ripser.noise.Rmd

---
title: "Ripser with Noise"
author: "Ken Wang"
date: "10/7/2020"
output:
  html_document:
    df_print: paged
  pdf_document: default
  html_notebook: default
editor_options:
  chunk_output_type: inline
---

```{r,message=FALSE,warning=FALSE}
library("ripserr")
library(tidyverse)
library(fitdistrplus)
```

```{r}
noise_num = 100
noise = data.frame(replicate(2,runif(noise_num,-1000,1000)))
names(noise) = c("x","y")

radius = 500
jitter = 50
data_num = 1000
a = runif(data_num,0,1) * 2 * pi
r = rnorm(data_num,radius,jitter)
data = data.frame(x = r * cos(a), y = r * sin(a))

dataa = rbind(data,noise)
dataa %>%
  ggplot()+
  geom_point(aes(x=x,y=y))
```

```{r}
rips = vietoris_rips(dataa)

deg0_num = data_num + noise_num - 1
plot1 = data.frame(num=1:deg0_num,length=rips$death[1:deg0_num])

plot1 %>%
  ggplot(aes(x=num,y=length))+
  geom_bar(stat="identity", fill="steelblue")+
  theme_minimal()
```

```{r}
deg1 = rips[(deg0_num+1):nrow(rips),]

deg1 %>%
  ggplot()+
  geom_point(aes(x=birth,y=death))+
  geom_abline(intercept = 0, slope = 1, color = "blue")+
  geom_segment(aes(x=birth,y=death,xend=birth,yend=birth))
```

```{r}
noise_num = 1000
noise = data.frame(replicate(2,runif(noise_num,-1000,1000)))
names(noise) = c("x","y")

radius = 500
jitter = 50
data_num = 1000
a = runif(data_num,0,1) * 2 * pi
r = rnorm(data_num,radius,jitter)
data = data.frame(x = r * cos(a), y = r * sin(a))

dataa = rbind(data,noise)
dataa %>%
  ggplot()+
  geom_point(aes(x=x,y=y))
```

```{r}
rips = vietoris_rips(dataa)

deg0_num = data_num + noise_num - 1
plot1 = data.frame(num=1:deg0_num,length=rips$death[1:deg0_num])

plot1 %>%
  ggplot(aes(x=num,y=length))+
  geom_bar(stat="identity", fill="steelblue")+
  theme_minimal()
```

```{r}
deg1 = rips[(deg0_num+1):nrow(rips),]

deg1 %>%
  ggplot()+
  geom_point(aes(x=birth,y=death))+
  geom_abline(intercept = 0, slope = 1, color = "blue")+
  geom_segment(aes(x=birth,y=death,xend=birth,yend=birth))
```