forked from rrrlw/visual-tda
-
Notifications
You must be signed in to change notification settings - Fork 0
/
figs-example.R
197 lines (182 loc) · 7.38 KB
/
figs-example.R
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
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
#####SETUP#####
# load library and dataset
library("ggplot2")
library("ggforce")
library("TDAstats")
# reproducibility
set.seed(1)
#####FIGURE 1#####
# load data and convert circle into annulus by adding noise
data("circle2d")
circle2d[, 1] <- circle2d[, 1] + rnorm(nrow(circle2d),
mean = 0, sd = 0.1)
circle2d[, 2] <- circle2d[, 2] + rnorm(nrow(circle2d),
mean = 0, sd = 0.1)
# setup data for visualization
phom.circ <- calculate_homology(circle2d)
temp.phom <- as.data.frame(phom.circ)
temp.phom$pers <- temp.phom$death - temp.phom$birth
temp.phom$dimension <- as.factor(temp.phom$dimension)
# plot circle2d in Cartesian
circ.df <- as.data.frame(circle2d)
colnames(circ.df) <- c("x", "y")
ggplot(data = circ.df, aes(x = x, y = y)) +
geom_point(size = I(1.5)) +
theme_bw() +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15)) +
xlab("X Cartesian coordinate") +
ylab("Y Cartesian coordinate") +
coord_fixed() +
ggtitle("(a) Sample dataset")
ggsave("Fig1a.eps", width = 4.5, height = 3.5)
# plot example of Vietoris-Rips complex
plot.diam <- 0.2
ggplot(data = circ.df) +
geom_circle(aes(x0 = x, y0 = y, r = I(plot.diam / 2)),
colour = NA, fill = "blue", alpha = 0.2) +
geom_point(aes(x = x, y = y),
colour = "white", size = I(1)) +
coord_fixed() +
theme_bw() +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15)) +
xlab("X Cartesian coordinate") +
ylab("Y Cartesian coordinate") +
ggtitle(paste("(b) VR complex for d =",
plot.diam))
ggsave("Fig1b.eps", device = cairo_ps,
width = 4.5, height = 3.5)
# plot conventional persistence diagram for circle2d
plot_persist(phom.circ) +
geom_point(data = temp.phom, aes(x = birth,
y = death,
colour = dimension,
shape = dimension),
size = I(2.5)) +
xlab("Feature appearance") +
ylab("Feature disappearance") +
ggtitle("(c) Diagonal persistence diagram") +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15))
ggsave("Fig1c.eps", width = 4.5, height = 3.5)
# plot flat persistence diagram for circle2d (unused currently)
plot_persist(phom.circ, flat = TRUE) +
geom_point(data = temp.phom, aes(x = birth,
y = pers,
colour = dimension,
shape = dimension),
size = I(2.5)) +
xlab("Feature appearance") +
ylab("Feature persistence") +
ggtitle("Flat persistence diagram") +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15))
ggsave("example-flat.eps", width = 4.5, height = 3.5)
# plot persistence barcode for circle2d; add black separators for JACT
phom.circ <- rbind(phom.circ[phom.circ[, "dimension"] == 0, ],
c(0, 0, 0), c(0, 0, 0), c(0, 0, 0),
phom.circ[phom.circ[, "dimension"] == 1, ])
num_0cycles <- sum(phom.circ[, "dimension"] == 0)
plot_barcode(phom.circ) +
geom_abline(slope = 0, intercept = num_0cycles - 1,
size = 0.25) +
ggtitle("(d) Persistence barcode") +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15))
ggsave("Fig1d.eps", width = 4.5, height = 3.5)
#####OMITTED FIGURE#####
# make bias example for persistence diagrams
phom.bias <- matrix(c(0, 0.5, 1.0,
0, 0.75, 1.1),
byrow = TRUE,
ncol = 3)
colnames(phom.bias) <- c("dimension", "birth", "death")
temp.phom <- as.data.frame(phom.bias)
temp.phom$pers <- temp.phom$death - temp.phom$birth
temp.phom$dimension <- as.factor(temp.phom$dimension)
plot_persist(phom.bias) +
geom_point(data = temp.phom, aes(x = birth,
y = death,
colour = dimension,
shape = dimension),
size = I(2.5)) +
xlab("Feature appearance") +
ylab("Feature disappearance") +
ggtitle("(a) Diagonalpersistence diagram") +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15))
ggsave("example-bias1.eps", width = 4.5, height = 3.5)
plot_persist(phom.bias, flat = TRUE) +
geom_point(data = temp.phom, aes(x = birth,
y = pers,
colour = dimension,
shape = dimension),
size = I(2.5)) +
xlim(c(0, 1)) +
ylim(c(0, 0.6)) +
xlab("Feature appearance") +
ggtitle("(b) Flat persistence diagram") +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15))
ggsave("example-bias2.eps", width = 4.5, height = 3.5)
#####FIGURE 2#####
# make sphere example to highlight benefits
data("sphere3d")
phom.sphere <- calculate_homology(sphere3d, dim = 2)
temp.phom <- as.data.frame(phom.sphere)
temp.phom$pers <- temp.phom$death - temp.phom$birth
temp.phom$dimension <- as.factor(temp.phom$dimension)
# add separators for JACT submission
phom.sphere <- rbind(phom.sphere[phom.sphere[, "dimension"] == 0, ],
c(0, 0, 0), c(0, 0, 0), c(0, 0, 0),
phom.sphere[phom.sphere[, "dimension"] == 1, ],
c(1, 0, 0), c(1, 0, 0), c(1, 0, 0),
phom.sphere[phom.sphere[, "dimension"] == 2, ])
num_0cycles <- sum(phom.sphere[, "dimension"] == 0)
num_1cycles <- sum(phom.sphere[, "dimension"] == 1)
# plot sphere barcode
plot_barcode(phom.sphere) +
ggtitle("(a) Persistence barcode") +
geom_abline(slope = 0,
intercept = num_0cycles - 1,
size = 0.25) +
geom_abline(slope = 0,
intercept = num_0cycles + num_1cycles - 1,
size = 0.25) +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15))
ggsave("Fig2a.eps", width = 4.5, height = 3.5)
plot_persist(phom.sphere) +
geom_point(data = temp.phom, aes(x = birth,
y = death,
colour = dimension,
shape = dimension),
size = I(2.5)) +
xlab("Feature appearance") +
ylab("Feature disappearance") +
ggtitle("(b) Diagonal persistence diagram") +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15))
ggsave("Fig2b.eps", width = 4.5, height = 3.5)
plot_persist(phom.sphere, flat = TRUE) +
geom_point(data = temp.phom, aes(x = birth,
y = pers,
colour = dimension,
shape = dimension),
size = I(2.5)) +
xlab("Feature appearance") +
ggtitle("(c) Flat persistence diagram") +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 14),
plot.title = element_text(size = 15))
ggsave("Fig2c.eps", width = 4.5, height = 3.5)