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+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6925 +10.21105/joss.06925 + +SetVis: Visualizing Large Numbers of Sets and +Intersections + + + +https://orcid.org/0000-0001-8662-8103 + +Ruddle +R. A. + + + + + +https://orcid.org/0000-0003-1912-4890 + +Hama +L. + + + + +https://orcid.org/0000-0003-4066-8614 + +Wochner +P + + + + +https://orcid.org/0000-0002-8177-5582 + +Strickson +O. T. + + + + + +University of Leeds, Leeds, United Kingdom + + + + +Alan Turing Institute, London, United Kingdom + + + +9 +103 +6925 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2024 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Python +set visualization +sets + + + + + + Summary +

Set-type data occurs in many domains such as life sciences + (Lamy + & Tsopra, 2019), health + (Landolfi + et al., 2022) and the retail industry + (Adnan + & Ruddle, 2018), as well as in generic applications such as + analysing structures of missing data + (Ruddle, + Adnan, & Hall, 2022) and association rule mining + (Wang + et al., 2020). SetVis is new matrix-based set visualization + software, implemented as a Python package which is available from + PyPi. + The documentation is available from + setvis.readthedocs.io + which contains various hands-on Jupyter notebooks guiding users to use + the package. SetVis uses a memory-efficient design, operates with + datasets held in RAM or a database such as PostgreSQL, and allows user + interaction graphically or programmatically. A technical evaluation + shows that SetVis uses orders of magnitude less memory than the UpSet + (Lex + et al., 2014) Python package + (Nothman, + 2022).

+ + + Statement of need +

Although a wide variety of set visualization software has been + developed + (Alsallakh + & Ren, 2016; + Jia + et al., 2021), most of such software generates Venn or Euler + diagrams so is only suitable for data that contain fewer than ten sets + (Jia + et al., 2021). Other software visualizes 50+ sets but either + has little support for set intersection tasks + (Alper + et al., 2011; + Dörk + et al., 2012; + Freiler + et al., 2008; + Kim + et al., 2007) or only visualizes pairwise intersections + (Molbiotools, + 2022; + Yalcin + et al., 2015).

+

The best-known software for analysing rich patterns in set data are + the R and Python UpSet plot packages + (Conway + et al., 2017; + Nothman, + 2022), but the memory requirement of both packages increases + linearly with the number of cells (i.e., rows + + + × + columns) in a dataset, which makes the packages unusable with big + data. The ACE software + (Ruddle, + Adnan, Kavanagh, et al., 2022) uses more memory-efficient data + structures, but first requires the whole of a dataset to have been + loaded into RAM (again, clearly an issue for big data), and is a + stand-alone Java application that cannot be integrated with Jupyter + Notebooks or similar workflows. The SetVis python package addresses + the above collective weaknesses because it: (a) operates with datasets + that may be either held in RAM or out of core (in a PostgreSQL + database), (b) stores sets and intersections in memory-efficient data + structures (like ACE), (c) can be used within Jupyter Notebooks (or + similar) to aid the replicability of analysis workflows, and (d) + allows users to interact graphically in a notebook as well as + programmatically.

+ + + Design + +

An example APC combination heatmap shows the fields (X + axis), each combination of missing values (Y axis) and the number of + records that are in each combination (colour) of the APC (Admitted + Patient Care) dataset included in the package. The top, 4th from top + and bottom six combinations are a monotone pattern. However, the + other seven combinations show that there is another pattern that has + gaps in the DIAG fields. +

+ + +

SetVis provides the same six built-in visualizations as ACE + (Ruddle, + Adnan, Kavanagh, et al., 2022). The main two show + visualizations of sets (in a bar chart) and set intersections (in a + heatmap). The other four visualizations make SetVis scalable to data + that contains large numbers of sets and/or intersections, by showing + histograms of set cardinality, intersection degree and intersection + cardinality, and an intersection degree bar chart. All of the + visualizations are interactive (implemented with Bokeh, + Bokeh + Development Team, 2018), but users may also interact + programmatically and freely interleave the two forms of interaction. + Examples and tutorials are provided with the installation. A + screenshot of SetVis version v0.1rc5 of the + heatmap visualizations within Jupyter notebooks is shown in Figure + [fig:heatmap].

+

Jupyter notebooks have been widely adopted in the Python data + science ecosystem for exploratory data analysis. It is considered good + practice for computational notebooks to obey principles of (i) + top-to-bottom re-executability and (ii) repeatability, including by + others + (Quaranta + et al., 2022). The SetVis design allows these principles to be + respected.

+

SetVis is underpinned by memory-efficient data structures. Set + membership information for each of set membership information for each + of + + K + sets can be represented with a mapping from an element (represented by + its index) to a tuple of + + K + booleans based on indicator functions for each of these sets:

+

+ + members:ElementIndex→{True,False}K.

+

One component of the resulting tuple indicates membership of a + particular set. Storing this mapping explicitly (e.g., as in UpSet + with a dataframe, + Conway + et al., 2017; + Nothman, + 2022) requires + + O(KN) + storage, where + + K + and + + N + are the number of sets and the number of elements. When + + + K + is large, as is the case for many real-world datasets, this can be + inefficient. The number of unique set intersections, + + + R, + is often much smaller than the number of records, + + + R≪N, + and can be at most + + N + (if each element is member of a unique combination of sets). SetVis + makes use of this idea, and considers + + members=intersectionMembers∘intersectionId + where + + intersectionId:ElementIndex→IntersectionIndex + maps an element index to an index referring to the particular + combination of sets to which that element belongs; and + + + intersectionMembers:IntersectionIndex→{True,False}K + is a bijection between an intersection index and the explicit + representation of this combination.

+

In SetVis, these mappings are stored as a pair of Pandas dataframes + (in an instance of the Membership class), + + + intersectionId + of size + + O(N) + and + + intersectionMembers + of size + + O(RK), + for a combined total of + + O(N+RK) + storage.

+ + + Technical evaluation +

Using a Ubuntu virtual machine with 44GB of RAM, we compared SetVis + (v0.1.0) with UpSetPlot (v0.8.0) based on two criteria: memory use and + compute time. The greatest difference was in memory usage. The UpSetR + package + (Conway + et al., 2017) was not tested, but uses a similar data structure + to UpSetPlot + (Nothman, + 2022).

+

Tests were run with set-type data that contained two columns, + 500,000 rows and 100 – 10,000 set intersections. UpSetPlot crashed + when the 500,000 row dataset contained more than 500 intersections. By + contrast, SetVis only used 113 MB RAM for 500,000 rows with the + maximum 10,000 set intersections (see Figure + [fig:both]A).

+ +

(A) Memory used by UpSetPlot and SetVis for set-type + data with 500,000 rows, two columns and a range of set + intersections. There were always 10% more sets than intersections. + (B) Memory used by UpSetPlot and SetVis for visualizing patterns of + missing data. The number of cells equals the number of rows + + + × + columns in a dataset. +

+ + +

The difference was even more pronounced when the packages were used + to analyze missing data (10,000 – 500,000 rows; 10 – 700 columns; each + row missing one value). UpSetPlot’s memory scaled linearly with the + number of cells (i.e., rows + + × + columns) in a dataset, whereas SetVis’s memory only increased + gradually (see Figure + [fig:both]B). There + was a similarly large difference when each row contained 1 – 50 + missing values (100 – 10,000 set intersections in each dataset), + because for missing data UpSetPlot keeps a copy of the input Pandas + dataframe, as well as having a memory-hungry design.

+ + + Acknowledgements +

This research was supported by the Alan Turing Institute and the + Engineering and Physical Sciences Research Council (EP/N013980/1; + EP/R511717/1).

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