{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Dimensionality reduction : Principal component analysis" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The text.latex.preview rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The mathtext.fallback_to_cm rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: Support for setting the 'mathtext.fallback_to_cm' rcParam is deprecated since 3.3 and will be removed two minor releases later; use 'mathtext.fallback : 'cm' instead.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The validate_bool_maybe_none function was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The savefig.jpeg_quality rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The keymap.all_axes rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The animation.avconv_path rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The animation.avconv_args rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n" ] } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(100, 10)\n", "[[0.28203457 0.17743954 0.75061475 0.80683474 0.99050514 0.41261768\n", " 0.37201809 0.77641296 0.34080354 0.93075733]\n", " [0.85841275 0.42899403 0.75087107 0.75454287 0.10312387 0.90255291\n", " 0.50525237 0.82645747 0.3200496 0.89552323]\n", " [0.38920168 0.01083765 0.90538198 0.09128668 0.31931364 0.95006197\n", " 0.95060715 0.57343789 0.63183721 0.44844552]]\n" ] } ], "source": [ "np.random.seed(42)\n", "X = np.random.normal(size=(100,3))\n", "R = np.random.random([3,10])\n", "X = np.dot(X,R)\n", "print(X.shape)\n", "np.savetxt('ndim.txt',X)\n", "print(R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Start by loading a multi-dimensional data set, from the file ndim.txt using numpy.loadtxt() " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(100, 10)\n" ] } ], "source": [ "X=np.loadtxt('ndim.txt')\n", "print(X.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dataset has 100 data points, which is the first index. The second index gives the number of characteristics per \n", "data point, i.e. the dimensionality of the data. How many dimensions does this data have?\n", "
ANSWER HERE: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Investigate this data set by making some plots. Do you think that it is a good candidate for dimensionality reduction? Why or why not? \n", "
ANSWER HERE: \n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:,0],X[:,1],c=X[:,3],s=X[:,4]*30)\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, let's see what principal component analysis tells us. We will use the sklearn.decomposition.PCA() routine. Start by instantiating a PCA object. If you don't specify a number of components, it will do a full decomposition into the same number of projected components as input components, and we can then investigate how many of these might be needed." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "from sklearn.decomposition import PCA\n", "pca=PCA() #instatiate a PCA object" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To do the PCA decomposition, we can invoke the fit() method, which will just load the decomposition into the instantiated object. To transform the original data into the new coordinate system, you can use the transform() method, which will return a new data array with coordinates in the transfomed system. You can do both of these steps together using the fit_transform() method." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "X_projected=pca.fit_transform(X) # do the PCA decomposition and get the transformed coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inverse_transform() method will take the transformed coordinates and transform them back to the original coordinate system. If you use all of the transformed dimensions, you should get back exactly what you started with. However, if you use fewer dimensions, you will not necessarily get the data back, depending on the degree of correlations in the system. Investigate how changing the number of components affects your ability to reproduce the original data. You can do this either by introducing the n_components keyword in the PCA() instantiation, or by setting the higher dimensions of the projected coordinates to zero, because these are sorted by their contribution to the variance (higher eigenvalues first). Then plot the difference between the original data and the inverse transformed data, paying attention to the values on the y-axis.\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import copy\n", "# if you want, you can set some of the components to zero before the inverse transform, or you can rerun\n", "# above by setting n_commponents in the PCA() instatiation\n", "tmp=copy.copy(X_projected)\n", "tmp[:, 2:10] = 0.\n", "X_inv = pca.inverse_transform(tmp) # get the inverse transformed coordinates\n", "\n", "for indata,outdata in zip(X,X_inv) :\n", " #plt.plot(indata)\n", " #plt.plot(outdata)\n", " plt.plot(indata-outdata)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How many dimensions do you need to be able to reproduce the input data>\n", "
ANSWER HERE: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can get at the same thing using the variances computed by the PCA routine. The attribute explained_variance_ contains the variances for each component. The attribute explained_variance_ratio_ expresses these as a fraction of the total variance. Plotting either of these will give you a \"scree plot.\"\n", "
\n", "Doing a cumulative sum on explained_variance_ratio_ will show the cumulative fraction of how much of the total variance is explained as each component is added.\n", "
\n", "Create both plots" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(10, 10)\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(pca.components_.shape)\n", "plt.figure()\n", "plt.plot(pca.explained_variance_) # plot the explained_variance_\n", "plt.figure()\n", "plt.plot(pca.explained_variance_ratio_) # plot the explained_variance_ratio\n", "plt.figure()\n", "plt.plot(np.cumsum(pca.explained_variance_ratio_)) # plot the cumulative sum of explained_variance_ratio_\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based on these plots, how many dimensions are needed to characterize the data?\n", "
ANSWER HERE: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can look at the eigenvectors themselves, which are stored in the components_ attribute. Plot these for the components that explain the data." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(10, 10)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(pca.components_.shape)\n", "for i in range(3) :\n", " plt.plot(pca.components_[i,:],label='component: {:d}'.format(i)) # plot the ith component\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can you describe what these eigenvectors represent?\n", "
ANSWER HERE: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that you can also turn things around and ask the PCA routine to tell you how many components are needed to account for a desired fraction of the total variance, by specifying this fraction in the PCA instatiation with the desired_fraction= keyword (note in later version of scikit-learn, this might be specified using n_components if value is between 0 and 1). The number of required components will be saved in the n_components_ attribute after the fit() is done." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of components needed: 3\n" ] } ], "source": [ "# turn things around to have PCA tell us the number of components needed to fit an input\n", "# fraction of the total variance\n", "desired_fraction = 0.99 # set desired_fraction here\n", "pca=PCA(desired_fraction) # instatiate the pca object using the desired_fraction keyword\n", "pca.fit(X) # do the PCA fit\n", "print('number of components needed: ', pca.n_components_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Does this match what you got from your plots of variances?\n", "
ANSWER HERE: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now let's try an actual data set.\n", "
\n", "Let's work with the APOGEE DR17 data set, looking at abundances of multiple elements. First we will download data from the SDSS Catalog archive server using an SQL query with astroquery.\n", "
\n", "To learn about what is in the data base, you can peruse the \n", " schema browser . We will be interested in quantities from the aspcapStar table (select that from the Tables item on the right), specifically FE_H (which gives the logarithm of the abundance of iron to hydrogen relative to that of the Sun), MG_FE (logarithmic abundance of magnesium relative to irorn relative to that ratio in the Sun), O_FE, SI_FE, AL_FE, MN_FE, NI_FE, and LOGG (surface gravity). Construct a query that selects the abundances from this table for object with 1 < logg < 2. Remember, the basic structure of an SQL query:\n", "
\n",
    "   SELECT  columnnames\n",
    "   FROM  tablename\n",
    "   WHERE conditions\n",
    "
\n", "To make sure all of the abundances are valid, required that each abundance be larger than -10 (bad values are flagged as -999). You can also select on apogeeStar.extratarg = 0 as we did last time" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " SELECT FE_H, MG_FE, O_FE, SI_FE, AL_FE, MN_FE, NI_FE FROM aspcapStar JOIN apogeeStar on apogeeStar.apstar_id = aspcapStar.apstar_id WHERE LOGG>1 AND LOGG<2 AND FE_H>-10 AND MG_FE>-10 AND O_FE>-10 AND SI_FE>-10 AND AL_FE>-10 AND MN_FE>-10 AND NI_FE>-10 AND apogeeStar.extratarg = 0 \n", "60252\n" ] } ], "source": [ "from astroquery.sdss import SDSS\n", "sql=\" SELECT FE_H, MG_FE, O_FE, SI_FE, AL_FE, MN_FE, NI_FE \\\n", " FROM aspcapStar \\\n", " JOIN apogeeStar on apogeeStar.apstar_id = aspcapStar.apstar_id \\\n", " WHERE LOGG>1 AND LOGG<2 AND FE_H>-10 AND MG_FE>-10 AND O_FE>-10 AND SI_FE>-10 \\\n", " AND AL_FE>-10 AND MN_FE>-10 AND NI_FE>-10 AND apogeeStar.extratarg = 0\\\n", " \"\n", "\n", "print(sql)\n", "dr17=SDSS.query_sql(sql, data_release=17) \n", "print(len(dr17))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How many objects did you get?\n", "
ANSWER HERE:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The basic question is whether there are significant correlations between the different elemental abundances. If so, you can represent the data with fewer quantities. We will use PCA to investigate this. First we need to bundle the data into a [nobjects,nabun] shaped array. You can use np.array() or np.vstack() to bundle the data, e.g." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(60252, 2)\n", "(60252, 2)\n" ] } ], "source": [ "print(np.vstack([dr17['FE_H'],dr17['O_FE']]).T.shape)\n", "print(np.array([dr17['FE_H'],dr17['O_FE']]).T.shape)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a data array including all seven dimensions" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(60252, 7)\n" ] } ], "source": [ "X=np.array([dr17['FE_H'],dr17['O_FE'],dr17['MG_FE'],dr17['SI_FE'],dr17['AL_FE'],\n", " dr17['MN_FE'],dr17['NI_FE']]).T # create data array\n", "labels=['Fe_H','O','Mg','Si','Ni','Al','Mn']\n", "\n", "# set up some labels for plots\n", "labels=['[Fe/H]','[O/Fe]','[Mg/Fe]','[Si/Fe]','[Al/Fe]','[Mn/Fe]','[Ni/Fe]']\n", "print(X.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, try to do a PCA decomposition as above" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(60252, 7) (60252, 7) (60252, 7)\n" ] } ], "source": [ "#do the PCA decomposition\n", "pca=PCA() #instatiate a PCA object\n", "X_projected=pca.fit_transform(X) # do the decomposition and get the transformed coordinates\n", "X_inv=pca.inverse_transform(X_projected) # get the inverse transformation\n", "print(X.shape,X_projected.shape,X_inv.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make the scree plots as above, with the explained_variance_, explained_variance_ratio_, and cumulative sum of explained_variance_ratio_" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(7, 7)\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(pca.components_.shape)\n", "# make the plots\n", "plt.figure()\n", "plt.plot(pca.explained_variance_)\n", "plt.figure()\n", "plt.plot(pca.explained_variance_ratio_)\n", "plt.figure()\n", "plt.plot(np.cumsum(pca.explained_variance_ratio_))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How many components are needed to epxlain the bulk (say 95%) of the total variance?\n", "
ANSWER HERE: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As above, look at the first few eigenvectors (as many as were needed to explain the bulk of the variance) and see if you can interpret anything. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(7, 7)\n" ] }, { "data": { "text/plain": [ "([,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ],\n", " )" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# look at the individual components and the fraction of the variance that they explain\n", "#plt.plot(X_projected[:,0],X_projected[:,1],'ro')\n", "print(pca.components_.shape)\n", "colors=['r','g','b','c','m','y','k']\n", "for i in range(3) :\n", " plt.plot(pca.components_[i,:],color=colors[i],label='component {:d}'.format(i)) # plot the ith component\n", "plt.legend()\n", " \n", "plt.xticks(range(len(labels)),labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Are there some elemental abundances that go in lockstep with others?\n", "
\n", " ANSWER HERE: " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.11" } }, "nbformat": 4, "nbformat_minor": 1 }