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File added
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# fix a proximity for a Vietoris complex
prox <- c(0.5, 1.0, 1.5)
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
# point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
# ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
# simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
# ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
# overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
# ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
# fix a proximity for a Vietoris complex
prox <- 0.1
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
# fix a proximity for a Vietoris complex
prox <- 0.5
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
# fix a proximity for a Vietoris complex
prox <- 1.0
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
# fix a proximity for a Vietoris complex
prox <- 1.5
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
# fix a proximity for a Vietoris complex
prox <- 1.9
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
# fix a proximity for a Vietoris complex
prox <- 2.0
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
# fix a proximity for a Vietoris complex
prox <- 1.7
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
# fix a proximity for a Vietoris complex
prox <- 1.6
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
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---
title: "R Notebook"
output: html_notebook
---
This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code.
Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Cmd+Shift+Enter*.
Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Cmd+Option+I*.
When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the *Preview* button or press *Cmd+Shift+K* to preview the HTML file).
The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike *Knit*, *Preview* does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.
```{r}
library(ggplot2)
# attach *ggtda*
library(ggtda)
```
```{r}
# generate the point cloud data
n <- 36; sd <- .2
set.seed(0)
first_column <- c(1.0, 2.0, 1.0, 2.0)
second_column <- c(1.0, 1.0, 2.0, 2.0)
d <- data.frame(
first_column,
second_column
)
# compute the persistent homology
ph <- as.data.frame(ripserr::vietoris_rips(as.matrix(d), dim = 1))
print(head(ph, n = 12))
ph <- transform(ph, dim = as.factor(dimension))
```
```{r}
# fix a proximity for a Vietoris complex
prox <- 1.5
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
ggsave("diamonds3.pdf")
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# combine the plots
gridExtra::grid.arrange(
p_d, p_sc,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
```
```{r}
# visualize the persistence data, indicating cutoffs at this proximity
p_bc <- ggplot(ph,
aes(start = birth, end = death, colour = dim)) +
theme_barcode() +
geom_barcode() +
labs(x = "Diameter", y = "Homological features") +
geom_vline(xintercept = prox, color = "darkgoldenrod", linetype = "dashed")
p_pd <- ggplot(ph) +
theme_persist() +
coord_fixed() +
stat_persistence(aes(start = birth, end = death, colour = dim, shape = dim)) +
geom_abline(intercept = 0, slope = 1, color = "darkgray") +
labs(x = "Birth", y = "Death") +
lims(x = c(0, 0.8), y = c(0, NA)) +
geom_point(data = data.frame(x = prox), aes(x, x),
colour = "darkgoldenrod", shape = "diamond", size = 4)
# combine the plots
gridExtra::grid.arrange(
p_bc, p_pd,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
```
Source diff could not be displayed: it is too large. Options to address this: view the blob.
---
title: "R Notebook"
output: html_notebook
---
This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code.
Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Cmd+Shift+Enter*.
Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Cmd+Option+I*.
When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the *Preview* button or press *Cmd+Shift+K* to preview the HTML file).
The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike *Knit*, *Preview* does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.
```{r}
library(ggplot2)
# attach *ggtda*
library(ggtda)
library(stringr)
```
```{r}
# generate the point cloud data
# noisy circle
n <- 36; sd <- .2
set.seed(0)
t <- stats::runif(n = n, min = 0, max = 2*pi)
d <- data.frame(
first_column = cos(t) + stats::rnorm(n = n, mean = 0, sd = sd),
second_column = sin(t) + stats::rnorm(n = n, mean = 0, sd = sd)
)
# compute the persistent homology
ph <- as.data.frame(ripserr::vietoris_rips(as.matrix(d), dim = 1))
print(head(ph, n = 12))
ph <- transform(ph, dim = as.factor(dimension))
```
```{r}
# fix a proximity for a Vietoris complex
prox <- 1.6
# visualize disks of fixed radii
# Use option theme_void() to get rid of all axis labels
# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
geom_point()
# Save plot as pdf
point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
ggsave(point_cloud_file_name)
# visualize the Vietoris complex for this proximity
p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
ggsave(simplicial_complex_file_name)
p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
theme_bw() +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank()) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
coord_fixed() +
stat_disk(radius = prox/2, fill = "aquamarine3") +
stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
stat_vietoris1(diameter = prox, alpha = .25) +
stat_vietoris0()
# Save plot as pdf
overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
ggsave(overlay_file_name)
# combine the plots
gridExtra::grid.arrange(
p_d, p_overlay,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
```
```{r}
# visualize the persistence data, indicating cutoffs at this proximity
p_bc <- ggplot(ph,
aes(start = birth, end = death, colour = dim)) +
theme_barcode() +
geom_barcode() +
labs(x = "Diameter", y = "Homological features") +
geom_vline(xintercept = prox, color = "darkgoldenrod", linetype = "dashed")
p_pd <- ggplot(ph) +
theme_persist() +
coord_fixed() +
stat_persistence(aes(start = birth, end = death, colour = dim, shape = dim)) +
geom_abline(intercept = 0, slope = 1, color = "darkgray") +
labs(x = "Birth", y = "Death") +
lims(x = c(0, 0.8), y = c(0, NA)) +
geom_point(data = data.frame(x = prox), aes(x, x),
colour = "darkgoldenrod", shape = "diamond", size = 4)
# combine the plots
gridExtra::grid.arrange(
p_bc, p_pd,
layout_matrix = matrix(c(1, 2), nrow = 1)
)
```
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