---
title: Using anomalous
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Using anomalous}
  %\VignetteEngine{knitr::knitr}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
                    collapse = TRUE,
                    comment = "#>"
                  )
```
The purpose of this vignette is to present a basic introductions and demonstrate the uses of the anomalous package.

# Context

The package contains native R implementations of the [PELT](https://doi.org/10.1080/01621459.2012.737745) and [CAPA](https://doi.org/10.1002/sam.11586) algorithms for changepoint and anomaly detection.
While slower then the optimised implementations found in the `changepoint` and `anomaly` packages repectively the results from use of this package should be identical; while the code structure is designed to make it easier to develop new cost functions. Currently this package does not support the full range of multivariate series partioning in the `changepoint` and `anomaly` packages.

The implementation in this package is build around an `S3` class `anomalous_partition` for storing information about the partitiaioning of the data and `R6` classes for the cost functions relating to fitting different distributions to the data.

The CAPA and PELT implementations make use of the methods of the `anomalous_partition` class. This allows for the replacement of the current `anomalous_partition` class with a new class with similarly names methods. 
The structure and creation of the `R6` classes for cost functions are outlined in a [seperate vignette](creating_cost_function.html)

To demonstrate the us o the package we used the data shown in Fig. 4 of <Lai et al. (2005)> who compare different methods for segmenting array comparative genomic hy-
bridization (aCGH) data from Glioblastoma multiforme (GBM), a type of brain tumor. These
arrays were developed to identify DNA copy number alteration corresponding to chromosomal
aberrations. High-throughput aCGH data are intensity ratios of diseased vs. control samples
indexed by the location on the genome. Values greater than 1 indicate diseased samples have
additional chromosomes and values less than 1 indicate fewer chromosomes. Detection of
these aberrations can aid future screening and treatments of diseases.

The data are included in the package and can be loaded with

```{r,setup}
library(anomalous)
data("Lai2005fig4")
y <- Lai2005fig4[, 5]
```

# Using CAPA for anomalies

Start by considering the detection of abberations as an anomaly problem.
Following the analysis presented in <rf killick> we model the data using a Normal distribution with a piecewise constant mean fitted with a likelihood based cost function. Assuming the mean, without abberations would be 0, we robustly estimate the standard deviation and set the cost as
```{r, capa_cost}
fCost <- gaussMean$new(y,m=0,s=median(abs(y)))
```
To match the penalites for the introduction of collective and point anomalies to the defaults in the `anomaly` package the record of the partions is created using
```{r, capa_rec}
p <- partition(beta = 4*log(length(y)), ## collective anomaly penalty
               betaP = 3*log(length(y)), ## point anomaly penalty
               min_length = 2 ## minimuum length of a collective anomaly
               )
```
The CAPA algorithm can then be run
```{r, run_capa}
res <- capa(p,fCost)
```
Calling the summary method of the output shows the same partitions as found in <gross> are detected.
```{r, summary_capa}
summary(res)
```
while the results can be plotted on the data using
```{r, out.width="70%"}
plot(res,yy=y)
```

# Using PELT for change points

This section repeats the Glioblastoma case study of <ref> to allow comparision in the usage of this package to the <changepoint> package which impliments PELT in C for a smaller number of cost functions.

The cost function is set up in exactly the same way as for the CAPA analyis.
The penalty for the penalisation of the introduction of a new segment is based on the BIC. An `anomalous_partion` can be created using this penalty
```{r, pelt_partition}
p <- partition(beta = 2*log(length(y)), betaP = NA, min_length=2)
```
Note that the partition veiws the changepoint segments as a series of collective anomalies, so there is no need to specify a point anomaly penalty.
Computing the partitioning
```{r, pelt_solve}
res <- pelt(p,fCost)
```
and plotting the outcome
```{r, pelt_plot, out.width="70%"}
plot(res,yy=y)
```

shows idientical results to <>.

# CROPS for varaible penalties

<> build upon PELT to provide a efficent algorithm for searhcing over the penalty term in the changepoint problem to determine, 
for a range of penalties, the possible changepoint locations. This algorithm is also suitable for use with CAPA so long as the point anomaly penalty is fixed.

Building upon the changepoint analysis we can consider the identification as an an anomaly problem. Since it is expected that the value is 0 mean we can look for changes around this by specifying the mean and variance of the background distribution
```{r, crops}
fCost <- gaussMean$new(y, m = 0,s = median(abs(y)), point_type="mean")
```
The analysis for a single set of penalties could proceed as before but instead let us consider using crops to study a range of penalties
```{r, crops_sim}
p <- crops(log(length(y)), 6*log(length(y)), fCost, alg=capa, betaP = 2*log(length(y)), min_length=2)
```

The output contains the `anomalous_partition` classes for different numbers of collective anomalies which can be plotted in the usual way.
```{r, crops_plot, out.width="70%"}
plot(p$outRec[["4"]],yy=y,main="Three collective anomalies")
plot(p$outRec[["5"]],yy=y,main="Five collective anomalies")
```