Clarification on Total Sum Scaling (TSS)

[zhengxiaoUVic]

Hello, Esteban, Xi, Suhana, Dr. Li, and boost-r users,

I am writing to inquire about the implementation of the Total Sum Scaling (TSS) transformation method in boost::normalize.st.

Upon reviewing the source code, it appears that the scale factor computations (Lines 83–86) are not invoked in the default TSS procedure. Instead, the raw data matrix is normalized solely by the library sizes (i.e., row sums), which aligns with the approach described by Sun et al. (2020; SPARK).

  gene_num   <- ncol(count)
  sample_num <- nrow(count)

  N <- rowSums(count)

  if (scaling.method == "TSS")
  {
    ##
    ## TSS(Total Sum Scaling)
    ##

    ### scale-factors
    raw_s_factors <- N
    scale_coeff <- exp((-1/nrow(count)) * sum(log(raw_s_factors)))
    scaled_s_factors <- scale_coeff * raw_s_factors

    ### normalized count matrix
    db.norm <- sweep(count, 1, N, FUN = "/")
    count_nor <- db.norm
  }

I also came across what seems to be a mistake in the TSS method presented in, for example, Jiang et al. (2022, p. 4649; BOOST-MI) and Li et al. (2021, p. 4131; BOOST-GP).

In those works, the size factor is defined as $s_i = \sum_{j=1}^p y_{ij} / \prod_{i=1}^n \sum_{j=1}^p y_{ij}$, where $i$ indexes the $n$ spots and $j$ indexes the $p$ genes. The numerator corresponds to the library size.

It might be tempting to assume that $\prod_{i=1}^n s_i = 1$, but this is not the case. The denominator lacks the $n$-th root and should be the geometric mean of the library sizes, as specified in the source code.

[estfernan]

Hello @zhengxiaoUVic,

Thank you for taking the time to review the code and for bringing these points to our attention.

Regarding your first note, I'll remove the unnecessary lines 83–86 (see 6863217). As you mentioned, those scale-factor computations were not used in the if-else case and are not required for a correct implementation of standard TSS.

On your second point, I would recommend contacting the authors directly to inform them of this inconsistency. The results of the paper should not be affected by the notation discrepancy, and the package itself should be performing as intended.

Thank you again for your careful reading and for raising these helpful observations.