{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Blastocyst Development in Mice: Single Cell TaqMan Arrays" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### presented at the EBI BioPreDyn Course 'The Systems Biology Modelling Cycle'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Max Zwiessele, Oliver Stegle, Neil Lawrence 12th May 2014 University of Sheffield and EBI." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we follow Buettner and Theis (2012) and use the GP-LVM to analyze some single cell data from Guo et al (2010). They performed qPCR TaqMan array on single cells from the developing blastocyst in mouse. The data is taken from the early stages of development when the Blastocyst is forming. At the 32 cell stage the data is already separated into the trophectoderm (TE) which goes onto form the placenta and the inner cellular mass (ICM). The ICM further differentiates into the epiblast (EPI)---which gives rise to the endoderm, mesoderm and ectoderm---and the primitive endoderm (PE) which develops into the amniotic sack. Guo et al selected 48 genes for expression measurement. They labelled the resulting cells and their labels are included as an aide to visualization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the paper, they first visualized their data using principal component analysis. In the first two principal components this fails to separate the domains. This is perhaps because the principal components are dominated by the variation in the 64 cell systems. This in turn may be because there are more cells from the data set in that regime, or additionally it could be that the natural variation across the 64 cell systems is greater. Both are probable causes of the dominance of these cells in the first two principal components. The first thing we do is plot the principal coordinates of the cells on the first two dominant directions. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### This Notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we will perform PCA on the original data, showing that the different regimes do not separate. Then, we follow Buettner and Theis (2012) in applying the GP-LVM to the data. There is a slight pathology in the result, one which they fixed by using priors that were dependent on the developmental stage. We then show how the Bayesian GP-LVM doesn't exhibit those pathologies and gives nice results that seems to show the lineage of the cells. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook is an extension of [SingleCellDataWithGPy](SingleCellDataWithGPy.ipynb) for tutorial needs." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pods, GPy, itertools\n", "%matplotlib inline\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we load in the data. We've provided a convenience function for loading in the data with GPy. It is loaded in as a `pandas` DataFrame. This allows us to summarize it with the `describe` attribute." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Acquiring resource: singlecell\n", "\n", "Details of data: \n", "qPCR TaqMan array single cell experiment in mouse. The data is taken from the early stages of development when the Blastocyst is forming. At the 32 cell stage the data is already separated into the trophectoderm (TE) which goes onto form the placenta and the inner cellular mass (ICM). The ICM further differentiates into the epiblast (EPI)---which gives rise to the endoderm, mesoderm and ectoderm---and the primitive endoderm (PE) which develops into the amniotic sack. Guo et al selected 48 genes for expression measurement. They labelled the resulting cells and their labels are included as an aide to visualization.\n", "\n", "Please cite:\n", "Guoji Guo, Mikael Huss, Guo Qing Tong, Chaoyang Wang, Li Li Sun, Neil D. Clarke, Paul Robson, Resolution of Cell Fate Decisions Revealed by Single-Cell Gene Expression Analysis from Zygote to Blastocyst, Developmental Cell, Volume 18, Issue 4, 20 April 2010, Pages 675-685, ISSN 1534-5807, http://dx.doi.org/10.1016/j.devcel.2010.02.012. (http://www.sciencedirect.com/science/article/pii/S1534580710001103) Keywords: DEVBIO\n", "\n", "After downloading the data will take up 233.1 bytes of space.\n", "\n", "Data will be stored in /Users/maxz/ods_data_cache/singlecell.\n", "\n", "You must also agree to the following license:\n", "ScienceDirect: http://www.elsevier.com/locate/termsandconditions?utm_source=sciencedirect&utm_medium=link&utm_campaign=terms\n", "\n", "Do you wish to proceed with the download? [yes/no]\n", "yes\n", "singlecell.csv\n", "Downloading http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/singlecell/singlecell.csv -> /Users/maxz/ods_data_cache/singlecell/singlecell.csv\n", "[==============================] 0.222/0.222MB\n" ] }, { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ActbAhcyAqp3Atp12aBmp4Cdx2Creb312CebpaDab2DppaI...Sox2Sall4Sox17SnailSox13Tcfap2aTcfap2cTcf23Utf1Tspan8
count4.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+02...4.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+024.370000e+02
mean2.089245e-082.400458e-083.011442e-082.009153e-081.416476e-082.661327e-081.828375e-082.329519e-082.993135e-082.077803e-08...2.180778e-082.146453e-082.077803e-082.585812e-082.473684e-082.670481e-082.009153e-082.231121e-082.263158e-082.606407e-08
std1.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+00...1.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+001.001146e+00
min-2.997659e+00-2.140030e+00-1.768643e+00-2.355953e+00-4.420191e+00-1.972546e+00-2.493296e+00-2.290915e+00-1.641875e+00-1.755517e+00...-2.246728e+00-2.015028e+00-2.960914e+00-1.964500e+00-2.033562e+00-1.886886e+00-2.238215e+00-2.089612e+00-1.825355e+00-2.035440e+00
25%-7.169942e-01-7.796685e-01-7.171038e-01-9.337937e-01-2.516838e-01-6.446426e-01-7.717112e-01-8.545864e-01-6.703301e-01-1.018770e+00...-7.734272e-01-9.343944e-01-6.515803e-01-7.255418e-01-7.276985e-01-8.376303e-01-9.886838e-01-9.197137e-01-9.236930e-01-7.673579e-01
50%9.227372e-02-1.782182e-01-1.842611e-012.928931e-012.146358e-01-1.353097e-012.772327e-01-6.806050e-02-2.415102e-011.097815e-01...7.709900e-038.293864e-02-3.701860e-02-1.972392e-01-1.336842e-01-2.656403e-012.828122e-01-1.836380e-02-1.127644e-01-2.462695e-01
75%6.808323e-016.245760e-013.312916e-018.234601e-016.738631e-014.854397e-018.213037e-019.125241e-014.854736e-019.259312e-01...8.608111e-018.312436e-016.177259e-011.082358e+005.329677e-019.967453e-018.099583e-011.022974e+008.257577e-016.422915e-01
max2.490650e+003.564713e+002.627702e+001.687127e+001.569268e+003.427747e+001.826346e+001.729923e+002.780331e+001.671790e+00...1.709987e+004.489121e+003.565258e+001.655467e+002.231074e+002.104293e+004.187598e+001.808619e+002.208022e+002.270316e+00
\n", "

8 rows × 48 columns

\n", "
" ], "text/plain": [ " Actb Ahcy Aqp3 Atp12a Bmp4 \\\n", "count 4.370000e+02 4.370000e+02 4.370000e+02 4.370000e+02 4.370000e+02 \n", "mean 2.089245e-08 2.400458e-08 3.011442e-08 2.009153e-08 1.416476e-08 \n", "std 1.001146e+00 1.001146e+00 1.001146e+00 1.001146e+00 1.001146e+00 \n", "min -2.997659e+00 -2.140030e+00 -1.768643e+00 -2.355953e+00 -4.420191e+00 \n", "25% -7.169942e-01 -7.796685e-01 -7.171038e-01 -9.337937e-01 -2.516838e-01 \n", "50% 9.227372e-02 -1.782182e-01 -1.842611e-01 2.928931e-01 2.146358e-01 \n", "75% 6.808323e-01 6.245760e-01 3.312916e-01 8.234601e-01 6.738631e-01 \n", "max 2.490650e+00 3.564713e+00 2.627702e+00 1.687127e+00 1.569268e+00 \n", "\n", " Cdx2 Creb312 Cebpa Dab2 DppaI \\\n", "count 4.370000e+02 4.370000e+02 4.370000e+02 4.370000e+02 4.370000e+02 \n", "mean 2.661327e-08 1.828375e-08 2.329519e-08 2.993135e-08 2.077803e-08 \n", "std 1.001146e+00 1.001146e+00 1.001146e+00 1.001146e+00 1.001146e+00 \n", "min -1.972546e+00 -2.493296e+00 -2.290915e+00 -1.641875e+00 -1.755517e+00 \n", "25% -6.446426e-01 -7.717112e-01 -8.545864e-01 -6.703301e-01 -1.018770e+00 \n", "50% -1.353097e-01 2.772327e-01 -6.806050e-02 -2.415102e-01 1.097815e-01 \n", "75% 4.854397e-01 8.213037e-01 9.125241e-01 4.854736e-01 9.259312e-01 \n", "max 3.427747e+00 1.826346e+00 1.729923e+00 2.780331e+00 1.671790e+00 \n", "\n", " ... Sox2 Sall4 Sox17 Snail \\\n", "count ... 4.370000e+02 4.370000e+02 4.370000e+02 4.370000e+02 \n", "mean ... 2.180778e-08 2.146453e-08 2.077803e-08 2.585812e-08 \n", "std ... 1.001146e+00 1.001146e+00 1.001146e+00 1.001146e+00 \n", "min ... -2.246728e+00 -2.015028e+00 -2.960914e+00 -1.964500e+00 \n", "25% ... -7.734272e-01 -9.343944e-01 -6.515803e-01 -7.255418e-01 \n", "50% ... 7.709900e-03 8.293864e-02 -3.701860e-02 -1.972392e-01 \n", "75% ... 8.608111e-01 8.312436e-01 6.177259e-01 1.082358e+00 \n", "max ... 1.709987e+00 4.489121e+00 3.565258e+00 1.655467e+00 \n", "\n", " Sox13 Tcfap2a Tcfap2c Tcf23 Utf1 \\\n", "count 4.370000e+02 4.370000e+02 4.370000e+02 4.370000e+02 4.370000e+02 \n", "mean 2.473684e-08 2.670481e-08 2.009153e-08 2.231121e-08 2.263158e-08 \n", "std 1.001146e+00 1.001146e+00 1.001146e+00 1.001146e+00 1.001146e+00 \n", "min -2.033562e+00 -1.886886e+00 -2.238215e+00 -2.089612e+00 -1.825355e+00 \n", "25% -7.276985e-01 -8.376303e-01 -9.886838e-01 -9.197137e-01 -9.236930e-01 \n", "50% -1.336842e-01 -2.656403e-01 2.828122e-01 -1.836380e-02 -1.127644e-01 \n", "75% 5.329677e-01 9.967453e-01 8.099583e-01 1.022974e+00 8.257577e-01 \n", "max 2.231074e+00 2.104293e+00 4.187598e+00 1.808619e+00 2.208022e+00 \n", "\n", " Tspan8 \n", "count 4.370000e+02 \n", "mean 2.606407e-08 \n", "std 1.001146e+00 \n", "min -2.035440e+00 \n", "25% -7.673579e-01 \n", "50% -2.462695e-01 \n", "75% 6.422915e-01 \n", "max 2.270316e+00 \n", "\n", "[8 rows x 48 columns]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = pods.datasets.singlecell()\n", "Ydf = s['Y']\n", "Y = Ydf.values\n", "labels = s['labels']\n", "marker = '<>^vsd'\n", "Ydf.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Try figuring out the data a little more detailed. \n", "- How many genes where measured, what are the distributions? \n", "- Try to plot some histograms of the data, so you see how it is distributed.\n", "- Can you plot a heatmap (`matplotlib.imshow()`)?" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Type your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we will define a little routine, which puts the legend on the right side of the plot, so that the legend does not overwright the data plot" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def legend_to_the_right(ax):\n", " box = ax.get_position()\n", " ax.set_position([box.x0, box.y0, box.width, box.height])\n", " _ = ax.legend(loc='center left', bbox_to_anchor=(1, 0.5), numpoints=1)\n", " \n", "def plot_latent(ax, x, y, marker, labels):\n", " GPy.plotting.matplot_dep.Tango.reset()\n", " # make sure labels are in order of input:\n", " ulabels = []\n", " for lab in labels:\n", " if not lab in ulabels:\n", " ulabels.append(lab)\n", " for i, [label, m] in enumerate(zip(ulabels, itertools.cycle(marker))):\n", " symbol = marker[i % len(marker)]\n", " ind = labels == label\n", " ax.plot(x[ind], y[ind], marker=symbol, \n", " markerfacecolor=GPy.plotting.matplot_dep.Tango.nextMedium(), \n", " linestyle='', \n", " label=label, mew=.2, alpha=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Principal Component Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we follow Guo et al in performing PCA on the data. Rather than calling a 'PCA routine', here we break the algorithm down into its steps: compute the data covariance, compute the eigenvalues and eigenvectors and sort according to magnitude of eigenvalue. Because we want to visualize the data, we've chose to compute the eigenvectors of the *inner product matrix* rather than the covariance matrix. This allows us to plot the eigenvalues directly. However, this is less efficient (in this case because the number of genes is smaller than the number of data) than computing the eigendecomposition of the covariance matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, using the helper function we can plot the results with appropriate labels." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Use the `GPy.util.pca.PCA` class to run PCA on the dataset (`Y`)\n", "- plot the result of the PCA using either the `plot_latent` function, or `PCA.plot_2d()`\n", "- plot the eigenvalue fractions for the first 10 dimensions, using `plt.bar`, or `PCA.plot_frac(Q=10)`" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "GPy.util.pca.PCA?\n", "# Type your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### GP-LVM on the Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Buettner and Theis applied a Gaussian process latent variable model to the data, but with a modified prior to ensure that small differences between cells at the same differential stage were preserved. Here we apply a standard GP-LVM (no modified prior) to the data. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Running A GPLVM on the given data is as easy as creating a class from the `GPy.models.GPLVM`\n", "- Beware of high running times, if dimensions are too big.\n", "- optimize the model and plot the latent space (using `m.plot_latent`, or `plot_latent` defined above).\n", "- Try different combinations of kernels, allowed kernels are:\n", " * `GPy.kern.Linear`\n", " * `GPy.kern.White`\n", " * `GPy.kern.Bias`\n", " * `GPy.kern.RBF`\n", "- Try out different kernels, we have found the best is to use `GPy.kern.RBF(Q,ARD=1)+GPy.kern.Bias(Q)`, where Q is the number of latent dimensions" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Type your code here" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtkAAAEcCAYAAAASgKgEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbEVRFEVRFEWZZ/4/Q1i/+5F5oisAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A result could look like this:\n", "fig, [ax1, ax2] = plt.subplots(1,2,figsize=(9,4))\n", "\n", "m.kern.plot_ARD(ax=ax1)\n", "m.plot_latent(labels=labels, marker=marker, legend=False, ax=ax2)\n", "\n", "_ = legend_to_the_right(ax2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a small bonus, you can plot the magnification factor, using\n", "```\n", "m.plot_magnification(labels=labels, marker=marker, legend=True)\n", "```\n", "here. \n", "\n", "- Can you see the difference between the shading of plot_latent, and plot_magnification?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Type your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian GP-LVM" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we show the new code that uses the Bayesian GP-LVM to fit the data. This means we can automatically determine the dimensionality of the model whilst fitting a non-linear dimensionality reduction. The approximations we use also mean that it is faster than the original GP-LVM.\n", "\n", "- You can find the BayesianGPLVM in `GPy.models.BayesianGPLVM`.\n", "- Fit a Bayesian GPLVM to the model\n", "- Try different combinations of kernels, allowed kernels are:\n", " * `GPy.kern.Linear`\n", " * `GPy.kern.White`\n", " * `GPy.kern.Bias`\n", " * `GPy.kern.RBF`\n", "- Plot the latent space and magnification and compare to GPLVM" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Type your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gives a really nice result. Broadly speaking two latent dimensions dominate the representation. When we visualize using these two dimensions we can see the entire cell phylogeny laid out nicely in the two dimensions. Additionally we can see the missclassification of the some cells, using the 'standard' approach of repeated k-means clustering and PCA on sub clustered (This was used to get the sample colors of the 64 cellstage)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Other Nonlinear Approaches" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do other non-linear approaches compare with the GP-LVM? We can use scikit-learn to try a few. First we consider Isomap, which often performs really well on data.\n", "\n", "- We fully put in the workflow for these approaches for you to have a look and compare agains. If you like, feel free to try to improve or change how to use the other nonlinear approaches. \n", "- Try out your own method?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Isomap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Isomap first builds a neighbourhood graph, and then uses distances along this graph to approximate the geodesic distance between points. These distances are then visualized by performing classical multidimensional scaling (which involves computing the eigendecomposition of the centred distance matrix). As the neighborhood size is increased to match the data, principal component analysis is recovered (or strictly speaking, principal coordinate analysis). The fewer the neighbors, the more 'non-linear' the isomap embeddings are. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAc0AAAEACAYAAADRMy13AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGmOMMRGyoGmMMcZEyIKmMcYYE6H/Dy+BWn9b6YZpAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_neighbors = 30\n", "import sklearn.manifold\n", "m = sklearn.manifold.Isomap(n_neighbors=n_neighbors, n_components=2)\n", "X = m.fit_transform(Ydf)\n", "fig, ax = plt.subplots(1)\n", "plot_latent(ax, X[:, 0], X[:, 1], marker, labels)\n", "_ = legend_to_the_right(ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Locally Linear Embedding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we try locally linear embedding. In locally linear embedding a neighborhood is also computed. Each point is then reconstructed by it's neighbors using a linear weighting. This implies a locally linear patch is being fitted to the data in that region. These patches are assimilated into a large $n\\times n$ matrix and a lower dimensional data set which reflects the same relationships is then sought. Quite a large number of neighbours needs to be selected for the data to not collapse in on itself. When a large number of neighbours is selected the embedding is more linear and begins to look like PCA. However, the algorithm does *not* converge to PCA in the limit as the number of neighbors approaches $n$. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdcAAAEACAYAAADhvzxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n6VxhDwiVygAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_neighbors = 200\n", "m = sklearn.manifold.LocallyLinearEmbedding(n_neighbors=n_neighbors, n_components=2)\n", "X = m.fit_transform(Y)\n", "fig, ax = plt.subplots(1)\n", "plot_latent(ax, X[:, 0], X[:, 1], marker, labels)\n", "_ = legend_to_the_right(ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### work funded by the BioPreDyn and MLPM projects, it is a collaboration with Nicolas Durrande, Johannes Jaeger." ] } ], "metadata": { "celltoolbar": "Raw Cell Format", "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": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }