hicTransform.rst

hicTransform

Background

hicTransform transforms a given input matrix into a new matrix using one of the following methods:

• obs_exp
• obs_exp_lieberman
• obs_exp_non_zero
• pearson
• covariance

All expected values are computed per genomic distances.

Usage

$ hicTransform -m matrix.cool --method obs_exp -o obs_exp.cool

For all images data from Rao 2014 was used.

Observed / Expected

All values, including non-zero values, are used to compute the expected values per genomic distance.

$$exp_{i,j} = \frac{ \sum diagonal(|i-j|) }{|diagonal(|i-j|)|}$$

Observed / Expected lieberman

The expected matrix is computed in the way as Lieberman-Aiden used it in the 2009 publication. It is quite similar to the obs/exp matrix computation.

$$exp_{i,j} = \frac{ \sum diagonal(|i-j|) } {(length\ of\ chromosome\ - |i-j|))}$$

Observed / Expected non zero

Only non-zero values are used to compute the expected values per genomic distance, i.e. only non-zero values are taken into account for the denominator.

$$exp_{i,j} = \frac{ \sum diagonal(i-j) }{ number\ of\ non-zero\ elements\ in\ diagonal(|i-j|)}$$

By adding the --ligation_factor flag, the expected matrix can be re-scaled in the same way as has been done by Homer software when computing observed/expected matrices with the option '-norm'.

$$exp_{i,j} = exp_{i,j} * \sum row(j) * \sum row(i) }{ \sum matrix }$$

Pearson correlation matrix

$$Pearson_{i,j} = \frac {C_{i,j} }{ \sqrt{C_{i,i} * C_{j,j} }}$$

C is the covariance matrix

The first image shows the Pearson correlation on the original interaction matrix, the second one shows the Person correlation matrix on an observed/expected matrix. A consecutive computation like this is used in the A/B compartment computation.

Covariance matrix

Cov_i, j = E[M_i, M_j] − μ_i * μ_j

where M is the input matrix and μ the mean.