Correction to: SpectralTAD: an R package for defining a hierarchy of topologically associated domains using spectral clustering

Correction to: BMC Bioinformatics 21, 319 (2020)

https://doi.org/10.1186/s12859-020-03652-w

Following publication of the original article [1], the authors identified misformatted equations in the published article. The correctly formatted equations are given below.

1. Calculating the normalized symmetric Laplacian:

$$\bar{L}=D^{-\frac{1}{2}}C{D}^{-\frac{1}{2}}$$

2. Solve the generalized eigenvalue problem:

$$\bar{L}\bar{V}=\lambda \bar{V}$$

3. The result is a matrix of eigenvectors ${\bar{V}}_{w\times k}$, where w is the window size, and k is the number of eigenvectors used, and a vector of eigenvalues where each entry λ_i corresponds to the i_th eigenvalue of the normalized Laplacian $\bar{L}$.

4. Normalize rows and columns to sum to 1:

$$\widehat{V_{i.}}=\frac{\overline{V_{i.}}}{\Vert {\bar{V}}_{i.}\Vert }$$

5. Find the mean silhouette score over all possible numbers of clusters m and organize into a vector of means:

$${\bar{s}}_m=\frac{{\sum }_{i=1}^m{s}_i}{m}$$

6. Find the value of m which maximizes ${\bar{s}}_m$

The original article has been updated.