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import matplotlib.pyplot as plt
import numpy as np
from sklearn import manifold
from sklearn.datasets import load_digits
import seaborn as sns
from sklearn.decomposition import PCA
%matplotlib inline
Load the digits data. This is a classic dataset of images of handwritten digits. It contains 1797 images with (8*8=64) pixels each.
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digits = load_digits()
digits.data.shape
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digits.data stores the images:
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digits.data[0]
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and digits.target is the classes (or labels) that the images belong to. There are 10 classes in total.
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digits.target
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We can display the first image.
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image_shape = (8,8)
plt.imshow( digits.data[0].reshape(image_shape), cmap=plt.cm.gray, interpolation='gaussian' )
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In [6]:
X = np.vstack([digits.data[digits.target==i]
for i in range(10)])
y = np.hstack([digits.target[digits.target==i]
for i in range(10)])
Then initialize a tsne model. For the meaning of the parameters see here.
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tsne = manifold.TSNE(n_components=2, init='pca', random_state=0)
Fit the model on the data.
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digits_proj = tsne.fit_transform(X)
Plot the results. Seaborn's hls palatte provides evenly spaced colors in HLS hue space, we can divide it into 10 colors.
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palette = np.array(sns.color_palette("hls", 10))
Make a scatter plot of the first component against the second component, with color based on the numbers.
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plt.figure(figsize = (6,6))
plt.scatter(digits_proj[:,0], digits_proj[:,1],c=palette[y])
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t-SNE clearly seperates the digits into clusters. We can add some text for each cluster, with the place of the text being the center of the cluster. We can use np.median to find the centers. To make it more convenient, we can make the code into a function.
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def plot_scatter(projection):
plt.figure(figsize = (6,6))
plt.scatter(projection[:,0], projection[:,1],c=palette[y])
for i in range(10):
# Position of each label.
xtext, ytext = np.median(projection[y == i, :], axis=0)
txt = plt.text(xtext, ytext, str(i), fontsize=24)
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plot_scatter(digits_proj)
We talked about MDS and Isomap in class as two other manifold learning methods. Sklearn also has implementations for this two algorithms: MDS and Isomap, so the usage is very similar. Examples for using this methods can be found here.
Can you make another two plots with these two methods? You only need to change the models and call the plot_scatter function.
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#TODO: plot results from MDS and Isomap
isomap = manifold.Isomap(n_components=2, n_neighbors=20)
X_isomap = isomap.fit_transform(X)
plot_scatter(X_isomap)
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MDS = manifold.MDS(n_components=2,max_iter=100, n_init=1)
X_MDS = MDS.fit_transform(X)
plot_scatter(X_MDS)
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from mpl_toolkits.basemap import Basemap
Now we can draw our first map:
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map = Basemap()
map.drawcoastlines()
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The default projection is the Equirectangular projection. We can change to another projection:
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map = Basemap(projection='ortho', lat_0=0, lon_0=0)
map.drawcoastlines()
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lat_0 and lon_0 sets the center of the map. Changing it allows us to see the other parts of the earth.
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map = Basemap(projection='ortho', lat_0=0, lon_0=90)
map.drawcoastlines()
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Fill the continents and oceans with some colors:
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map = Basemap(projection='ortho', lat_0=0, lon_0=0)
map.drawmapboundary(fill_color='aqua')
map.fillcontinents(color='coral',lake_color='aqua')
map.drawcoastlines()
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Add country lines:
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map = Basemap(projection='ortho', lat_0=0, lon_0=0)
map.drawmapboundary(fill_color='aqua')
map.fillcontinents(color='coral',lake_color='aqua')
map.drawcoastlines()
map.drawcountries()
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The map is essentially a matplotlib object, so we can use matplotlib's methods to access it, for example, draw some points on the map.
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map = Basemap(projection='ortho', lat_0=0, lon_0=-30)
map.drawmapboundary(fill_color='aqua')
map.fillcontinents(color='coral',lake_color='aqua')
map.drawcoastlines()
x, y = map(-10, 0) #x=longitude, y=latitude
map.plot(x, y, marker='D',color='m')
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Try with this: put a dot on your favourite city and put its name next to it. You can use the text function. (It may be necessary to rotate your map).
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#TODO: draw a point for a city on the map.
map = Basemap(projection='ortho', lat_0=40, lon_0=-100)
map.drawmapboundary(fill_color='aqua')
map.fillcontinents(color='coral',lake_color='aqua')
map.drawcoastlines()
nylat = 40.78; nylon = -73.98
x, y = map(nylon, nylat)
map.plot(x, y, marker='D',color='r')
plt.text(x, y, 'New York',fontsize=12,fontweight='bold',ha='left',va='center',color='k',
bbox=dict(facecolor='b', alpha=0.2))
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It is also possible to only draw a region within a given "box" by passing the coordinates of the lower-left corner and upper-right corner.
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map = Basemap(llcrnrlon=-10.5,llcrnrlat=35,urcrnrlon=4.,urcrnrlat=44.,
resolution='i', projection='tmerc', lat_0 = 39.5, lon_0 = -3.25)
map.drawmapboundary(fill_color='aqua')
map.fillcontinents(color='coral',lake_color='aqua')
map.drawcoastlines()
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#TODO: plot the region with the city that you just plotted at the center.
map = Basemap(llcrnrlat=40.55,urcrnrlat=40.82,\
llcrnrlon=-74.1, urcrnrlon=-73.82, lat_ts=40.5,resolution='i')
map.drawmapboundary(fill_color='aqua')
map.fillcontinents(color='coral',lake_color='aqua')
map.drawcoastlines()
nylat = 40.78; nylon = -73.98
x, y = map(nylon, nylat)
map.plot(x, y, marker='D',color='r')
plt.text(x, y, 'New York',fontsize=12,fontweight='bold',ha='left',va='center',color='k',
bbox=dict(facecolor='b', alpha=0.2))
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