# Clustering of Hi-C contact maps

#### Shubham Chaturvedi, Pierre Neuvial, Nathalie Vialaneix

#### 2025-11-19

    # IMPORTANT: this vignette can not be created if HiTC is not installed
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# Introduction

Hi-C is a sequencing-based molecular assay designed to measure intra and inter-chromosomal interactions between the DNA molecule. In particular, the identification of Topologically-Associated Domains (TADs), that is, of regions of the genome in which physical interactions are frequent, provides insight into the three-dimensional organization of a genome [2].

Hi-C data are in the form of two-dimensional contact maps, i.e., matrices whose \(i,j\) entry quantifies the intensity of the physical interaction between two genome regions \(i\) and \(j\) at the DNA level. In this vignette, we demonstrate the use of `adjclust::hicClust` to perform adjacency-constrained hierarchical agglomerative clustering (HAC) of Hi-C contact maps. The output of this function is a dendrogram, which can be cut to identify TADs. The algorithm used for adjacency-constrained (HAC) is described in [3,4].

    library("adjclust")

# Loading and displaying a sample Hi-C contact map

The data set `hic_imr90_40_XX` is an object of class `HTCexp` which has been obtained from the `HiTC` package [4]. It is a contact map corresponding to the first 500 x 500 bins on chromosome X vs chromosome X.

    load(system.file("extdata", "hic_imr90_40_XX.rda", package = "adjclust"))

The script used to create this map can be found by executing the following command:

    system.file("system/create_hic_chrXchrX.R", package="adjclust")

    ## [1] "/tmp/RtmpKXPwXI/Rinst558ea27653c5f/adjclust/system/create_hic_chrXchrX.R"

Now we have a look at the data.

    HiTC::mapC(hic_imr90_40_XX)

# Using `hicClust`

`hicClust` operates directly on objects of class `HTCexp`

    fit <- hicClust(hic_imr90_40_XX)

It is also possible to work on binned data. Below we choose a bin size of \(5 \times 10^5\):

    binned <- HiTC::binningC(hic_imr90_40_XX, binsize = 1e5)
    fitB <- hicClust(binned)
    fitB

    ##
    ## Call:
    ## hicClust(binned)
    ##
    ## Cluster method   : hicClust
    ## Number of objects: 205

    HiTC::mapC(binned)

The output is of class `chac`. In particular, it can be plotted as a dendrogram silently relying on the function `plot.dendrogram`:

    plot(fitB, mode = "corrected")

Moreover, the output contains an element named `merge` which describes the successive merges of the clustering, and an element `gains` which gives the improvement in the criterion optimized by the clustering at each successive merge.

    head(cbind(fitB$merge, fitB$gains))

    ##      [,1] [,2]
    ## [1,]   -3   -4
    ## [2,]   -2    1
    ## [3,]    2   -5
    ## [4,]   -1    3
    ## [5,]    4   -6
    ## [6,]  -17  -18

# Other types of input

Contacts maps can also be stored as objects of class `Matrix::dsCMatrix`, or as plain text files. These types of input are also accepted as first argument to `hicClust`.

# References

[1] Ambroise C., Dehman A., Neuvial P., Rigaill G., and Vialaneix N. (2019). Adjacency-constrained hierarchical clustering of a band similarity matrix with application to genomics. Algorithms for Molecular Biology, 14, 22.

[2] Dixon J.R., et al (2012). Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature, 485(7398), 376.

[3] Randriamihamison N., Vialaneix N., and Neuvial P. (2021). Applicability and interpretability of Ward’s hierarchical agglomerative clustering with or without contiguity constraints. Journal of Classification, 38, 363–389.

[4] Servant N., et al (2012). HiTC: Exploration of High-Throughput ‘C’ experiments. Bioinformatics, 28(21), 2843-2844.

# Session information

    sessionInfo()

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