miniMDS is a tool for inferring and plotting 3D structures from normalized Hi-C data, using partitioned MDS, a novel approximation to multidimensional scaling (MDS). It produces a single 3D structure from a Hi-C BED file, representing an ensemble average of chromosome conformations within the population of cells. Using parallelization, it is able to process high-resolution data quickly with limited memory requirements. The human genome can be inferred at kilobase-resolution within several hours on a desktop computer. Standard MDS results in inaccuracies for sparse high-resolution data, but miniMDS focuses on local substructures to achieve greater accuracy. miniMDS also supports inter-chromosomal structural inference. Together with Mayavi, miniMDS produces publication-quality images and gifs.

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miniMDS: 3D structural inference from high-resolution Hi-C data
L Rieber, S Mahony
Bioinformatics (2017) 33 (14):i261-i266
[Open Access Article].


Open source code (released under the MIT license) is available from:




  • python 2.7
  • numpy
  • scikit-learn
  • pymp
  • mayavi (optional; for plotting)
  • ImageMagick (optional; for creating gifs)
  • scipy (optional; for creating figures from paper)
  • matplotlib (optional; for creating figures from paper)


Please run (in the scripts directory) and report any issues.


python -l [path to low-res BED] -o [output path] [path to high-res BED]


Input file format

miniMDS uses intra- or inter-chromosomal BED files as input. Data must be normalized prior to use (for example, using


chrA bin1_start bin1_end chrB bin2_start bin2_end normalized_contact_frequency

Example – chr22 intra-chromosomal data at 10-Kbp resolution:

chr22 16050000 16060000 chr22 16050000 16060000 12441.5189291


Intra-chromosomal miniMDS

Intra-chromosomal analysis is performed using

To view help:

python -h

By default, standard MDS (not partitioned MDS) is used:

python GM12878_combined_22_100kb.bed

However, this will not offer the benefits of miniMDS and is not recommended.

Structures are not saved by default. Use the -o option with the path where you want to save the structure.

python -o GM12878_combined_22_100kb_structure.tsv GM12878_combined_22_100kb.bed

Structures are saved to tsv files. The header contains the name of the chromosome, the resolution, and the starting genomic coordinate. Each line in the file contains the point number followed by the 3D coordinates (with “nan” for missing data).

Example – chr22 at 10-Kbp resolution:




0 0.589878298045 0.200029092422 0.182515056542

1 0.592088232028 0.213915817254 0.186657230841

2 nan nan nan


To run partitioned MDS, you must have a normalized BED file at a lower resolution than the BED file you want to infer. For example, to use a 100-Kbp-resolution BED file to aid in the inference of a 10-Kbp-resolution file:

python -l GM12878_combined_22_100kb.bed -o GM12878_combined_22_10kb_structure.tsv GM12878_combined_22_10kb.bed

The resolution you choose for the low-res file depends on your tradeoff between speed and accuracy. Lower resolutions are faster but less accurate. For now, the high resolution must be a factor of the low resolution. For example, a 500-Kb-resolution file can be used to infer a 100-Kb-resolution structure, but a 250-Kb-resolution file cannot.

Other parameters (optional)

Controlling the number of partitions

The miniMDS algorithm creates partitions in the high-resolution data and performs MDS on each partition individually. A greater number of partitions can increase speed but also reduce accuracy. On the other hand, for very sparse data a greater number of partitions can actually increase accuracy. If your output appears “clumpy”, increase the number of partitions.

The number of partitions cannot be set directly because partitions are created empirically to maximize clustering of the data. However, the degree of clustering of the data can be tweaked with the following parameters:

-m: minimum partition size (as a fraction of the data). Default = 0.05

-p: smoothing parameter (between 0 and 1). Default = 0.1

Make these parameters smaller to increase the number of partitions. For very high resolution data (such as 5-Kbp), m=0.01 and p=0.01 is recommended:

python -l GM12878_combined_22_100kb.bed -o GM12878_combined_22_5kb_structure.tsv -m 0.01 -p 0.01 GM12878_combined_22_5kb.bed

You can limit the maximum RAM (in Kb) used by any given partition using -R (default = 32000):

python -l GM12878_combined_22_100kb.bed -o GM12878_combined_22_5kb_structure.tsv -R 50000 GM12878_combined_22_5kb.bed

Number of threads

miniMDS uses multithreading to achieve greater speed. By default, 3 threads are requested, because this is safe for standard 4-core desktop computers. However, the number of threads used will never exceed the number of processors or the number of partitions, regardless of what is requested. You can change the number of requested threads using -n.

For example, to run miniMDS with four threads:

python -l GM12878_combined_22_100kb.bed -o GM12878_combined_22_10kb_structure.tsv -n 4 GM12878_combined_22_10kb.bed

Classical MDS

Classical MDS (cMDS), also called principal coordinates analysis, is a variant of MDS that is faster under certain circumstances. The miniMDS tool supports cMDS but NOT with partitioned MDS. Use the –classical option.

python --classical GM12878_combined_22_10kb.bed

This mode is mainly used for testing.

Inter-chromosomal miniMDS

Inter-chromosomal analysis is performed using

To view help:

python -h

The usage of is similar to, however inter-chromosomal files are required in addition to intra-chromosomal. To avoid entering filenames separately for each chromosome, you must name your files using a standard format.

Intra-chromosomal format:

{prefix}_{ChrA}_{resolution}{kb or Mb}.bed



Inter-chromosomal format:

{prefix}_{ChrA}_{ChrB}_{resolution}{kb or Mb}.bed

where A is before B in:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 X



Enter the prefix and resolution of the inter-chromosomal and intra-chromosomal files, respectively:

python [inter-chromosomal file prefix] [intra-chromosomal file prefix] [inter-chromosomal resolution] [intra-chromosomal resolution]

For example, if your files are stored in the directory data:

python data/GM12878_combined_interchromosomal data/GM12878_combined_intrachromosomal 1000000 10000

Because of the challenges of inter-chromosomal inference, it is recommended that a resolution no greaer than 1-Mbp be used for inter-chromosomal data.

By default, partitioned MDS is not performed. To perform partitioned MDS on each intra-chromosomal structure, use the option -l followed by the resolution of the low-res intra-chromosomal files. (It is assumed that the naming of these files is otherwise identical to that of the high-res intra-chromosomal files.)

python -l 100000 data/GM12878_combined_interchromosomal data/GM12878_combined_intrachromosomal 1000000 10000

This will perform partitioned MDS on each of the intra-chromosomal structures at 10-Kbp resolution and then assemble the chromosomes into a whole-genome structure using 1-Mbp-resolution inter-chromosomal data. Remember that structures are not saved by default.

Other parameters (optional)

All of the parameters from are also available for

Specifying chromosomes

By default, uses all human chromosomes other than Y. You can specify chromosomes using the option -c.

To perform interchromosomal analysis on chromosomes 1 and 8:

python -l 100000 -c 1 8 data/GM12878_combined_interchromosomal data/GM12878_combined_intrachromosomal 1000000 10000

Note: it is often necessary to use this option if you are using a genome other than human, so that it won’t search for chromosomes that don’t exist.


Read a structure into a Cluster object:

cluster = data_tools.clusterFromFile(path)


cluster = data_tools.clusterFromFile("GM12878_combined_22_100kb_structure.tsv")

Create an interactive 3D plot in Mayavi. (Mayavi allows you to rotate the image and save a view.)

plotting.plot_cluster_interactive(cluster, color=(1,0,0), radius=None)

By default, the radius is the to-scale radius of heterochromatin.

Multiple clusters can be plotted simultaneously:

chroms = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, X)
clusters = [data_tools.clusterFromFile("GM12878_combined_{}_100kb_structure.tsv".format(chrom) for chrom in chroms)]
plotting.plot_clusters_interactive(clusters) has 23 built-in colors designed to be as different to the human eye as possible. By default, these colors are used when plotting multiple clusters. You can also specify a list of colors:

chroms = (1, 2)
clusters = [data_tools.clusterFromFile("GM12878_combined_{}_100kb_structure.tsv".format(chrom) for chrom in chroms)]
plotting.plot_clusters_interactive(clusters, colors=[(1,0,0), (0,0,1)])

The radius can also be specified, as above.

The option cut creates a cross-section of the plot. For example, this is useful for viewing the interior of the nucleus.

chroms = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, X)
clusters = [data_tools.clusterFromFile("GM12878_combined_{}_100kb_structure.tsv".format(chrom) for chrom in chroms)]
plotting.plot_clusters_interactive(clusters, cut=True)

A plot can be saved as a gif:

plotting.plot_cluster_gif(cluster, outname, color=(1,0,0), radius=None, increment=10)

A smaller value of increment will lead to a smoother gif.

Multiple clusters can also be plotted in a single gif:

plotting.plot_clusters_gif(clusters, outname, colors=default_colors, radius=None, increment=10)