRfAAKCqMiSE4auq\n/XsJuAKZiGjn2pVzwNf9cIAHH2zsSfZjoQyuQCYi2rn6t/u3iXZKoQwiItq+dmUAA/116hAREe0+\nu3IIGuivU4eIiGj36aoHbJrmK0zT/LNeNYaIiGi36LgHbJrmXQBuBPBQ75pDRES0O3TTA34AwBsR\n7uYhIiKiDWjZAzZN81cA3Lzi4Zssy/qsaZo/uimtIiIi2uEkIUTrZ62hGsC/ZlnWsRZP7fxNiIiI\ntp+Wo8Nbtgp6ZoaHHbQyPp7hdWoDr1P7eK3aw+vUPl6r9oyPZ1o+p9t9wALs3RIREW1YVz1gy7L+\nCcA/9agtREREu8aurYRFREQUJwYwERFRDBjAREREMWAAExERxYABTEREFAMGMBERUQwYwERERDFg\nABMREcWAAUxERBQDBjAREVEMGMBEREQxYAATERHFgAFMREQUAwYwERFRDBjAREREMWAAExERxYAB\nTEREFAMGMBERUQwYwERERDFgABMREcWAAUxERBQDBjAREVEMGMBEREQxYAATERHFgAFMREQUAwYw\nERFRDBjAREREMWAAExERxYABTEREFAMGMBERUQwYwERERDFgABMREcWAAUxERBQDBjAREVEMGMBE\nREQxYAATERHFgAFMREQUAwYwERFRDBjAREREMWAAExERxYABTEREFAMGMBERUQwYwERERDFgABMR\nEcWAAUxERBQDBjAREVEMGMBEREQxYAATERHFgAFMREQUAwYwERFRDBjAREREMWAAExERxYABTERE\nFAMGMBERUQwYwERERDFgABMREcWAAUxERBQDBjAREVEMGMBEREQxYAATERHFgAFMREQUAwYwERFR\nDBjAREREMWAAExERxYABTEREFAMGMBERUQzUjX6BaZqDAP4ngAwAHcDbLcv6l143jIiIaCfrpAf8\nmwC+ZlnWjwK4CcDHe9kgIiKi3WDDPWAAHwVgV/+uASj3rjlERES7w7oBbJrmrwC4ecXDN1mW9W+m\naV4E4E8BvG2zGkdERLRTSUKIDX+RaZrPAnAvgHdYlvUPbXzJxt+EiIho+5JaPaGTRVhXAvgcgJ+3\nLOs77X7dzExho2+164yPZ3id2sDr1D5eq/bwOrWP16o94+OZls/pZA74gwhXP/+eaZoAsGBZ1is6\neB0iIqJda8MBbFnWyzejIURERLsJC3EQERHFoKNFWERERNQd9oCJiIhiwAAmIiKKAQOYiIgoBgxg\nIiKiGDCAiYiIYsAAJiIiikEnlbA2xDTNNIA/BzAEwAHwWsuyzm72+25HPGt540zTfAWAn7Ms65fi\nbku/ME1TBnAPgGsQnlz2Bsuynoi3Vf3NNM3nAviwZVk/Fndb+pFpmhqATwI4BMAAcKtlWV+Ot1X9\nyTRNBcAfAziK8ByEX7cs69Fmz92KHvAbAPw/y7JejDBc3rUF77ld8azlDTBN8y6EpVFbFj3fZV4O\nQLcs6/kAfgvAnTG3p6+ZpvkuhL8wjbjb0sd+CcCMZVkvAvCTAH4/5vb0s58GEFiW9SMAbgFw21pP\n3PQAtiwr+iUJhHdP85v9ntvYRwH8UfXvPGu5tQcAvBEM4JVeAODvAcCyrG8BeE68zel7PwDwSvDn\naD2fA3C8+ncZgBdjW/qaZVl/DeDXqh8exjqZ19Mh6BbnB38dwNUAbuzle25XPGu5fetcq8+apvmj\nMTSp32UBLNZ97JumKVuWFcTVoH5mWdZfmaZ5OO529DPLsooAYJpmBmEYvzfeFvU3y7J80zQ/BeAV\nAH5uref1NIAty/oEgE+s8bmXmOHxSV8BcFkv33c7WutarThr+X9vecP60Ho/V9TUIsJ1BBGGL3XN\nNM2LAfwVgI9blvUXcben31mWdZNpmlMAvmWa5hWWZa0a0dz0IWjTNN9tmuZrqh8WwaGLNdWdtXzM\nsqx/iLs9tG09AOClAGCa5vMAPBJvc2i7M01zAsBXAbzLsqxPxdycvmaa5mtM03x39cMygKD6Z5VN\nXwWNsOfyadM0Xw9AAfC6LXjP7YpnLW+cqP6hZV8E8BOmaT5Q/Zj/5trDn6O1vQfAIIDjpmlGc8E/\nZVlWJcY29avPA/iUaZr/hHAtz9ssy7KbPZGnIREREcWAhTiIiIhiwAAmIiKKAQOYiIgoBgxgIiKi\nGDCAiYiIYsAAJiIiigEDmIiIKAYMYCIiohj8f6zjCn+s2+V1AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c87da50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X_new = clf.inverse_transform(X_trans)\n",
"plt.plot(X[:, 0], X[:, 1], 'o', alpha=0.2)\n",
"plt.plot(X_new[:, 0], X_new[:, 1], 'ob', alpha=0.8)\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The light points are the original data, while the dark points are the projected version. We see that after truncating 5% of the variance of this dataset and then reprojecting it, the \"most important\" features of the data are maintained, and we've compressed the data by 50%!\n",
"\n",
"This is the sense in which \"dimensionality reduction\" works: if you can approximate a data set in a lower dimension, you can often have an easier time visualizing it or fitting complicated models to the data."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}