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6. Artificial Datasets with Scikit-Learn

By Bernd Klein. Last modified: 22 Feb 2022.

Generate Synthetical Data with Python

A problem with machine learning, especially when you are starting out and want to learn about the algorithms, is that it is often difficult to get suitable test data. Some cost a lot of money, others are not freely available because they are protected by copyright. Therefore, artificially generated test data can be a solution in some cases.

For this reason, this chapter of our tutorial deals with the artificial generation of data. This chapter is about creating artificial data. In the previous chapters of our tutorial we learned that Scikit-Learn (sklearn) contains different data sets. On the one hand, there are small toy data sets, but it also offers larger data sets that are often used in the machine learning community to test algorithms or also serve as a benchmark. It provides us with data coming from the 'real world'.

Robots creating data

All this is great, but in many cases this is still not sufficient. Maybe you find the right kind of data, but you need more data of this kind or the data is not completely the kind of data you were looking for, e.g. maybe you need more complex or less complex data. This is the point where you should consider to create the data yourself. Here, sklearn offers help. It includes various random sample generators that can be used to create custom-made artificial datasets. Datasets that meet your ideas of size and complexity.

The following Python code is a simple example in which we create artificial weather data for some German cities. We use Pandas and Numpy to create the data:

import numpy as np
import pandas as pd


cities = ['Berlin', 'Frankfurt', 'Hamburg', 
          'Nuremberg', 'Munich', 'Stuttgart',
          'Hanover', 'Saarbruecken', 'Cologne',
          'Constance', 'Freiburg', 'Karlsruhe'
         ]

n= len(cities)
data = {'Temperature': np.random.normal(24, 3, n),
        'Humidity': np.random.normal(78, 2.5, n),
        'Wind': np.random.normal(15, 4, n)
       }
df = pd.DataFrame(data=data, index=cities)
df
Temperature Humidity Wind
Berlin 26.121739 74.845777 15.373365
Frankfurt 20.420286 81.056835 14.856911
Hamburg 29.193375 80.978768 16.336794
Nuremberg 21.942546 80.720798 15.202862
Munich 21.458094 78.741256 12.417495
Stuttgart 23.876411 77.805232 13.613026
Hanover 23.903780 77.796696 4.735164
Saarbruecken 20.874207 82.651544 17.887182
Cologne 25.578876 78.312430 14.697579
Constance 28.072362 76.546416 13.577886
Freiburg 22.873955 76.374111 13.824095
Karlsruhe 25.357613 83.042720 19.233689

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Another Example

We will create artificial data for four nonexistent types of flowers. If the names remind you of programming languages and pizza, it will be no coincidence:

The RGB avarage colors values are correspondingly:

The average diameter of the calyx is:

Flos pythonem
(254, 0, 0)
Flos Java
(245, 107, 0)
Flos margarita
(206, 99, 1)
Flos artificialis
(255, 254, 101)
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

from scipy.stats import truncnorm

def truncated_normal(mean=0, sd=1, low=0, upp=10):
    return truncnorm(
        (low - mean) / sd, (upp - mean) / sd, loc=mean, scale=sd)

def truncated_normal_floats(mean=0, sd=1, low=0, upp=10, num=100):
    res = truncated_normal(mean=mean, sd=sd, low=low, upp=upp)
    return res.rvs(num)

def truncated_normal_ints(mean=0, sd=1, low=0, upp=10, num=100):
    res = truncated_normal(mean=mean, sd=sd, low=low, upp=upp)
    return res.rvs(num).astype(np.uint8)

# number of items for each flower class:
number_of_items_per_class = [190, 205, 230, 170]
flowers = {}
# flos Pythonem:
number_of_items = number_of_items_per_class[0]
reds = truncated_normal_ints(mean=254, sd=18, low=235, upp=256,
                             num=number_of_items)
greens = truncated_normal_ints(mean=107, sd=11, low=88, upp=127,
                             num=number_of_items)
blues = truncated_normal_ints(mean=0, sd=15, low=0, upp=20,
                             num=number_of_items)
calyx_dia = truncated_normal_floats(3.8, 0.3, 3.4, 4.2,
                             num=number_of_items)
data = np.column_stack((reds, greens, blues, calyx_dia))
flowers["flos_pythonem"] = data

# flos Java:
number_of_items = number_of_items_per_class[1]
reds = truncated_normal_ints(mean=245, sd=17, low=226, upp=256,
                             num=number_of_items)
greens = truncated_normal_ints(mean=107, sd=11, low=88, upp=127,
                             num=number_of_items)
blues = truncated_normal_ints(mean=0, sd=10, low=0, upp=20,
                             num=number_of_items)
calyx_dia = truncated_normal_floats(3.3, 0.3, 3.0, 3.5,
                             num=number_of_items)
data = np.column_stack((reds, greens, blues, calyx_dia))
flowers["flos_java"] = data

# flos Java:
number_of_items = number_of_items_per_class[2]
reds = truncated_normal_ints(mean=206, sd=17, low=175, upp=238,
                             num=number_of_items)
greens = truncated_normal_ints(mean=99, sd=14, low=80, upp=120,
                             num=number_of_items)
blues = truncated_normal_ints(mean=1, sd=5, low=0, upp=12,
                             num=number_of_items)
calyx_dia = truncated_normal_floats(4.1, 0.3, 3.8, 4.4,
                             num=number_of_items)
data = np.column_stack((reds, greens, blues, calyx_dia))
flowers["flos_margarita"] = data

# flos artificialis:
number_of_items = number_of_items_per_class[3]
reds = truncated_normal_ints(mean=255, sd=8, low=2245, upp=2255,
                             num=number_of_items)
greens = truncated_normal_ints(mean=254, sd=10, low=240, upp=255,
                             num=number_of_items)
blues = truncated_normal_ints(mean=101, sd=5, low=90, upp=112,
                             num=number_of_items)
calyx_dia = truncated_normal_floats(2.9, 0.4, 2.4, 3.5,
                             num=number_of_items)
data = np.column_stack((reds, greens, blues, calyx_dia))
flowers["flos_artificialis"] = data


data = np.concatenate((flowers["flos_pythonem"], 
                      flowers["flos_java"],
                      flowers["flos_margarita"],
                      flowers["flos_artificialis"]
                     ), axis=0)

# assigning the labels
target = np.zeros(sum(number_of_items_per_class)) # 4 flowers
previous_end = 0
for i in range(1, 5):
    num = number_of_items_per_class[i-1]
    beg = previous_end
    target[beg: beg + num] += i
    previous_end = beg + num
    
conc_data = np.concatenate((data, target.reshape(target.shape[0], 1)),
                           axis=1)

np.savetxt("data/strange_flowers.txt", conc_data, fmt="%2.2f",)
import matplotlib.pyplot as plt

target_names = list(flowers.keys())
feature_names = ['red', 'green', 'blue', 'calyx']
n = 4
fig, ax = plt.subplots(n, n, figsize=(16, 16))

colors = ['blue', 'red', 'green', 'yellow']

for x in range(n):
    for y in range(n):
        xname = feature_names[x]
        yname = feature_names[y]
        for color_ind in range(1, len(target_names)+1):
            ax[x, y].scatter(data[target==color_ind, x], 
                             data[target==color_ind, y],
                             label=target_names[color_ind-1],
                             c=colors[color_ind-1])

        ax[x, y].set_xlabel(xname)
        ax[x, y].set_ylabel(yname)
        ax[x, y].legend(loc='upper left')


plt.show() # scatter of strange flowers data

scatter of strange flowers data: Graph 0

Generate Synthetic Data with Scikit-Learn

It is a lot easier to use the possibilities of Scikit-Learn to create synthetic data.

The functionalities available in sklearn can be grouped into

  1. Generators for classifictation and clustering
  2. Generators for creating data for regression
  3. Generators for manifold learning
  4. Generators for decomposition

Generators for Classification and Clustering

We start with the the function make_blobs of sklearn.datasets to create 'blob' like data distributions. By setting the value of centers to n_classes, we determine the number of blobs, i.e. the clusters. n_samples corresponds to the total number of points equally divided among clusters. If random_state is not set, we will have random results every time we call the function. We pass an int to this parameter for reproducible output across multiple function calls.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs

n_classes = 4
data, labels = make_blobs(n_samples=1000, 
                          centers=n_classes, 
                          random_state=100)

labels[:7]

OUTPUT:

array([1, 3, 1, 3, 1, 3, 2])

We will visualize the previously created blob custers with matplotlib:

# some blobs
fig, ax = plt.subplots()

colours = ('green', 'orange', 'blue', "pink")
for label in range(n_classes):
    ax.scatter(x=data[labels==label, 0], 
               y=data[labels==label, 1], 
               c=colours[label], 
               s=40, 
               label=label)

ax.set(xlabel='X',
       ylabel='Y',
       title='Blobs Examples')


ax.legend(loc='upper right')

OUTPUT:

<matplotlib.legend.Legend at 0x7fd5a3e48e80>

some blobs: Graph 1

The centers of the blobs were randomly chosen in the previous example. In the following example we set the centers of the blobs explicitly. We create a list with the center points and pass it to the parameter centers:

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs

centers = [[2, 3], [4, 5], [7, 9]]
data, labels = make_blobs(n_samples=1000, 
                          centers=np.array(centers),
                          random_state=1)

labels[:7]

OUTPUT:

array([0, 1, 1, 0, 2, 2, 2])

Let us have a look at the previously created blob clusters:

# some more blobs
fig, ax = plt.subplots()

colours = ('green', 'orange', 'blue')
for label in range(len(centers)):
    ax.scatter(x=data[labels==label, 0], 
               y=data[labels==label, 1], 
               c=colours[label], 
               s=40, 
               label=label)

ax.set(xlabel='X',
       ylabel='Y',
       title='Blobs Examples')


ax.legend(loc='upper right')

OUTPUT:

<matplotlib.legend.Legend at 0x7fd5a3deb220>

some more blobs: Graph 2

Usually, you want to save your artificially created datasets in a file. For this purpose, we can use the function savetxt from numpy. Before we can do this we have to reaarange our data. Each row should contain both the data and the label:

import numpy as np

labels = labels.reshape((labels.shape[0],1))
all_data = np.concatenate((data, labels), axis=1)
all_data[:7]

OUTPUT:

array([[ 1.72415394,  4.22895559,  0.        ],
       [ 4.16466507,  5.77817418,  1.        ],
       [ 4.51441156,  4.98274913,  1.        ],
       [ 1.49102772,  2.83351405,  0.        ],
       [ 6.0386362 ,  7.57298437,  2.        ],
       [ 5.61044976,  9.83428321,  2.        ],
       [ 5.69202866, 10.47239631,  2.        ]])

For some people it might be complicated to understand the combination of reshape and concatenate. Therefore, you can see an extremely simple example in the following code:

import numpy as np

a = np.array( [[1, 2], [3, 4]])
b = np.array( [5, 6])
b = b.reshape((b.shape[0], 1))
print(b)

x = np.concatenate( (a, b), axis=1)
x

OUTPUT:

[[5]
 [6]]
array([[1, 2, 5],
       [3, 4, 6]])

We use the numpy function savetxt to save the data. Don't worry about the strange name, it is just for fun and for reasons which will be clear soon:

np.savetxt("squirrels.txt", 
           all_data,
           fmt=['%.3f', '%.3f', '%1d'])
all_data[:10]

OUTPUT:

array([[ 1.72415394,  4.22895559,  0.        ],
       [ 4.16466507,  5.77817418,  1.        ],
       [ 4.51441156,  4.98274913,  1.        ],
       [ 1.49102772,  2.83351405,  0.        ],
       [ 6.0386362 ,  7.57298437,  2.        ],
       [ 5.61044976,  9.83428321,  2.        ],
       [ 5.69202866, 10.47239631,  2.        ],
       [ 6.14017298,  8.56209179,  2.        ],
       [ 2.97620068,  5.56776474,  1.        ],
       [ 8.27980017,  8.54824406,  2.        ]])

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Reading the data and conversion back into 'data' and 'labels'

We will demonstrate now, how to read in the data again and how to split it into data and labels again:

file_data = np.loadtxt("squirrels.txt")

data = file_data[:,:-1]
labels = file_data[:,2:]

labels = labels.reshape((labels.shape[0]))

We had called the data file squirrels.txt, because we imagined a strange kind of animal living in the Sahara desert. The x-values stand for the night vision capabilities of the animals and the y-values correspond to the colour of the fur, going from sandish to black. We have three kinds of squirrels, 0, 1, and 2. (Be aware that our squirrals are imaginary squirrels and have nothing to do with the real squirrels of the Sahara!)

# sahara squirrel dataset graph
import matplotlib.pyplot as plt

colours = ('green', 'red', 'blue', 'magenta', 'yellow', 'cyan')
n_classes = 3

fig, ax = plt.subplots()
for n_class in range(0, n_classes):
    ax.scatter(data[labels==n_class, 0], data[labels==n_class, 1], 
               c=colours[n_class], s=10, label=str(n_class))

ax.set(xlabel='Night Vision',
       ylabel='Fur color from sandish to black, 0 to 10 ',
       title='Sahara Virtual Squirrel')


ax.legend(loc='upper right')

OUTPUT:

<matplotlib.legend.Legend at 0x7fd5a3d22100>

sahara squirrel dataset graph: Graph 3

We will train our articifical data in the following code:

from sklearn.model_selection import train_test_split

data_sets = train_test_split(data, 
                       labels, 
                       train_size=0.8,
                       test_size=0.2,
                       random_state=42 # garantees same output for every run
                      )

train_data, test_data, train_labels, test_labels = data_sets
# import model
from sklearn.neighbors import KNeighborsClassifier

# create classifier
knn = KNeighborsClassifier(n_neighbors=8)

# train
knn.fit(train_data, train_labels)

# test on test data:
calculated_labels = knn.predict(test_data)
calculated_labels

OUTPUT:

array([2., 0., 1., 1., 0., 1., 2., 2., 2., 2., 0., 1., 0., 0., 1., 0., 1.,
       2., 0., 0., 1., 2., 1., 2., 2., 1., 2., 0., 0., 2., 0., 2., 2., 0.,
       0., 2., 0., 0., 0., 1., 0., 1., 1., 2., 0., 2., 1., 2., 1., 0., 2.,
       1., 1., 0., 1., 2., 1., 0., 0., 2., 1., 0., 1., 1., 0., 0., 0., 0.,
       0., 0., 0., 1., 1., 0., 1., 1., 1., 0., 1., 2., 1., 2., 0., 2., 1.,
       1., 0., 2., 2., 2., 0., 1., 1., 1., 2., 2., 0., 2., 2., 2., 2., 0.,
       0., 1., 1., 1., 2., 1., 1., 1., 0., 2., 1., 2., 0., 0., 1., 0., 1.,
       0., 2., 2., 2., 1., 1., 1., 0., 2., 1., 2., 2., 1., 2., 0., 2., 0.,
       0., 1., 0., 2., 2., 0., 0., 1., 2., 1., 2., 0., 0., 2., 2., 0., 0.,
       1., 2., 1., 2., 0., 0., 1., 2., 1., 0., 2., 2., 0., 2., 0., 0., 2.,
       1., 0., 0., 0., 0., 2., 2., 1., 0., 2., 2., 1., 2., 0., 1., 1., 1.,
       0., 1., 0., 1., 1., 2., 0., 2., 2., 1., 1., 1., 2.])
from sklearn import metrics

print("Accuracy:", metrics.accuracy_score(test_labels, calculated_labels))

OUTPUT:

Accuracy: 0.97

Other Interesting Distributions

import numpy as np


import sklearn.datasets as ds
data, labels = ds.make_moons(n_samples=150, 
                             shuffle=True, 
                             noise=0.19, 
                             random_state=None)

data += np.array(-np.ndarray.min(data[:,0]), 
                 -np.ndarray.min(data[:,1]))

np.ndarray.min(data[:,0]), np.ndarray.min(data[:,1])

OUTPUT:

(0.0, 0.8397536185996841)
# moon graphs
import matplotlib.pyplot as plt
fig, ax = plt.subplots()

ax.scatter(data[labels==0, 0], data[labels==0, 1], 
               c='orange', s=40, label='oranges')
ax.scatter(data[labels==1, 0], data[labels==1, 1], 
               c='blue', s=40, label='blues')

ax.set(xlabel='X',
       ylabel='Y',
       title='Moons')


#ax.legend(loc='upper right');

OUTPUT:

[Text(0.5, 0, 'X'), Text(0, 0.5, 'Y'), Text(0.5, 1.0, 'Moons')]

moon graphs: Graph 4

We want to scale values that are in a range [min, max] in a range [a, b].

$$f(x) = \frac{(b-a)\cdot(x - min)}{max - min} + a$$

We now use this formula to transform both the X and Y coordinates of data into other ranges:

min_x_new, max_x_new = 33, 88
min_y_new, max_y_new = 12, 20

data, labels = ds.make_moons(n_samples=100, 
                             shuffle=True, 
                             noise=0.05, 
                             random_state=None)

min_x, min_y = np.ndarray.min(data[:,0]), np.ndarray.min(data[:,1])
max_x, max_y = np.ndarray.max(data[:,0]), np.ndarray.max(data[:,1])

#data -= np.array([min_x, 0]) 
#data *= np.array([(max_x_new - min_x_new) / (max_x - min_x), 1])
#data += np.array([min_x_new, 0]) 

#data -= np.array([0, min_y]) 
#data *= np.array([1, (max_y_new - min_y_new) / (max_y - min_y)])
#data += np.array([0, min_y_new]) 



data -= np.array([min_x, min_y]) 
data *= np.array([(max_x_new - min_x_new) / (max_x - min_x), (max_y_new - min_y_new) / (max_y - min_y)])
data += np.array([min_x_new, min_y_new]) 


#np.ndarray.min(data[:,0]), np.ndarray.max(data[:,0])
data[:6]

OUTPUT:

array([[53.07099336, 15.90410956],
       [55.21647263, 19.34394191],
       [45.75636593, 19.54503076],
       [34.24651697, 14.76831821],
       [86.07862392, 16.51836655],
       [76.39415741, 12.73351101]])
def scale_data(data, new_limits, inplace=False ):
    if not inplace:
        data = data.copy()
    min_x, min_y = np.ndarray.min(data[:,0]), np.ndarray.min(data[:,1])
    max_x, max_y = np.ndarray.max(data[:,0]), np.ndarray.max(data[:,1])
    min_x_new, max_x_new = new_limits[0]
    min_y_new, max_y_new = new_limits[1]
    data -= np.array([min_x, min_y]) 
    data *= np.array([(max_x_new - min_x_new) / (max_x - min_x), (max_y_new - min_y_new) / (max_y - min_y)])
    data += np.array([min_x_new, min_y_new]) 
    if inplace:
        return None
    else:
        return data
    
    
data, labels = ds.make_moons(n_samples=100, 
                             shuffle=True, 
                             noise=0.05, 
                             random_state=None)

scale_data(data, [(1, 4), (3, 8)], inplace=True)
data[:10]

OUTPUT:

array([[3.39057004, 3.66886442],
       [2.85764807, 5.69178552],
       [1.74187254, 7.69735938],
       [2.28205797, 4.45884219],
       [2.3737917 , 7.67001322],
       [2.07535734, 4.73062139],
       [2.98442234, 4.98907794],
       [2.90376839, 5.79475827],
       [3.87626907, 5.46100223],
       [2.95439099, 6.25897644]])
# moon graph
fig, ax = plt.subplots()

ax.scatter(data[labels==0, 0], data[labels==0, 1], 
               c='orange', s=40, label='oranges')
ax.scatter(data[labels==1, 0], data[labels==1, 1], 
               c='blue', s=40, label='blues')

ax.set(xlabel='X',
       ylabel='Y',
       title='moons')
 

ax.legend(loc='upper right');

moon graph: Graph 5

import sklearn.datasets as ds
data, labels = ds.make_circles(n_samples=100, 
                             shuffle=True, 
                             noise=0.05, 
                             random_state=None)
fig, ax = plt.subplots()

ax.scatter(data[labels==0, 0], data[labels==0, 1], 
               c='orange', s=40, label='oranges')
ax.scatter(data[labels==1, 0], data[labels==1, 1], 
               c='blue', s=40, label='blues')

ax.set(xlabel='X',
       ylabel='Y',
       title='circles')


ax.legend(loc='upper right')

OUTPUT:

<matplotlib.legend.Legend at 0x7fd5a1dc7220>

artificial-datasets-with-scikit-learn: Graph 6

print(__doc__)

import matplotlib.pyplot as plt

from sklearn.datasets import make_classification
from sklearn.datasets import make_blobs
from sklearn.datasets import make_gaussian_quantiles

plt.figure(figsize=(8, 8))
plt.subplots_adjust(bottom=.05, top=.9, left=.05, right=.95)

plt.subplot(321)
plt.title("One informative feature, one cluster per class", fontsize='small')
X1, Y1 = make_classification(n_features=2, n_redundant=0, n_informative=1,
                             n_clusters_per_class=1)
plt.scatter(X1[:, 0], X1[:, 1], marker='o', c=Y1,
            s=25, edgecolor='k')

plt.subplot(322)
plt.title("Two informative features, one cluster per class", fontsize='small')
X1, Y1 = make_classification(n_features=2, n_redundant=0, n_informative=2,
                             n_clusters_per_class=1)
plt.scatter(X1[:, 0], X1[:, 1], marker='o', c=Y1,
            s=25, edgecolor='k')

plt.subplot(323)
plt.title("Two informative features, two clusters per class",
          fontsize='small')
X2, Y2 = make_classification(n_features=2, 
                             n_redundant=0, 
                             n_informative=2)
plt.scatter(X2[:, 0], X2[:, 1], marker='o', c=Y2,
            s=25, edgecolor='k')

plt.subplot(324)
plt.title("Multi-class, two informative features, one cluster",
          fontsize='small')
X1, Y1 = make_classification(n_features=2, 
                             n_redundant=0, 
                             n_informative=2,
                             n_clusters_per_class=1, 
                             n_classes=3)
plt.scatter(X1[:, 0], X1[:, 1], marker='o', c=Y1,
            s=25, edgecolor='k')


plt.subplot(325)
plt.title("Gaussian divided into three quantiles", fontsize='small')
X1, Y1 = make_gaussian_quantiles(n_features=2, n_classes=3)
plt.scatter(X1[:, 0], X1[:, 1], marker='o', c=Y1,
            s=25, edgecolor='k')

plt.show()  # various graphs

OUTPUT:

Automatically created module for IPython interactive environment

various graphs: Graph 7

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Exercises

Exercise 1

Create two clusters which look similar to this one:

Two clusters separable by a straight line through the origin

Two testsets which are separable with a perceptron without a bias node.

Exercise 2

Create two clusters similar to the following image:

Two clusters not separable by a straight line through the origin

Exercise 3

Create a dataset with five classes "Tiger", "Lion", "Penguin", "Dolphin", and "Python". The sets should look similar to the following diagram:

testset_blobs_and_circle.png

Solutions

Solution to Exercise 1

# solution to exercise1 graph
data, labels = make_blobs(n_samples=100, 
                            cluster_std = 0.5,
                            centers=[[1, 4] ,[4, 1]],
                            random_state=1)

fig, ax = plt.subplots()

colours = ["orange", "green"]
label_name = ["Tigers", "Lions"]
for label in range(0, 2):
    ax.scatter(data[labels==label, 0], data[labels==label, 1], 
               c=colours[label], s=40, label=label_name[label])


ax.set(xlabel='X',
       ylabel='Y',
       title='dataset')


ax.legend(loc='upper right')

OUTPUT:

<matplotlib.legend.Legend at 0x7fd5a1b40370>

solution to exercise1 graph: Graph 8

Solution to Exercise 2

# solution to exercise2 graph
data, labels = make_blobs(n_samples=100, 
                            cluster_std = 0.5,
                            centers=[[2, 2] ,[4, 4]],
                            random_state=1)

fig, ax = plt.subplots()

colours = ["orange", "green"]
label_name = ["ham", "spam"]
for label in range(0, 2):
    ax.scatter(data[labels==label, 0], data[labels==label, 1], 
               c=colours[label], s=40, label=label_name[label])


ax.set(xlabel='X',
       ylabel='Y',
       title='dataset')


ax.legend(loc='upper right')

OUTPUT:

<matplotlib.legend.Legend at 0x7fd5a1aad550>

solution to exercise2 graph: Graph 9

Solution to Exercise 3

import sklearn.datasets as ds
data, labels = ds.make_circles(n_samples=100, 
                               shuffle=True, 
                               noise=0.05, 
                               random_state=42)

centers = [[3, 4], [5, 3], [4.5, 6]]
data2, labels2 = make_blobs(n_samples=100, 
                            cluster_std = 0.5,
                            centers=centers,
                            random_state=1)


#for i in range(len(centers)-1, -1, -1):
#    labels2[labels2==0+i] = i+2
labels2 += +2
    
print(labels2)
labels = np.concatenate([labels, labels2])
data = data * [1.2, 1.8] + [3, 4]

data = np.concatenate([data, data2], axis=0)

OUTPUT:

[2 4 4 3 4 4 3 3 2 4 4 2 4 4 3 4 2 4 4 4 4 2 2 4 4 3 2 2 3 2 2 3 2 3 3 3 3
 3 4 3 3 2 3 3 3 2 2 2 2 3 4 4 4 2 4 3 3 2 2 3 4 4 3 3 4 2 4 2 4 3 3 4 2 2
 3 4 4 2 3 2 3 3 4 2 2 2 2 3 2 4 2 2 3 3 4 4 2 2 4 3]
# solution graph
fig, ax = plt.subplots()

colours = ["orange", "blue", "magenta", "yellow", "green"]
label_name = ["Tiger", "Lion", "Penguin", "Dolphin", "Python"]
for label in range(0, len(centers)+2):
    ax.scatter(data[labels==label, 0], data[labels==label, 1], 
               c=colours[label], s=40, label=label_name[label])


ax.set(xlabel='X',
       ylabel='Y',
       title='dataset')


ax.legend(loc='upper right')

OUTPUT:

<matplotlib.legend.Legend at 0x7fd5a1a61d00>

solution graph: Graph 10

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