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GitLab upgrade completed. Current version is 17.11.3.
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SketchedLearning
SPM Notebook
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57f2dd50
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57f2dd50
authored
4 years ago
by
Vincent Schellekens
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Compressive clustering.ipynb
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f89e844a
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this notebook, we explore compressive clustering on a 2-d toy example dataset."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# General imports\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# We import the pycle toolbox for sketched learning; we will need three submodules\n",
"import pycle\n",
"from pycle import sketching, compressive_learning, utils\n",
"\n",
"# Fix the random seed for reproducibility\n",
"np.random.seed(0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's start by generating a toy example dataset from a Gaussian mixture model."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"d = 2 # Dimension\n",
"K = 5 # Number of Gaussians\n",
"n = int(1e5) # Number of samples we want to generate\n",
"# We use the generatedataset_GMM method from pycle (we ask that the entries are <= 1, and imbalanced clusters)\n",
"X = pycle.utils.generatedataset_GMM(d,K,n,normalize='l_inf-unit-ball',balanced=False, separation_min=2) \n",
"\n",
"# Bounds on the dataset, necessary for compressive k-means\n",
"bounds = np.array([-np.ones(d),np.ones(d)]) # We assumed the data is normalized between -1 and 1\n",
"\n",
"# Visualize the dataset\n",
"plt.figure(figsize=(5,5))\n",
"plt.title(\"Full dataset\")\n",
"plt.scatter(X[:,0],X[:,1],s=1, alpha=0.1)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We first compress the dataset as a single sketch vector. Let's define the parameters of the feature map $\\Phi$ first."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Dataset size: (100000, 2)\n",
"Sketch size: (100,)\n"
]
}
],
"source": [
"# Pick the dimension m (5*K*d is usually (just) enough for clustering)\n",
"m = 10*K*d \n",
"\n",
"# Kernel bandwith (squared)\n",
"sigma2 = 0.05\n",
"\n",
"# We want m Gaussian frequencies in dimension d, with squared kernel bandwith sigma2\n",
"W = pycle.sketching.drawFrequencies(\"Gaussian\",d,m,sigma2)\n",
"\n",
"# To generate the map, we provide a nonlinearity rho (here complex exponential for RFF) and the projections W\n",
"Phi = pycle.sketching.SimpleFeatureMap(\"ComplexExponential\",W)\n",
"\n",
"# We sketch X with Phi: we map a 100000x2 dataset -> a 100-dimensional complex vector\n",
"z = pycle.sketching.computeSketch(X,Phi)\n",
"\n",
"print(\"Dataset size: \", X.shape)\n",
"print(\"Sketch size: \", z.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, to solve k-means from the sketch, we call the CLOMPR algorithm."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"(weights,centroids) = pycle.compressive_learning.CLOMPR(\"k-means\",z,Phi,K,bounds,nRepetitions=5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's see how well we did:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"SSE from sketch: 1018.8545093592352\n",
"SSE from k-means: 990.8373999288126\n"
]
}
],
"source": [
"# Visualize the centroids (we re-use the dataset for visual comparison)\n",
"plt.figure(figsize=(5,5))\n",
"plt.title(\"Compressively learned centroids\")\n",
"plt.scatter(X[:,0],X[:,1],s=1, alpha=0.15)\n",
"plt.scatter(centroids[:,0],centroids[:,1],s=1000*weights)\n",
"plt.legend([\"Data\",\"Centroids\"])\n",
"plt.show()\n",
"\n",
"print(\"SSE from sketch: {}\".format(pycle.utils.SSE(X,centroids)))\n",
"\n",
"# Compare to k-means\n",
"from sklearn.cluster import KMeans\n",
"kmeans_estimator = KMeans(n_clusters=K)\n",
"kmeans_estimator.fit(X)\n",
"centroids_kmeans = kmeans_estimator.cluster_centers_\n",
"print(\"SSE from k-means: {}\".format(pycle.utils.SSE(X,centroids_kmeans)))\n"
]
}
],
"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": "3.6.9"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
%% Cell type:markdown id: tags:
In this notebook, we explore compressive clustering on a 2-d toy example dataset.
%% Cell type:code id: tags:
```
python
# General imports
import
numpy
as
np
import
matplotlib.pyplot
as
plt
# We import the pycle toolbox for sketched learning; we will need three submodules
import
pycle
from
pycle
import
sketching
,
compressive_learning
,
utils
# Fix the random seed for reproducibility
np
.
random
.
seed
(
0
)
```
%% Cell type:markdown id: tags:
Let's start by generating a toy example dataset from a Gaussian mixture model.
%% Cell type:code id: tags:
```
python
d
=
2
# Dimension
K
=
5
# Number of Gaussians
n
=
int
(
1e5
)
# Number of samples we want to generate
# We use the generatedataset_GMM method from pycle (we ask that the entries are <= 1, and imbalanced clusters)
X
=
pycle
.
utils
.
generatedataset_GMM
(
d
,
K
,
n
,
normalize
=
'
l_inf-unit-ball
'
,
balanced
=
False
,
separation_min
=
2
)
# Bounds on the dataset, necessary for compressive k-means
bounds
=
np
.
array
([
-
np
.
ones
(
d
),
np
.
ones
(
d
)])
# We assumed the data is normalized between -1 and 1
# Visualize the dataset
plt
.
figure
(
figsize
=
(
5
,
5
))
plt
.
title
(
"
Full dataset
"
)
plt
.
scatter
(
X
[:,
0
],
X
[:,
1
],
s
=
1
,
alpha
=
0.1
)
plt
.
show
()
```
%% Output
%% Cell type:markdown id: tags:
We first compress the dataset as a single sketch vector. Let's define the parameters of the feature map $
\P
hi$ first.
%% Cell type:code id: tags:
```
python
# Pick the dimension m (5*K*d is usually (just) enough for clustering)
m
=
10
*
K
*
d
# Kernel bandwith (squared)
sigma2
=
0.05
# We want m Gaussian frequencies in dimension d, with squared kernel bandwith sigma2
W
=
pycle
.
sketching
.
drawFrequencies
(
"
Gaussian
"
,
d
,
m
,
sigma2
)
# To generate the map, we provide a nonlinearity rho (here complex exponential for RFF) and the projections W
Phi
=
pycle
.
sketching
.
SimpleFeatureMap
(
"
ComplexExponential
"
,
W
)
# We sketch X with Phi: we map a 100000x2 dataset -> a 100-dimensional complex vector
z
=
pycle
.
sketching
.
computeSketch
(
X
,
Phi
)
print
(
"
Dataset size:
"
,
X
.
shape
)
print
(
"
Sketch size:
"
,
z
.
shape
)
```
%% Output
Dataset size: (100000, 2)
Sketch size: (100,)
%% Cell type:markdown id: tags:
Now, to solve k-means from the sketch, we call the CLOMPR algorithm.
%% Cell type:code id: tags:
```
python
(
weights
,
centroids
)
=
pycle
.
compressive_learning
.
CLOMPR
(
"
k-means
"
,
z
,
Phi
,
K
,
bounds
,
nRepetitions
=
5
)
```
%% Cell type:markdown id: tags:
Let's see how well we did:
%% Cell type:code id: tags:
```
python
# Visualize the centroids (we re-use the dataset for visual comparison)
plt
.
figure
(
figsize
=
(
5
,
5
))
plt
.
title
(
"
Compressively learned centroids
"
)
plt
.
scatter
(
X
[:,
0
],
X
[:,
1
],
s
=
1
,
alpha
=
0.15
)
plt
.
scatter
(
centroids
[:,
0
],
centroids
[:,
1
],
s
=
1000
*
weights
)
plt
.
legend
([
"
Data
"
,
"
Centroids
"
])
plt
.
show
()
print
(
"
SSE from sketch: {}
"
.
format
(
pycle
.
utils
.
SSE
(
X
,
centroids
)))
# Compare to k-means
from
sklearn.cluster
import
KMeans
kmeans_estimator
=
KMeans
(
n_clusters
=
K
)
kmeans_estimator
.
fit
(
X
)
centroids_kmeans
=
kmeans_estimator
.
cluster_centers_
print
(
"
SSE from k-means: {}
"
.
format
(
pycle
.
utils
.
SSE
(
X
,
centroids_kmeans
)))
```
%% Output
SSE from sketch: 1018.8545093592352
SSE from k-means: 990.8373999288126
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