1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
|
"""
Simple example datasets for OT
"""
import numpy as np
import scipy as sp
def get_1D_gauss(n,m,s):
"""return a 1D histogram for a gaussian distribution (n bins, mean m and std s)
Parameters
----------
n : int
number of bins in the histogram
m : float
mean value of the gaussian distribution
s : float
standard deviaton of the gaussian distribution
Returns
-------
h : np.array (n,)
1D histogram for a gaussian distribution
"""
x=np.arange(n,dtype=np.float64)
h=np.exp(-(x-m)**2/(2*s**2))
return h/h.sum()
def get_2D_samples_gauss(n,m,sigma):
"""return n samples drawn from 2D gaussian N(m,sigma)
Parameters
----------
n : int
number of bins in the histogram
m : np.array (2,)
mean value of the gaussian distribution
sigma : np.array (2,2)
covariance matrix of the gaussian distribution
Returns
-------
X : np.array (n,2)
n samples drawn from N(m,sigma)
"""
if np.isscalar(sigma):
sigma=np.array([sigma,])
if len(sigma)>1:
P=sp.linalg.sqrtm(sigma)
res= np.random.randn(n,2).dot(P)+m
else:
res= np.random.randn(n,2)*np.sqrt(sigma)+m
return res
def get_data_classif(dataset,n,nz=.5,theta=0,**kwargs):
""" dataset generation for classification problems
Parameters
----------
dataset : str
type of classification problem (see code)
n : int
number of training samples
nz : float
noise level (>0)
Returns
-------
X : np.array (n,d)
n observation of size d
y : np.array (n,)
labels of the samples
"""
if dataset.lower()=='3gauss':
y=np.floor((np.arange(n)*1.0/n*3))+1
x=np.zeros((n,2))
# class 1
x[y==1,0]=-1.; x[y==1,1]=-1.
x[y==2,0]=-1.; x[y==2,1]=1.
x[y==3,0]=1. ; x[y==3,1]=0
x[y!=3,:]+=1.5*nz*np.random.randn(sum(y!=3),2)
x[y==3,:]+=2*nz*np.random.randn(sum(y==3),2)
elif dataset.lower()=='3gauss2':
y=np.floor((np.arange(n)*1.0/n*3))+1
x=np.zeros((n,2))
y[y==4]=3
# class 1
x[y==1,0]=-2.; x[y==1,1]=-2.
x[y==2,0]=-2.; x[y==2,1]=2.
x[y==3,0]=2. ; x[y==3,1]=0
x[y!=3,:]+=nz*np.random.randn(sum(y!=3),2)
x[y==3,:]+=2*nz*np.random.randn(sum(y==3),2)
elif dataset.lower()=='gaussrot' :
rot=np.array([[np.cos(theta),np.sin(theta)],[-np.sin(theta),np.cos(theta)]])
m1=np.array([-1,1])
m2=np.array([1,-1])
y=np.floor((np.arange(n)*1.0/n*2))+1
n1=np.sum(y==1)
n2=np.sum(y==2)
x=np.zeros((n,2))
x[y==1,:]=get_2D_samples_gauss(n1,m1,nz)
x[y==2,:]=get_2D_samples_gauss(n2,m2,nz)
x=x.dot(rot)
else:
x=0
y=0
print("unknown dataset")
return x,y
|
