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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Recitation 11/02/2018\n",
"\n",
"### Source\n",
"This notebook is an O'Reilly Tutorial on t-SNE which demonstrates the key mathematical assumptions of the algorithm. We will walk through this tutorial, and watch parts of a Google Talk given by Laurens van der Maaten to reinforce our understanding of t-SNE.\n",
"\n",
"Original OReilly Tutorial: https://github.com/oreillymedia/t-SNE-tutorial\n",
"\n",
"Laurens van der Maaten's Video Tutorial on Large-Scale t-SNE: https://www.youtube.com/watch?v=RJVL80Gg3lA&list=UUtXKDgv1AVoG88PLl8nGXmw\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## An Illustrated Introduction to the t-SNE Algorithm\n",
"\n",
"In the Big Data era, data is not only becoming bigger and bigger; it is also becoming more and more complex. This translates into a spectacular increase of the dimensionality of the data. For example, the dimensionality of a set of images is the number of pixels in any image, which ranges from thousands to millions.\n",
"\n",
"Computers have no problem processing that many dimensions. However, we humans are limited to three dimensions. Computers still need us (thankfully), so we often need ways to effectively visualize high-dimensional data before handing it over to the computer.\n",
"\n",
"How can we possibly reduce the dimensionality of a dataset from an arbitrary number to two or three, which is what we're doing when we visualize data on a screen?\n",
"\n",
"The answer lies in the observation that many real-world datasets have a low intrinsic dimensionality, even though they're embedded in a high-dimensional space. Imagine that you're shooting a panoramic landscape with your camera, while rotating around yourself. We can consider every picture as a point in a 16,000,000-dimensional space (assuming a 16 megapixels camera). Yet, the set of pictures approximately lie in a three-dimensional space (yaw, pitch, roll). This low-dimensional space is embedded within the high-dimensional space in a complex, nonlinear way. Hidden in the data, this structure can only be recovered via specific mathematical methods.\n",
"\n",
"This is the topic of manifold learning, also called nonlinear dimensionality reduction, a branch of machine learning (more specifically, unsupervised learning). It is still an active area of research today to develop algorithms that can automatically recover a hidden structure in a high-dimensional dataset.\n",
"\n",
"This post is an introduction to a popular dimensonality reduction algorithm: t-distributed stochastic neighbor embedding (t-SNE). Developed by Laurens van der Maaten and Geoffrey Hinton (see the original paper here), this algorithm has been successfully applied to many real-world datasets. Here, we'll follow the original paper and describe the key mathematical concepts of the method, when applied to a toy dataset (handwritten digits). We'll use Python and the scikit-learn library."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"!pip install seaborn\n",
"!pip install moviepy"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"# That's an impressive list of imports.\n",
"import numpy as np\n",
"from numpy import linalg\n",
"from numpy.linalg import norm\n",
"from scipy.spatial.distance import squareform, pdist\n",
"\n",
"# We import sklearn.\n",
"import sklearn\n",
"from sklearn.manifold import TSNE\n",
"from sklearn.datasets import load_digits\n",
"from sklearn.preprocessing import scale\n",
"\n",
"# We'll hack a bit with the t-SNE code in sklearn 0.15.2.\n",
"from sklearn.metrics.pairwise import pairwise_distances\n",
"from sklearn.manifold.t_sne import (_joint_probabilities,\n",
" _kl_divergence)\n",
"#from sklearn.utils.extmath import _ravel\n",
"# Random state.\n",
"RS = 20150101\n",
"\n",
"# We'll use matplotlib for graphics.\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.patheffects as PathEffects\n",
"import matplotlib\n",
"%matplotlib inline\n",
"\n",
"# We import seaborn to make nice plots.\n",
"import seaborn as sns\n",
"sns.set_style('darkgrid')\n",
"sns.set_palette('muted')\n",
"sns.set_context(\"notebook\", font_scale=1.5,\n",
" rc={\"lines.linewidth\": 2.5})\n",
"\n",
"# We'll generate an animation with matplotlib and moviepy.\n",
"# from moviepy.video.io.bindings import mplfig_to_npimage\n",
"# import moviepy.editor as mpy\n",
"import PIL"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1797, 64)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Load Digits Dataset\n",
"digits = load_digits()\n",
"digits.data.shape"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# We first reorder the data points according to the handwritten numbers.\n",
"X = np.vstack([digits.data[digits.target==i]\n",
" for i in range(10)])\n",
"y = np.hstack([digits.target[digits.target==i]\n",
" for i in range(10)])"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"digits_proj = TSNE(random_state=RS).fit_transform(X)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x1a14742ef0>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x1a147464a8>,\n",
" <matplotlib.collections.PathCollection at 0x1a149625f8>,\n",
" [Text(35.1412,49.0518,'0'),\n",
" Text(-1.20464,-15.7391,'1'),\n",
" Text(-48.6733,-17.7098,'2'),\n",
" Text(-38.29,20.2608,'3'),\n",
" Text(33.918,-39.8033,'4'),\n",
" Text(8.07994,21.03,'5'),\n",
" Text(49.5953,2.4024,'6'),\n",
" Text(-5.96337,-48.3856,'7'),\n",
" Text(-15.3029,-1.47993,'8'),\n",
" Text(-15.0129,33.071,'9')])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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Q0rnyAxoeW5Tai/oZltc50lA9nQnP26bNwLdubWr3TEL+1dfjOOqYIb+uiJEneCGEOIRY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NNrdmdeLKhwuPc1EeDHAX3+lIwBfsA5a0BS6VCOy26XK5XWSPnybwzp3oFE/ZkXicb7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\nAzCNIl/1chXZAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a14742ef0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def scatter(x, colors):\n",
" # We choose a color palette with seaborn.\n",
" palette = np.array(sns.color_palette(\"hls\", 10))\n",
"\n",
" # We create a scatter plot.\n",
" f = plt.figure(figsize=(8, 8))\n",
" ax = plt.subplot(aspect='equal')\n",
" sc = ax.scatter(x[:,0], x[:,1], lw=0, s=40,\n",
" c=palette[colors.astype(np.int)])\n",
" plt.xlim(-25, 25)\n",
" plt.ylim(-25, 25)\n",
" ax.axis('off')\n",
" ax.axis('tight')\n",
"\n",
" # We add the labels for each digit.\n",
" txts = []\n",
" for i in range(10):\n",
" # Position of each label.\n",
" xtext, ytext = np.median(x[colors == i, :], axis=0)\n",
" txt = ax.text(xtext, ytext, str(i), fontsize=24)\n",
" txt.set_path_effects([\n",
" PathEffects.Stroke(linewidth=5, foreground=\"w\"),\n",
" PathEffects.Normal()])\n",
" txts.append(txt)\n",
"\n",
" return f, ax, sc, txts\n",
"\n",
"scatter(digits_proj, y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mathematical Framework\n",
"\n",
"Let's explain how the algorithm works. First, a few definitions.\n",
"\n",
"A data point is a point $x_i$ in the original data space $\\mathbf{R}^D$, where $D=64$ is the dimensionality of the data space. Every point is an image of a handwritten digit here. There are $N=1797$ points.\n",
"\n",
"A map point is a point $y_i$ in the map space $\\mathbf{R}^2$. This space will contain our final representation of the dataset. There is a bijection between the data points and the map points: every map point represents one of the original images.\n",
"\n",
"How do we choose the positions of the map points? We want to conserve the structure of the data. More specifically, if two data points are close together, we want the two corresponding map points to be close too. Let's $\\left| x_i - x_j \\right|$ be the Euclidean distance between two data points, and $\\left| y_i - y_j \\right|$ the distance between the map points. We first define a conditional similarity between the two data points:\n",
"\n",
"$p_{j|i} = \\frac{\\exp\\left(-\\left| x_i - x_j\\right|^2 \\big/ 2\\sigma_i^2\\right)}{\\displaystyle\\sum_{k \\neq i} \\exp\\left(-\\left| x_i - x_k\\right|^2 \\big/ 2\\sigma_i^2\\right)}$\n",
"\n",
"This measures how close $x_j$ is from $x_i$, considering a Gaussian distribution around $x_i$ with a given variance $\\sigma_i^2$. This variance is different for every point; it is chosen such that points in dense areas are given a smaller variance than points in sparse areas. The original paper details how this variance is computed exactly.\n",
"\n",
"Now, we define the similarity as a symmetrized version of the conditional similarity:\n",
"\n",
"$p_{ij} = \\frac{p_{j|i} + p_{i|j}}{2N}$\n",
"\n",
"We obtain a similarity matrix for our original dataset. What does this matrix look like?\n",
"\n",
"### Similarity Matrix\n",
"\n",
"The following function computes the similarity with a constant $sigma$."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def _joint_probabilities_constant_sigma(D, sigma):\n",
" P = np.exp(-D**2/2 * sigma**2)\n",
" P /= np.sum(P, axis=1)\n",
" return P"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now compute the similarity with a $sigma_i$ depending on the data point (found via a binary search, according to the original t-SNE paper). This algorithm is implemented in the _joint_probabilities private function in scikit-learn's code."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# Pairwise distances between all data points.\n",
"D = pairwise_distances(X, squared=True)\n",
"# Similarity with constant sigma.\n",
"P_constant = _joint_probabilities_constant_sigma(D, .002)\n",
"# Similarity with variable sigma.\n",
"P_binary = _joint_probabilities(D, 30., False)\n",
"# The output of this function needs to be reshaped to a square matrix.\n",
"P_binary_s = squareform(P_binary)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now display the distance matrix of the data points, and the similarity matrix with both a constant and variable sigma."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5,1,'$p_{j|i}$ (variable $\\\\sigma$)')"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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x49nWUIhjlZXF36TutjbeO9nZrKNHdt0Bh9hYXgePh9cw2nol1i6rtfsiwWrl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\nMNMrzpdssYg6nz6NGyYUAsA/fRpRvSK4b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mnNsiiiUcl2O86VyWBhRaDLHxHUidvQV6+K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EAWmhEAA5X8h2O0BZtaoejnQa4M/vx7kmJlC/0VFNt+33g5pQr2tAp8sFcGe1akZBgl8RfMbv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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a14a0ed30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12, 4))\n",
"pal = sns.light_palette(\"blue\", as_cmap=True)\n",
"\n",
"plt.subplot(131)\n",
"plt.imshow(D[::10, ::10], interpolation='none', cmap=pal)\n",
"plt.axis('off')\n",
"plt.title(\"Distance matrix\", fontdict={'fontsize': 16})\n",
"\n",
"plt.subplot(132)\n",
"plt.imshow(P_constant[::10, ::10], interpolation='none', cmap=pal)\n",
"plt.axis('off')\n",
"plt.title(\"$p_{j|i}$ (constant $\\sigma$)\", fontdict={'fontsize': 16})\n",
"\n",
"plt.subplot(133)\n",
"plt.imshow(P_binary_s[::10, ::10], interpolation='none', cmap=pal)\n",
"plt.axis('off')\n",
"plt.title(\"$p_{j|i}$ (variable $\\sigma$)\", fontdict={'fontsize': 16})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can already observe the 10 groups in the data, corresponding to the 10 numbers.\n",
"\n",
"Let's also define a similarity matrix for our map points.\n",
"\n",
"$q_{ij} = \\frac{f(\\left| x_i - x_j\\right|)}{\\displaystyle\\sum_{k \\neq i} f(\\left| x_i - x_k\\right|)} \\quad \\textrm{with} \\quad f(z) = \\frac{1}{1+z^2}$\n",
"\n",
"This is the same idea as for the data points, but with a different distribution (t-Student with one degree of freedom, or Cauchy distribution, instead of a Gaussian distribution). We'll elaborate on this choice later.\n",
"\n",
"Whereas the data similarity matrix $\\big(p_{ij}\\big)$ is fixed, the map similarity matrix $\\big(q_{ij}\\big)$ depends on the map points. What we want is for these two matrices to be as close as possible. This would mean that similar data points yield similar map points.\n",
"\n",
"### A physical analogy\n",
"\n",
"Let's assume that our map points are all connected with springs. The stiffness of a spring connecting points $i$ and $j$ depends on the mismatch between the similarity of the two data points and the similarity of the two map points, that is, $p_{ij} - q_{ij}$. Now, we let the system evolve according to the laws of physics. If two map points are far apart while the data points are close, they are attracted together. If they are nearby while the data points are dissimilar, they are repelled.\n",
"\n",
"The final mapping is obtained when the equilibrium is reached.\n",
"\n",
"Here is an illustration of a dynamic graph layout based on a similar idea. Nodes are connected via springs and the system evolves according to law of physics (example by Mike Bostock).\n",
"\n",
"### Algorithm\n",
"\n",
"Remarkably, this physical analogy stems naturally from the mathematical algorithm. It corresponds to minimizing the Kullback-Leiber divergence between the two distributions $\\big(p_{ij}\\big)$ and $\\big(q_{ij}\\big)$:\n",
"\n",
"$KL(P||Q) = \\sum_{i, j} p_{ij} , \\log \\frac{p_{ij}}{q_{ij}}.$\n",
"\n",
"This measures the distance between our two similarity matrices.\n",
"\n",
"To minimize this score, we can use a method called gradient descent--at this point in 95-865, you do *not* need to know gradient descent. We will cover gradient descent toward the end of the course."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The Student t-Distribution\n",
"\n",
"Let's now explain the choice of the t-Student distribution for the map points, while a normal distribution is used for the data points. It is well known that the volume of the $N$-dimensional ball of radius $r$ scales as $r^N$. When $N$ is large, if we pick random points uniformly in the ball, most points will be close to the surface, and very few will be near the center.\n",
"\n",
"This is illustrated by the following simulation, showing the distribution of the distances of these points, for different dimensions."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
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AnMLwncXhw4frq6++UteuXXXLLbcoLCzMro/JZNIzzzzj0AABwJX+/e9/y2q1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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a148be240>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"npoints = 1000\n",
"plt.figure(figsize=(15, 4))\n",
"for i, D in enumerate((2, 5, 10)):\n",
" # Normally distributed points.\n",
" u = np.random.randn(npoints, D)\n",
" # Now on the sphere.\n",
" u /= norm(u, axis=1)[:, None]\n",
" # Uniform radius.\n",
" r = np.random.rand(npoints, 1)\n",
" # Uniformly within the ball.\n",
" points = u * r**(1./D)\n",
" # Plot.\n",
" ax = plt.subplot(1, 3, i+1)\n",
" ax.set_xlabel('Ball radius')\n",
" if i == 0:\n",
" ax.set_ylabel('Distance from origin')\n",
" ax.hist(norm(points, axis=1),\n",
" bins=np.linspace(0., 1., 50))\n",
" ax.set_title('D=%d' % D, loc='left')\n",
"#plt.savefig('images/spheres-generated.png', dpi=100, bbox_inches='tight')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When reducing the dimensionality of a dataset, if we used the same Gaussian distribution for the data points and the map points, we would get an imbalance in the distribution of the distances of a point's neighbors. This is because the distribution of the distances is so different between a high-dimensional space and a low-dimensional space. Yet, the algorithm tries to reproduce the same distances in the two spaces. This imbalance would lead to an excess of attraction forces and a sometimes unappealing mapping. This is actually what happens in the original SNE algorithm, by Hinton and Roweis (2002).\n",
"\n",
"The t-SNE algorithm works around this problem by using a t-Student with one degree of freedom (or Cauchy) distribution for the map points. This distribution has a much heavier tail than the Gaussian distribution, which compensates the original imbalance. For a given similarity between two data points, the two corresponding map points will need to be much further apart in order for their similarity to match the data similarity. This can be seen in the following plot."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1a1517a828>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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F9fU0/rtISkokP+zs7IiOjs5yPDr6HqA2e2X+XNrl2oEcHh5OWFgYPXv2NDre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\nv/OWcbYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a14911860>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"z = np.linspace(0., 5., 1000)\n",
"gauss = np.exp(-z**2)\n",
"cauchy = 1/(1+z**2)\n",
"plt.plot(z, gauss, label='Gaussian distribution')\n",
"plt.plot(z, cauchy, label='Cauchy distribution')\n",
"plt.legend()\n",
"#plt.savefig('images/distributions-generated.png', dpi=100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The t-SNE algorithm provides an effective method to visualize a complex dataset. It successfully uncovers hidden structures in the data, exposing natural clusters and smooth nonlinear variations along the dimensions. It has been implemented in many languages, including Python, and it can be easily used thanks to the scikit-learn library."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [default]",
"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": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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