Clustering.Rmd

---
title: "Cluster analysis"
author: "Leo Lahti, Sudarshan Shetty et al."
bibliography: 
- bibliography.bib
output:
  BiocStyle::html_document:
    number_sections: no
    toc: yes
    toc_depth: 4
    toc_float: true
    self_contained: true
    thumbnails: true
    lightbox: true
    gallery: true
    use_bookdown: false
    highlight: haddock
---
<!--
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteIndexEntry{microbiome tutorial - clustering}
  %\usepackage[utf8]{inputenc}
  %\VignetteEncoding{UTF-8}  
-->


## Multivariate (infinite) Gaussian mixture model

Fit and visualize Variational Dirichlet process multivariate infinite Gaussian mixture. This variational version has been partially written in C and it is relatively fast. Kindly cite [this article](http://bioinformatics.oxfordjournals.org/content/26/21/2713.short). Note that the implementation uses diagonal covariances on the Gaussian modes. The C code was partially derived from [Honkela et al. 2008](http://www.sciencedirect.com/science/article/pii/S0925231208000659).

```{r LCA2, fig.width=6, fig.height=5, warning=FALSE, message=FALSE, eval=FALSE}
library(netresponse)

# Generate simulated data
res <- generate.toydata(Dim = 2)
D <- res$data
component.means <- res$means
component.sds   <- res$sds

# Fit the mixture
m <- mixture.model(D, mixture.method = "vdp", pca.basis = FALSE)

# Plot the data, and indicate estimated modes with colors. 
# If data dimensionality exceeds 2, 
# the results are visualized on PCA projection
# (with pca.basis = TRUE the data is projected on PCA coordinates;
# without loss of information. This trick can help to avoid overlearning 
# as the variational mixture relies
# on diagonal covariance matrices, so the ellipsoidal axes of the 
# Gaussian modes are parallel to the coordinate axes.)
p <- PlotMixtureMultivariate(D, means = m$mu, sds = m$sd, ws = m$w, modes = apply(m$qofz,1,which.max))
plot(p)
```

## Univariate (infinite) Gaussian mixture model

Fit and visualize Variational Dirichlet process univariate infinite Gaussian mixture. Kindly cite [this article](http://bioinformatics.oxfordjournals.org/content/26/21/2713.short) for the code.

```{r LCA1, fig.width=7, fig.height=5, warning=FALSE, message=FALSE, eval=FALSE}
# Generate simulated bimodal univariate data
x <- c(rnorm(200), rnorm(200, mean = 5))

# Variational Dirichlet process univariate Gaussian mixture
m <- mixture.model(x, mixture.method = "vdp", max.responses = 10) 

# Plot the data and estimated modes
p <- PlotMixtureUnivariate(x, means = m$mu, sds = m$sd, ws = m$w, binwidth = 0.1, qofz = m$qofz)

plot(p)
```

## Clustering samples with mixed variables

Gower distance is useful for samples with mixed-type variables (binary, factor, numeric)):

```{r clustering-gower, fig.width=10, fig.height=4, warning=FALSE, message=FALSE, eval=FALSE}
# Example data
data("dietswap")

library(FD)
d <- gowdis(as(sample_data(dietswap), "data.frame"))

plot(hclust(d))
```