Lab 1: Introduction to Python#
Loading data#
Boston data#
import pandas as pd
import numpy as np
data_url = "http://lib.stat.cmu.edu/datasets/boston"
raw_df = pd.read_csv(data_url, sep="\s+", skiprows=22, header=None)
data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])
target = raw_df.values[1::2, 2]
data dimension#
print(data.shape)
(506, 13)
subset of data#
data[:,1]
data[1:3,0:2]
array([[0.02731, 0. ],
[0.02729, 0. ]])
Iris data#
from sklearn.datasets import load_iris
iris = load_iris()
print(iris.data.shape)
print(iris.target_names)
(150, 4)
['setosa' 'versicolor' 'virginica']
The first two features#
X = iris.data[:, :2]
y = iris.target
Plot the first two features#
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from sklearn.decomposition import PCA
plt.figure(2, figsize=(8, 6))
plt.clf()
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Set1,
edgecolor='k')
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
plt.xlim(x_min, x_max)
plt.ylim(y_min, y_max)
plt.xticks(())
plt.yticks(())
plt.show()
Plot the first three PCA dimensions#
# Create a figure
fig = plt.figure()
# Add a 3D subplot
ax = fig.add_subplot(111, projection='3d')
X_reduced = PCA(n_components=3).fit_transform(iris.data)
ax.scatter(X_reduced[:, 0], X_reduced[:, 1], X_reduced[:, 2], c=y,
cmap=plt.cm.Set1, edgecolor='k', s=40)
ax.set_title("First three PCA directions")
ax.set_xlabel("1st eigenvector")
ax.set_ylabel("2nd eigenvector")
ax.set_zlabel("3rd eigenvector")
plt.show()
Digit data#
from sklearn.datasets import load_digits
digits = load_digits()
print(digits.data.shape)
print(digits.target)
(1797, 64)
[0 1 2 ... 8 9 8]
Plot an image#
import matplotlib.pyplot as plt
plt.gray()
plt.matshow(digits.images[17])
plt.show()
<Figure size 640x480 with 0 Axes>
Simulating data#
Generate random numbers [0,1]#
from random import seed
from random import random
seed(14)
for _ in range(10):
value = random()
print(value)
0.10682853770165568
0.7025855239868555
0.6520420203142754
0.9403523895661179
0.27111522656032316
0.25577551343303917
0.7340593641446967
0.6584500182400758
0.3029879738883551
0.6842331280769555
Generate random integers#
from random import seed
from random import randint
# seed random number generator
seed(1)
# generate some integers
for _ in range(10):
value = randint(0, 10)
print(value)
2
9
1
4
1
7
7
7
10
6
Generating a random sample without replacement#
# select a random sample without replacement
from random import seed
from random import sample
# seed random number generator
seed(1)
# prepare a sequence
sequence = [i for i in range(20)]
print(sequence)
# select a subset without replacement
subset = sample(sequence, 5)
print(subset)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
[4, 18, 2, 8, 3]
Generating random numbers from distributions#
import random
# seed random number generator
random.seed(1)
# generate some Gaussian values
print("Normal distribution")
for _ in range(10):
value = random.gauss(0, 1)
print(value)
# generate uniform
print("\nUniform")
for _ in range(10):
value = random.uniform(0, 1)
print(value)
# generate exponential
print("\nExponential")
for _ in range(10):
value = random.expovariate(10)
print(value)
# generate Gamma
print("\nGamma")
value = list(range(10))
for i in range(10):
value[i] = random.gammavariate(1,10)
print(value)
# generate multivariate normal
print("\nMultivariate normal")
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import multivariate_normal
rmvn = np.array([x[:] for x in [[0.1]*2]*10])
for i in range(10):
rmvn[i,] = multivariate_normal.rvs(mean = [0.5, -0.2], cov=[[2.0, 0.3], [0.3, 0.5]])
print(rmvn)
plt.scatter(rmvn[:,0], rmvn[:,1], s= 30*(rmvn[:,0]**2+rmvn[:,1]**2), c="red", alpha=0.5)
Show code cell output
Normal distribution
1.2881847531554629
1.4494456086997711
0.06633580893826191
-0.7645436509716318
-1.0921732151041414
0.03133451683171687
-1.022103170010873
-1.4368294451025299
0.19931197648375384
0.13337460465860485
Uniform
0.8357651039198697
0.43276706790505337
0.762280082457942
0.0021060533511106927
0.4453871940548014
0.7215400323407826
0.22876222127045265
0.9452706955539223
0.9014274576114836
0.030589983033553536
Exponential
0.0025775205901396527
0.07796041064717965
0.27993297008677476
0.04799800085423127
0.02441110881957027
0.054838311851086355
0.0029470817314445606
0.025063251747169862
0.05760534377901244
0.06848065433446529
Gamma
[2.65378588315137, 2.6249077647307697, 2.4689980651293686, 6.15452086198919, 3.4218277115754687, 0.21723971267174863, 18.175572426085274, 8.129544896439866, 10.280448736365472, 2.05679767145641]
Multivariate normal
[[ 0.30650083 -0.89580518]
[ 1.56961999 -0.12427087]
[ 2.18404603 -1.16025976]
[-0.02231196 -1.40528589]
[-0.78170321 0.73021941]
[ 1.52533226 -0.38167431]
[-0.44385809 -0.38314051]
[-0.54355961 -0.01323893]
[-0.49547243 -1.07938955]
[ 0.61724648 -0.98384832]]
<matplotlib.collections.PathCollection at 0x30c64c8e0>
Generate 2D classification points#
from sklearn.datasets import make_blobs
from matplotlib import pyplot
from pandas import DataFrame
# generate 2d classification dataset
X, y = make_blobs(n_samples=100, centers=3, n_features=2)
# scatter plot, dots colored by class value
df = DataFrame(dict(x=X[:,0], y=X[:,1], label=y))
colors = {0:'red', 1:'blue', 2:'green'}
fig, ax = pyplot.subplots()
grouped = df.groupby('label')
for key, group in grouped:
group.plot(ax=ax, kind='scatter', x='x', y='y', label=key, color=colors[key])
pyplot.show()
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Generating circle data for classification#
from sklearn.datasets import make_circles
from matplotlib import pyplot
from pandas import DataFrame
# generate 2d classification dataset
X, y = make_circles(n_samples=100, noise=0.05)
# scatter plot, dots colored by class value
df = DataFrame(dict(x=X[:,0], y=X[:,1], label=y))
colors = {0:'red', 1:'blue'}
fig, ax = pyplot.subplots()
grouped = df.groupby('label')
for key, group in grouped:
group.plot(ax=ax, kind='scatter', x='x', y='y', label=key, color=colors[key])
pyplot.show()
Show code cell output
