Lluís Revilla Sancho

In this post I will explain the history behind
[BaseSet](https://cran.r-project.org/package=BaseSet "BaseSet on CRAN")
then a brief introduction to sets, followed by showing what you can do
with [BaseSet](https://docs.ropensci.org/BaseSet/).

## Brief BaseSet history

I study diseases to try to find what causes them at a research institute
associated with an hospital.Thanks to recent technological advances we
can analyze many things from a single patient's sample.Having so much
information available can be overwhelming, making it difficult to find
the causes of diseases (but it is much better than not having enough
information!).

In order to make it easier to focus and aggregate knowledge, scientists
have been storing what we know of each gene in several ways.As more
information was gathered, efforts to group these genes into those to
focus on or discard as causes of different processes of interest started
to emerge^[1](#fn:1){.footnote-ref role="doc-noteref"}^.Scientists
categorize genes according to where they are, what do they do, how they
function, and with which other genes they interact.There are also many
different sub-groups within these categories.

This has lead to several ways of storing this information, and depending
on which database and which method you use you end up with different
groups.This in turn means that we aren't so sure of how to group genes
and as new experiments are carried out these groupings might change.

I had previously created a package
([BioCor](https://bioconductor.org/packages/BioCor/ "BioCor: Comparing sets of genes"))
to compare these gene sets which returns a numerical value of how
similar two groups of genes are.But I found out that depending on which
database I used I got very different results.So I wanted an easy way to
know in which groups a gene was present, but I also wanted this
information unified from several data sources to account for this
uncertainty.

I started [experimenting](https://github.com/llrs/GSEAdv/ "GSEAdv") by
extending a class present on
[GSEABase](https://bioconductor.org/packages/GSEABase/ "Bioconductor package")
that I had used previously.I also found out that there were some efforts
by other people through the
[Bioconductor](https://bioconductor.org "Project for high-throughput genomic data")
slack channel.So I got in touch with them and we shared some ideas on
how to do this.

To explore different ways to solve the problem we ended up developing
three different packages that aim to do similar things but take
different approaches.At the moment BaseSet published on CRAN and
[BiocSet](https://bioconductor.org/packages/BiocSet/ "BiocSet displays different biological sets in a triple tibble format")
is published on
Bioconductor.[unisets](https://github.com/kevinrue/unisets) is available
on GitHub although development has stalled due to time constraints.These
packages provide methods to work with sets, the mathematical name for
groups of elements.

## Sets

Sets are not only used for tennis games.In mathematics if you have a
group of multiple elements such as `c("apple", "bannana", "pineaple")`
it is called a set.A set is a group of elements, usually just unique
elements are used (no `c("apple", "bannana", "pineaple", "apple")`).

To learn and understand the world we group elements together.Usually it
is clear what should be inside a group, like the elements above, all of
them are fruits.Sometimes it is not so clear if an element belongs to a
certain group: [Are tomatoes
fruits?](https://en.wikipedia.org/wiki/Tomato#Fruit_versus_vegetable "Wikipedia page about tomatoes and its classification")

An element can also belong to several groups.Basketball is a team sport,
but is also played with a ball.So basketball can be in both groups, as
we see on
[Wikipedia](https://en.wikipedia.org/wiki/Basketball "Wikipedia: Basketball"):

> [Categories](https://en.wikipedia.org/wiki/Help:Category "Help:Category"):
> [Basketball](https://en.wikipedia.org/wiki/Category:Basketball "Category:Basketball")
> \| [Sports originating in the United
> States](https://en.wikipedia.org/wiki/Category:Sports_originating_in_the_United_States "Category:Sports originating in the United States")
> \| [Team
> sports](https://en.wikipedia.org/wiki/Category:Team_sports "Category:Team sports")
> \| [Summer Olympic
> sports](https://en.wikipedia.org/wiki/Category:Summer_Olympic_sports "Category:Summer Olympic sports")
> \| [Ball
> games](https://en.wikipedia.org/wiki/Category:Ball_games "Category:Ball games")
> \| [Games and sports introduced in
> 1891](https://en.wikipedia.org/wiki/Category:Games_and_sports_introduced_in_1891 "Category:Games and sports introduced in 1891")

Some say that tomatoes should be both considered as fruits and as
vegetables, so they could also be in both sets.We can do this for any
element we can think of, pencils, mathematical operations, numbers,
words, genes...

When we have more than one set we might be interested in which elements
are in two groups, which fruits are also vegetables, or which fruits are
not vegetables.These operations are called set operations.Every time you
have used `%in%` or `merge` in your code you have been using a set
operation.There are many set operations, the most commonly used are
"intersection", for which R has the `intersect` function, and "union",
which is done with `c` on vectors.The equivalents on `data.frame`s are
done with `merge` and its arguments (if you are familiar with the
`*_join` verbs from dplyr, the many arguments of `merge` are one of the
reasons why there are so many `*_join` functions).

As you see R already provides some functions to work with sets.So why
write a new package for sets?Let's see it with some code:

## Using BaseSet

First load the package:

::: {.highlight}
``` {.chroma tabindex="0"}
library("BaseSet")packageVersion("BaseSet")[1] '0.0.14'
```
:::

In order to work with sets the package defines its own class named
`TidySet`.We can transform our data with the `tidySet` function:

::: {.highlight}
``` {.chroma tabindex="0"}
sets <- list(fruits = c("apple", "bannana", "pineaple"))TS <- tidySet(sets)TS  elements   sets fuzzy1    apple fruits     12  bannana fruits     13 pineaple fruits     1
```
:::

We can explore some properties of this set:

::: {.highlight}
``` {.chroma tabindex="0"}
nElements(TS)[1] 3
```
:::

::: {.highlight}
``` {.chroma tabindex="0"}
nSets(TS)[1] 1
```
:::

then add more fruits

::: {.highlight}
``` {.chroma tabindex="0"}
TS1 <- add_elements(TS, "orange")nElements(TS1)[1] 4
```
:::

::: {.highlight}
``` {.chroma tabindex="0"}
TS1  elements   sets fuzzy1    apple fruits     12  bannana fruits     13 pineaple fruits     1
```
:::

We can see it has one more element but it isn't displayed, that's is
because we didn't record to what set this element belongs to:

::: {.highlight}
``` {.chroma tabindex="0"}
relation <- data.frame(sets = "fruits", elements = "orange")TS1 <- add_relation(TS, relation)TS1  elements   sets fuzzy1    apple fruits     12  bannana fruits     13 pineaple fruits     14   orange fruits     1
```
:::

As you might have noticed there is a third column named fuzzy that so
far is always 1.This column contains a value between 0 and 1 and
represents the membership of an element to that set.A value of 1
indicates full membership and 0 that there isn't any relationship.Values
between encode the uncertainty.We will demonstrate this later, but first
let's create a new set to do some operations with it:

::: {.highlight}
``` {.chroma tabindex="0"}
relation <- data.frame(sets = c("vegetables", "fruits"),                        elements = c("tomatoes", "tomatoes"))TS2 <- add_relation(TS1, relation)TS2  elements       sets fuzzy1    apple     fruits     12  bannana     fruits     13 pineaple     fruits     14   orange     fruits     15 tomatoes vegetables     16 tomatoes     fruits     1
```
:::

Now that we have two sets we can perform more operations:

::: {.highlight}
``` {.chroma tabindex="0"}
intersection(TS2, c("vegetables", "fruits"))  elements              sets fuzzy1 tomatoes vegetables∩fruits     1
```
:::

::: {.highlight}
``` {.chroma tabindex="0"}
union(TS2, c("vegetables", "fruits"))  elements              sets fuzzy1    apple vegetables∪fruits     12  bannana vegetables∪fruits     13 pineaple vegetables∪fruits     14   orange vegetables∪fruits     15 tomatoes vegetables∪fruits     1
```
:::

Note that the names of the resulting sets have been automatically set up
using the [appropriate
symbols](https://www.mathsisfun.com/sets/symbols.html "Link to a website with some set operations symbols").

So far we have set up how to count and merge different sets but one of
the goals of BaseSet is to also encode the uncertainty when we assign an
element to a set.

To account for uncertainty mathematicians have come up with the idea of
fuzzy sets.Fuzzy sets are sets but instead of knowing for sure that an
element belongs to the set, there is a value, the fuzzy value or
membership, that measures the uncertainty of an element belonging to a
set.

A typical example involves ratings.Imagine classification methods that,
given a picture, classify the probability of each object being in the
picture.It might return probabilities such as:

::: {.highlight}
``` {.chroma tabindex="0"}
classification <- matrix(c(0.1, 0.2, 0.6, 0.85, 0.6, 0.5, 0.25, 0.16),                         nrow = 2, ncol = 4, byrow = TRUE,                         dimnames = list(c("image1", "image2"),                                          c("Cat", "Dog", "Duck", "Fish")))classification # Algorithm classification       Cat Dog Duck Fishimage1 0.1 0.2 0.60 0.85image2 0.6 0.5 0.25 0.16
```
:::

::: {.highlight}
``` {.chroma tabindex="0"}
TS <- tidySet(classification) # Transform dataTS  elements sets fuzzy1   image1  Cat  0.102   image2  Cat  0.603   image1  Dog  0.204   image2  Dog  0.505   image1 Duck  0.606   image2 Duck  0.257   image1 Fish  0.858   image2 Fish  0.16
```
:::

We can calculate how probable it is that the image is classified to just
one object.

::: {.highlight}
``` {.chroma tabindex="0"}
element_size(TS)   elements size probability1    image1    0      0.04322    image1    1      0.32523    image1    2      0.48024    image1    3      0.14125    image1    4      0.01026    image2    0      0.12607    image2    1      0.38108    image2    2      0.36209    image2    3      0.119010   image2    4      0.0120
```
:::

Given this memberships there is just a 0.3252 probability that the
machine would classify the first image as just one thing, so it is more
probable that the first image will be
misclassified^[2](#fn:2){.footnote-ref role="doc-noteref"}^.

For the second image it is more probable to contain just one object than
two, but there is still high uncertainty as the probability to classify
to none of the 4 objects is 0.1260 ^[3](#fn:3){.footnote-ref
role="doc-noteref"}^.

This was not evident from the "output" of the classification but is
equally important to know in many situations.

## Finishing

I [submitted](https://github.com/ropensci/software-review/issues/359)
this package to [rOpenSci](https://ropensci.org "rOpenSci") peer-review
because I wanted more feedback on these fuzzy sets methods and wasn't
sure of the mix I made of S4 methods and S3 methods.

The topic is not a common one so although I submitted the package on
January for review it started on June (after 2 months of hiatus due to
COVID).This long waiting time occurred because it was hard for the
editor (thanks [Anna Krystalli](/author/anna-krystalli)!) to find two
reviewers with all that was going on.

Once two reviewers were found the feedback started coming (Many thanks
[Zebulun Arendsee](https://github.com/arendsee) and [Jennifer
Chang](https://github.com/j23414)!).The reviewers pointed out
inconsistencies on the order of the output, suggested more methods,
pointed out mismatches between the documentation and the code.

Most importantly much of the comments and exchange was around some
methods and explanations for fuzzy sets which were not
clear^[4](#fn:4){.footnote-ref role="doc-noteref"}^.

I made my best efforts to improve the package and hope you'll find it
useful in your projects.[Try it
out!](https://docs.ropensci.org/BaseSet/)

::: {.footnotes role="doc-endnotes"}

------------------------------------------------------------------------

1.  ::: {#fn:1}
    See [this
    article](https://doi.org/10.1371/journal.pcbi.1002375 "Ten Years of Pathway Analysis: Current Approaches and Outstanding Challenges")
    reviewing the different methods
    used. [↩︎](#fnref:1){.footnote-backref role="doc-backlink"}
    :::

2.  ::: {#fn:2}
    We add up the probability of being one feature (and not the others,
    i.e.: `(1- x)`) for all the elements:
    `0.1*(1-0.2)*(1-0.6)*(1-0.85) + (1-0.1)*0.2*(1-0.6)*(1-0.85) + (1-0.1)*(1-0.2)*0.6*(1-0.85) + (1-0.1)*(1-0.2)*(1-0.6)*0.85` [↩︎](#fnref:2){.footnote-backref
    role="doc-backlink"}
    :::

3.  ::: {#fn:3}
    Similar to the other calculation, this probability is
    `(1-0.6)*(1-0.5)*(1-0.25)*(1-0.16)`. [↩︎](#fnref:3){.footnote-backref
    role="doc-backlink"}
    :::

4.  ::: {#fn:4}
    If there is still something unclear; let me know!Open an
    [issue](https://github.com/ropensci/BaseSet/issues/new). [↩︎](#fnref:4){.footnote-backref
    role="doc-backlink"}
    :::
:::


In this post I will explain the history behind BaseSet then a brief introduction to sets, followed by showing what you can do with BaseSet.

Introducing BaseSet for mathematical sets

rOpenSci

Stefanie Butland

## rOpenSci HQ

We're thrilled to [announce three new rOpenSci Software Review
Editors](/blog/2020/10/27/editors2020/): Laura DeCicco, Julia Gustavsen,
and Mauro Lepore and we released the fifth version (v0.5) of the
[rOpenSci Developer Guide](/blog/2020/10/22/devguide-0.5.0/).

Our Community Call on The Wild World of Data Repositories took place Dec
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## Software Peer Review

2 community-contributed packages passed [software peer
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If you want to be a reviewer fill out [this short
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## Software

7 new packages on CRAN.

- **[allcontributors](https://ropenscilabs.github.io/allcontributors/)** -
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## On the Blog

#### From the community

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#### From the rOpenSci team

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rOpenSci HQ   We’re thrilled to announce three new rOpenSci Software Review Editors: Laura DeCicco, Julia Gustavsen, and Mauro Lepore and we released the fifth version (v0.5) of the rOpenSci Developer Guide. Our Community Call on The Wild World of Data Repositories took place Dec 16 with an audience of 153 people!

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Introducing BaseSet for mathematical sets

2 Months in 2 Minutes - rOpenSci News, December 2020