5.1.17. jaccard

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# 5.1.17. jaccard

Whereas the bedtools `intersect` tool enumerates each an every intersection between two sets of genomic intervals, one often needs a single statistic reflecting the similarity of the two sets based on the intersections between them. The Jaccard statistic is used in set theory to represent the ratio of the intersection of two sets to the union of the two sets. Similarly, Favorov et al [1] reported the use of the Jaccard statistic for genome intervals: specifically, it measures the ratio of the number of intersecting base pairs between two sets to the number of base pairs in the union of the two sets. The bedtools jaccard tool implements this statistic, yet modifies the statistic such that the length of the intersection is subtracted from the length of the union. As a result, the final statistic ranges from 0.0 to 1.0, where 0.0 represents no overlap and 1.0 represent complete overlap.

    [1] Exploring Massive, Genome Scale Datasets with the GenometriCorr Package.
    Favorov A, Mularoni L, Cope LM, Medvedeva Y, Mironov AA, et al. (2012)
    PLoS Comput Biol 8(5): e1002529. doi:10.1371/journal.pcbi.1002529

Note

The `jaccard` tool requires that your data is pre-sorted by chromosome and then by start position (e.g., `sort -k1,1 -k2,2n in.bed > in.sorted.bed` for BED files).

See also

reldist intersect

## 5.1.17.1. Usage and option summary

Usage:

    bedtools jaccard [OPTIONS] -a <BED/GFF/VCF> -b <BED/GFF/VCF>

Option | Description
--- | ---
-a | BED/GFF/VCF file A. Each feature in A is compared to B in search of overlaps. Use “stdin” if passing A with a UNIX pipe.
-b | BED/GFF/VCF file B. Use “stdin” if passing B with a UNIX pipe.
-f | Minimum overlap required as a fraction of A. Default is 1E-9 (i.e. 1bp).
-r | Require that the fraction of overlap be reciprocal for A and B. In other words, if -f is 0.90 and -r is used, this requires that B overlap at least 90% of A and that A also overlaps at least 90% of B.

## 5.1.17.2. Default behavior

By default, `bedtools jaccard` reports the length of the intersection, the length of the union (minus the intersection), the final Jaccard statistic reflecting the similarity of the two sets, as well as the number of intersections.

    $ cat a.bed
    chr1  10  20
    chr1  30  40

    $ cat b.bed
    chr1  15   20

    $ bedtools jaccard -a a.bed -b b.bed
    intersection  union   jaccard n_intersections
    5     20      0.25    1

## 5.1.17.3. Controlling which intersections are included

One can also control which intersections are included in the statistic by requiring a certain fraction of overlap with respect to the features in A (via the `-f` parameter) or also by requiring that the fraction of overlap is reciprocal (`-r`) in A and B.

    $ cat a.bed
    chr1  10  20
    chr1  30  40

    $ cat b.bed
    chr1  15   20

Require 10% overlap with respect to the intervals in A:

    $ bedtools jaccard -a a.bed -b b.bed -f 0.1
    intersection  union   jaccard n_intersections
    5 20  0.25    1

Require 60% overlap with respect to the intervals in A:

    $ bedtools jaccard -a a.bed -b b.bed -f 0.6
    intersection  union   jaccard n_intersections
    0 25  0.25    0

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