squat

Statistics for QUAternion Temporal data

https://github.com/lmjl-alea/squat

Repository

Statistics for QUAternion Temporal data

README.Rmd

---
output: github_document
---



```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```

# squat


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The goal of squat is to provide extensions of common statistical methods for the
analysis of unit quaternion time series. Available statistical methods for QTS 
samples are currently: 

* random generation according to the Gaussian functional model via 
[`rnorm_qts()`](https://lmjl-alea.github.io/squat/reference/rnorm_qts.html), 
* [`scale()`](https://lmjl-alea.github.io/squat/reference/scale.html), 
* [`mean()`](https://lmjl-alea.github.io/squat/reference/mean.qts_sample.html), 
* [`median()`](https://lmjl-alea.github.io/squat/reference/median.qts_sample.html),
* distance matrix computation via 
[`dist()`](https://lmjl-alea.github.io/squat/reference/dist.html) including the 
possibility of separating amplitude and phase variability,
* tangent principal component analysis via [`prcomp()`](https://lmjl-alea.github.io/squat/reference/prcomp.qts_sample.html),
* k-means with optional alignment via [`kmeans()`](https://lmjl-alea.github.io/squat/reference/kmeans.html).

## Installation

You can install the official version from CRAN via:
``` r
install.packages("squat")
```
or you can opt to install the development version from [GitHub](https://github.com/) with:
``` r
# install.packages("devtools")
devtools::install_github("LMJL-Alea/squat")
```

## Example

```{r, message=FALSE}
library(squat)
```

First, let us visualize the sample of QTS from the `vespa64` dataset included in the package. The package provides two ways of doing this: either via a static plot or via an animated one (which uses [**gganimate**](https://gganimate.com) behind the scenes and will prompt you to install it in case you have not already).

Here is the static version:
```{r}
plot(vespa64$igp)
```

You can also use `ggplot2::autoplot()` instead of `plot()` to save the resulting `ggplot` object for further customization.

Here is the animated version:
```{r, eval = FALSE,message = FALSE, warning = FALSE, results = FALSE}
p <- ggplot2::autoplot(vespa64$igp, with_animation = TRUE)
gganimate::anim_save("man/figures/README-animated-plot.gif", p)
```

You can compute the geometric mean of the sample and append it to the sample for visualization:

```{r}
m <- mean(vespa64$igp)
sample_and_mean <- append(vespa64$igp, m)
plot(sample_and_mean, highlighted = c(rep(FALSE, 64), TRUE))
```

You can compute the pairwise distance matrix (based on the DTW for now):
```{r}
D <- dist(
  vespa64$igp,
  is_domain_interval = TRUE,
  transformation = "srvf",
  metric = "l2",
  warping_class = "bpd"
)
C <- exp(-D / (sqrt(2) * sd(D)))
C <- (C - min(C)) / diff(range(C))
C <- C |> 
  as.matrix() |> 
  corrr::as_cordf()
corrr::network_plot(C)
```

You can perform tangent principal component analysis and visualize it:
```{r}
tpca <- prcomp(vespa64$igp)
plot(tpca, what = "PC1")
plot(tpca, what = "scores")
screeplot(tpca)
```

You can finally perform a k-means clustering and visualize it:
```{r}
km <- kmeans(
  vespa64$igp,
  n_clusters = 2,
  is_domain_interval = TRUE,
  transformation = "srvf",
  warping_class = "bpd"
)
plot(km)
```

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