---
title: "Quick Start with Rdimtools Package"
# in order to solve discrepancy in the title, do
# > options(rmarkdown.html_vignette.check_title = FALSE)
author: Kisung You
#date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
#output:
  #pdf_document:
   # fig_caption: true
vignette: >
  %\VignetteIndexEntry{Quick Start with Rdimtools Package}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

In this vignette, we will demonstrate basic functionalities of **Rdimtools** package by walking through from installation to analysis with the famous *iris* dataset. 


## 1. Install and Load

**Rdimtools** can be installed in two handy options. A release version from CRAN can be installed
```{r eval=FALSE}
install.packages("Rdimtools")
```
or a development version is available from GitHub with `devtools` package.
```{r eval=FALSE}
## install.packages("devtools")
devtools::install_github("kisungyou/Rdimtools")
```

Now we are ready to go by loading the library.
```{r setup, message=FALSE, warning=FALSE}
library(Rdimtools)
```

## 2. Intrinsic Dimension Estimation


```{r echo=FALSE, include=FALSE}
vernow = utils::packageVersion("Rdimtools")
ndo    = (sum(unlist(lapply(ls("package:Rdimtools"), startsWith, "do."))))
nest   = (sum(unlist(lapply(ls("package:Rdimtools"), startsWith, "est."))))
```

As of current release version `r vernow`, there are `r nest` intrinsic dimension estimation (IDE) algorithms. In the following example, we will only show 5 methods' performance.


```{r message=FALSE, warning=FALSE, fig.align='center', fig.width=7, fig.height=3}
# load the iris data
X   = as.matrix(iris[,1:4])
lab = as.factor(iris[,5])

# we will compare 5 methods (out of 17 methods from version 1.0.0)
vecd = rep(0,5)
vecd[1] = est.Ustat(X)$estdim       # convergence rate of U-statistic on manifold
vecd[2] = est.correlation(X)$estdim # correlation dimension
vecd[3] = est.made(X)$estdim        # manifold-adaptive dimension estimation
vecd[4] = est.mle1(X)$estdim        # MLE with Poisson process
vecd[5] = est.twonn(X)$estdim       # minimal neighborhood information

# let's visualize
plot(1:5, vecd, type="b", ylim=c(1.5,3.5), 
     main="estimating dimension of iris data",
     xaxt="n",xlab="",ylab="estimated dimension")
xtick = seq(1,5,by=1)
axis(side=1, at=xtick, labels = FALSE)
text(x=xtick,  par("usr")[3], 
     labels = c("Ustat","correlation","made","mle1","twonn"), pos=1, xpd = TRUE)
```

As the true dimension is not known for a given dataset, different methods bring about heterogeneous estimates. That's why we deliver 17 methods at an unprecedented scale to provide a broader basis for your decision.

## 3. Dimension Reduction

Currently, **Rdimtools** (ver `r vernow`) delivers `r ndo` dimension reduction/feature selection/manifold learning algorithms. Among a myriad of methods, we compare Principal Component Analysis (`do.pca`), Laplacian Score (`do.lscore`), and Diffusion Maps (`do.dm`) are compared, each from a family of algorithms for linear reduction, feature extraction, and nonlinear reduction.

```{r message=FALSE, warning=FALSE, fig.align='center', fig.width=7}
# run 3 algorithms mentioned above
mypca = do.pca(X, ndim=2)
mylap = do.lscore(X, ndim=2)
mydfm = do.dm(X, ndim=2, bandwidth=10)

# extract embeddings from each method
Y1 = mypca$Y
Y2 = mylap$Y
Y3 = mydfm$Y
  
# visualize
par(mfrow=c(1,3))
plot(Y1, pch=19, col=lab, xlab="axis 1", ylab="axis 2", main="PCA")
plot(Y2, pch=19, col=lab, xlab="axis 1", ylab="axis 2", main="Laplacian Score")
plot(Y3, pch=19, col=lab, xlab="axis 1", ylab="axis 2", main="Diffusion Maps")
```

As the figure above shows, in general, different algorithms show heterogeneous nature of the data. We hope **Rdimtools** be a valuable toolset to help practitioners and scientists discover many facets of the data.
