/
barycenter.py
executable file
·143 lines (115 loc) · 4.52 KB
/
barycenter.py
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
132
133
134
135
136
137
138
139
140
141
142
143
#!/usr/bin/python
# -*- coding: utf-8 -*-
# Filename: barycenter.py
# G-mode barycenter
# Escrevendo em python3 e usando python2.6:
from __future__ import print_function, unicode_literals, absolute_import, division
##### IMPORT ######
from numpy import array, median, amax, amin, argmax, where, histogramdd, unravel_index, diagonal, fabs
from numpy import all as aall
from numpy import sum as asum
from scipy.spatial import cKDTree
from itertools import tee, izip, imap
from collections import Counter, deque
# functions
# MAD
def mad(X, K=1.4826):
return K*median(fabs(X - median(X, axis=0)), axis=0)
# boolean function
boo = lambda x, xlim: x <= xlim[1] and x >= xlim[0]
def mad(X, K=1.4826):
return K*median(fabs(X - median(X, axis=0)), axis=0)
def boolist(index, values, lim):
if all([boo(item[0],item[1]) for item in izip(values,lim)]):
return index
def pairwise(iterable):
"s -> (s0,s1), (s1,s2), (s2, s3), ..."
a, b = tee(iterable)
next(b, None)
return izip(a, b)
def volume(lst):
p = 1
for i in lst: p *= i[1] - i[0]
return p
#
# K-Nearest Neighbours
#
def barycenter_KNN(data, index, label):
''' KNN with closest pairs'''
#print(len(index))
tree = cKDTree(data[index],leafsize=int(data.shape[0]/2))
closest = deque()
for ind, item in enumerate(data[index]):
i = int(tree.query(item, k=2)[1][1])
if label[i] != label[ind]:
closest.append(i)
else:
closest.append(None)
score = Counter(closest)
popular = score.most_common(2)
common = popular[0][0]
neigh = popular[0][1]
if common == None:
common = popular[1][0]
neigh = popular[1][1]
#print(popular)
if neigh > 1:
seed = [i for i, item in enumerate(closest) if item == common]
seed.append(common)
return map(lambda j: index[j], set(seed))
else:
return []
#
# Divide the sample in sectors, select the most crowded one,
# and find the most popular one and his friends to be the seed.
#
def barycenter_hist(grid, design, data, minsize=5):
''' KNN with histogramdd.'''
upper = amax(data, axis=0)
lower = amin(data, axis=0)
rng = range(data.shape[1])
nbin = map(int,array([grid]*data.shape[1]))
hist, edges = histogramdd(data,bins=nbin,range=tuple(zip(lower, upper)))
ind = unravel_index(argmax(hist), hist.shape)
if amax(hist) > minsize:
del hist
limits = array([list(pairwise(edges[i])) for i in rng])
zone = [limits[i][j] for i, j in izip(rng,ind)]
elems_ind = filter(lambda x: x != None, \
imap(lambda i, y: boolist(i,y,zone), range(data.shape[0]), data))
return barycenter_KNN(data, elems_ind, design)
else:
grid = grid - 1
if grid > 0:
return barycenter_hist(grid, design, data)
else:
return []
#
# Initial seed by density. Recursive histogramdd.
#
def barycenter_density(data, grid, upper, lower, vmin, dens = 0e0):
''' Recursively search for the initial seed on the densest regions of the sample.
Uses numpy.histogramdd to divide multidimensional samples on regions. '''
rng = range(data.shape[1])
# Number of division on each variable
nbin = map(int,array([grid]*data.shape[1]))
# Define the number of points (hist) and the limits (edges) on each region.
hist, edges = histogramdd(data,bins=nbin,range=tuple(zip(lower, upper)))
# Transform the limits into a paired list.
limits = array([list(pairwise(edges[i])) for i in rng])
# Find the indexes of the region limits that contains the max number of points.
ind = unravel_index(argmax(hist), hist.shape)
# Define the zone containing the maximum number of points.
zone = array([limits[i,j] for i, j in izip(rng, ind)])
# Calculate density:
density = amax(hist) / volume(zone)
# Elements inside the zone:
inside = filter(lambda x: x != None, \
imap(lambda i, y: boolist(i,y,zone), xrange(data.shape[0]), data))
# If density keep growing and vmin not reached, the function works recursively.
# Stops when any of thoses conditions are not satisfied anymore.
if density > dens and aall(mad(data[inside]) > diagonal(vmin)):
zone = zone.T
return barycenter_density(data, grid, zone[1], zone[0], vmin, density)
else:
return inside