The goal of BaseSet is to facilitate working with sets in an efficient way. The package implements methods to work on sets, doing intersection, union, complementary, power sets, cartesian product and other set operations in a tidy way.

The package supports classical and fuzzy sets. Fuzzy sets are similar to classical sets but there is some vagueness on the relationship between the element and the set.

It also allows to import from several formats used in the life science world. Like the GMT and the GAF or the OBO format file for ontologies.

You can save information about the elements, sets and their relationship on the object itself. For instance origin of the set, categorical or numeric data associated with sets…

Watch BaseSet working on the examples below and in the vignettes. You can also find related packages and the differences with BaseSet. If you have some questions or bugs open an issue (remember the Code of Conduct)

The package depends on some packages from Bioconductor. In order to install some of its dependencies you’ll need first to install `{BiocManager}`

:

You can install the latest version of BaseSet from Github with:

We can create a set like this:

```
sets <- list(A = letters[1:5], B = c("a", "f"))
sets_analysis <- tidySet(sets)
sets_analysis
#> elements sets fuzzy
#> 1 a A 1
#> 2 b A 1
#> 3 c A 1
#> 4 d A 1
#> 5 e A 1
#> 6 a B 1
#> 7 f B 1
```

Perform typical operations like union, intersection. You can name the resulting set or let the default name:

```
union(sets_analysis, sets = c("A", "B"))
#> elements sets fuzzy
#> 1 a A∪B 1
#> 2 b A∪B 1
#> 3 c A∪B 1
#> 4 d A∪B 1
#> 5 e A∪B 1
#> 6 f A∪B 1
# Or we can give a name to the new set
union(sets_analysis, sets = c("A", "B"), name = "D")
#> elements sets fuzzy
#> 1 a D 1
#> 2 b D 1
#> 3 c D 1
#> 4 d D 1
#> 5 e D 1
#> 6 f D 1
# Or the intersection
intersection(sets_analysis, sets = c("A", "B"))
#> elements sets fuzzy
#> 1 a A∩B 1
# Keeping the other sets:
intersection(sets_analysis, sets = c("A", "B"), name = "D", keep = TRUE)
#> elements sets fuzzy
#> 1 a A 1
#> 2 b A 1
#> 3 c A 1
#> 4 d A 1
#> 5 e A 1
#> 6 a B 1
#> 7 f B 1
#> 8 a D 1
```

And compute size of sets among other things:

The elements in one set not present in other:

```
subtract(sets_analysis, set_in = "A", not_in = "B", keep = FALSE)
#> elements sets fuzzy
#> 1 b A∖B 1
#> 2 c A∖B 1
#> 3 d A∖B 1
#> 4 e A∖B 1
```

Or any other verb from dplyr. We can add columns, filter, remove them and add information about the sets:

```
library("magrittr")
#>
#> Attaching package: 'magrittr'
#> The following object is masked from 'package:BaseSet':
#>
#> subtract
set.seed(4673) # To make it reproducible in your machine
sets_enriched <- sets_analysis %>%
mutate(Keep = sample(c(TRUE, FALSE), 7, replace = TRUE)) %>%
filter(Keep == TRUE) %>%
select(-Keep) %>%
activate("sets") %>%
mutate(sets_origin = c("Reactome", "KEGG"))
sets_enriched
#> elements sets fuzzy sets_origin
#> 1 a A 1 Reactome
#> 2 b A 1 Reactome
#> 3 c A 1 Reactome
#> 4 d A 1 Reactome
#> 5 e A 1 Reactome
#> 6 f B 1 KEGG
# Activating sets makes the verb affect only them:
elements(sets_enriched)
#> elements
#> 1 a
#> 2 b
#> 3 c
#> 4 d
#> 5 e
#> 6 f
relations(sets_enriched)
#> elements sets fuzzy
#> 1 a A 1
#> 2 b A 1
#> 3 c A 1
#> 4 d A 1
#> 5 e A 1
#> 6 f B 1
sets(sets_enriched)
#> sets sets_origin
#> 1 A Reactome
#> 2 B KEGG
```

In fuzzy sets the elements are vaguely related to the set by a numeric value usually between 0 and 1. This implies that the association is not guaranteed.

```
relations <- data.frame(sets = c(rep("A", 5), "B", "B"),
elements = c("a", "b", "c", "d", "e", "a", "f"),
fuzzy = runif(7))
fuzzy_set <- tidySet(relations)
fuzzy_set
#> elements sets fuzzy
#> 1 a A 0.1837246
#> 2 b A 0.4567009
#> 3 c A 0.8152075
#> 4 d A 0.5800610
#> 5 e A 0.5724973
#> 6 a B 0.9381182
#> 7 f B 0.9460158
```

The equivalent operations performed on classical sets are possible with fuzzy sets:

```
union(fuzzy_set, sets = c("A", "B"))
#> elements sets fuzzy
#> 1 a A∪B 0.9381182
#> 2 b A∪B 0.4567009
#> 3 c A∪B 0.8152075
#> 4 d A∪B 0.5800610
#> 5 e A∪B 0.5724973
#> 6 f A∪B 0.9460158
# Or we can give a name to the new set
union(fuzzy_set, sets = c("A", "B"), name = "D")
#> elements sets fuzzy
#> 1 a D 0.9381182
#> 2 b D 0.4567009
#> 3 c D 0.8152075
#> 4 d D 0.5800610
#> 5 e D 0.5724973
#> 6 f D 0.9460158
# Or the intersection
intersection(fuzzy_set, sets = c("A", "B"))
#> elements sets fuzzy
#> 1 a A∩B 0.1837246
# Keeping the other sets:
intersection(fuzzy_set, sets = c("A", "B"), name = "D", keep = TRUE)
#> elements sets fuzzy
#> 1 a A 0.1837246
#> 2 b A 0.4567009
#> 3 c A 0.8152075
#> 4 d A 0.5800610
#> 5 e A 0.5724973
#> 6 a B 0.9381182
#> 7 f B 0.9460158
#> 8 a D 0.1837246
```

Assuming that the fuzzy value is a probability, we can calculate which is the probability of having several elements:

```
# A set could be empty
set_size(fuzzy_set)
#> sets size probability
#> 1 A 0 0.014712455
#> 2 A 1 0.120607154
#> 3 A 2 0.318386944
#> 4 A 3 0.357078627
#> 5 A 4 0.166499731
#> 6 A 5 0.022715089
#> 7 B 0 0.003340637
#> 8 B 1 0.109184679
#> 9 B 2 0.887474684
# The more probable size of the sets:
set_size(fuzzy_set) %>%
group_by(sets) %>%
filter(probability == max(probability))
#> # A tibble: 2 x 3
#> # Groups: sets [2]
#> sets size probability
#> <chr> <dbl> <dbl>
#> 1 A 3 0.357
#> 2 B 2 0.887
# Probability of belonging to several sets:
element_size(fuzzy_set)
#> elements size probability
#> 1 a 0 0.05051256
#> 2 a 1 0.77713204
#> 3 a 2 0.17235540
#> 4 b 0 0.54329910
#> 5 b 1 0.45670090
#> 6 c 0 0.18479253
#> 7 c 1 0.81520747
#> 8 d 0 0.41993900
#> 9 d 1 0.58006100
#> 10 e 0 0.42750268
#> 11 e 1 0.57249732
#> 12 f 0 0.05398419
#> 13 f 1 0.94601581
```

With fuzzy sets we can filter at certain levels (called alpha cut):

```
fuzzy_set %>%
filter(fuzzy > 0.5) %>%
activate("sets") %>%
mutate(sets_origin = c("Reactome", "KEGG"))
#> elements sets fuzzy sets_origin
#> 1 c A 0.8152075 Reactome
#> 2 d A 0.5800610 Reactome
#> 3 e A 0.5724973 Reactome
#> 4 a B 0.9381182 KEGG
#> 5 f B 0.9460158 KEGG
```

There are several other packages related to sets, which partially overlap with BaseSet functionality:

sets

Implements a more generalized approach, that can store functions or lists as an element of a set (while BaseSet only allows to store a character or factor), but it is harder to operate in a tidy/long way. Also the operations of intersection and union need to happen between two different objects, while a single TidySet object (the class implemented in BaseSet) can store one or thousands of sets.`{GSEABase}`

Implements a class to store sets and related information, but it doesn’t allow to store fuzzy sets and it is also quite slow as it creates several classes for annotating each set.`{BiocSet}`

Implements a tidy class for sets but does not handle fuzzy sets. It also has less functionality to operate with sets, like power sets and cartesian product. BiocSet was influenced by the development of this package.`{hierarchicalSets}`

This package is focused on clustering of sets that are inside other sets and visualizations. However, BaseSet is focused on storing and manipulate sets including hierarchical sets.`{set6}`

This package implements different classes for different type of sets including fuzzy sets, conditional sets. However, it doesn’t handle information associated to elements, sets or relationship.

On bioinformatics when looking for the impact of an experiment enrichment methods are applied. This involves obtaining several sets of genes from several resources and methods. Usually these curated sets of genes are taken at face value. However, there are several resources of sets and they do not agree between them, regardless they are used without considering any uncertainty on sets composition.

Fuzzy theory has long studied sets whose elements have degrees of membership and/or uncertainty. Therefore one way to improve the methods involve using fuzzy methods and logic on this field. As I couldn’t find any package that provided methods for this I set on creating it (after trying to expand the existing one I knew).

This package is intended to be easy to use for someone who is working with collections of sets but flexible about the methods and logic it can use. To be consistent, the standard fuzzy logic is the default but it might not be the right one for your data. Consider changing the defaults to match with the framework the data was obtained with.

Please note that the BaseSet project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.