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Three years ago Nicolas Bray and I published a post-publication review of the paper “Network link prediction by global silencing of indirect correlations” (Barzel and Barabási, Nature Biotechnology, 2013). Despite our less than positive review of the work, the paper has gone on to garner 95 citations since its publication (source: Google Scholar). In fact, in just this past year the paper has  paper has been cited 44 times, an impressive feat with the result that the paper has become the first author’s most cited work.

Ultimate impact

In another Barabási paper (with Wang and Song) titled Quantifying Long-Term Scientific Impact  (Science, 2013), the authors provide a formula for estimating the total number of citations a paper will acquire during its lifetime. The estimate is

$c^{\infty} = m(e^{\lambda_i-1}),$

where $m$ and $\lambda_i$ are parameters learned from a few years of citation data. The authors call $c^{\infty}$ the ultimate impact because, they explain, “the total number of citations a paper will ever acquire [is equivalent to] the discovery’s ultimate impact”. With 95 citations in 3 years, the Barzel-Barabási “discovery” is therefore on track for significant “ultimate impact” (I leave it as an exercise for the reader to calculate the estimate for $c^{\infty}$ from the citation data). The ultimate impactful destiny of the paper is perhaps no surprise…Barzel and Barabási knew as much when writing it, describing its implication for systems biology as “Overall this silencing method will help translate the abundant correlation data into insights about the system’s interactions” and stating in a companion press release that After silencing, what you are left with is the pre­cise wiring dia­gram of the system… In a sense we get a peek into the black box.”

Drive by citations

Now that three years had passed since the publication of the press release and with the ultimate impact revealed, I was curious to see inside the 95 black boxes opened with global silencing, and to examine the 95 wiring diagrams that were thus precisely figured out.

So I delved into the citation list and examined, paper-by-paper, to what end the global silencing method had been used. Strikingly, I did not find, as I expected, precise wiring diagrams, or even black boxes. A typical example of what I did find is illustrated in the paper Global and portioned reconstructions of undirected complex networks by Xu et al. (European Journal Of Physics B, 2016) where the authors mention the Barzel-Barabási paper only once, in the following sentence of the introduction:

“To address this inverse problem, many methods have been proposed and they usually show robust and high performance with appropriate observations [9,10,11, 12,13,14,15,16,17,18,19,20,21].”

(Barzel-Barabási is reference [16]).

Andrew Perrin has coined the term drive by citations for “references to a work that make a very quick appearance, extract a very small, specific point from the work, and move on without really considering the existence or depth of connection [to] the cited work.” While its tempting to characterize the Xu et al. reference of Barzel-Barabási as a drive by citation the term seems overly generous, as Xu et al. have literally extracted nothing from Barzel-Barabási at all. It turns out that almost all of the 95 citations of Barzel-Barabási are of this type. Or not even that. In some cases I found no logical connection at all to the paper. Consider, for example, the Ph.D. thesis Dysbiosis in Inflammatory Bowel Disease, where Barzel-Barabási, as well as the Feizi et al. paper which Nicolas Bray and I also reviewed, are cited as follows:

The Ribosomal Database Project (RDP) is a web resource of curated reference sequences of bacterial, archeal, and fungal rRNAs. This service also facilitates the data analysis by providing the tools to build rRNA-derived phylogenetic trees, as well as aligned and annotated rRNA sequences (Barzel and Barabasi 2013; Feizi, Marbach et al. 2013).

(Neither papers has anything to do with building rRNA-derived phylogenetic trees or aligning rRNA sequences).

While this was probably an accidental error, some of the drive by citations were more sinister. For example, WenJun Zhang is an author who has cited Barzel-Barabási as

We may use an incomplete network to predict missing interactions (links) (Clauset et al., 2008; Guimera and Sales-Pardo, 2009; Barzel and Barabási, 2013; Lü et al., 2015; Zhang, 2015d, 2016a, 2016d; Zhang and Li, 2015).

in exactly the same way in three papers titled Network Informatics: A new science, Network pharmacology: A further description and Network toxicology: a new science. In fact this author has cited the work in exactly the same way in several other papers which appear to be copies of each other for a total of 7 citations all of which are placed in dubious “papers”. I suppose one may call this sort of thing hit and run citation.

I also found among the 95 citations one paper strongly criticizing the Barzel-Barabási paper in a letter to Nature Biotechnology (the title is Silence on the relevant literature and errors in implementation) , as well as the (to me unintelligible) response by the authors.

In any case, after carefully examining each of the 95 references citing Barzel and Barabási I was able to find only one paper that actually applied global silencing to biological data, and two others that benchmarked it. There are other ways a paper could impact derivative work, for example by virtue of the models or mathematics developed, be of use, but I could not find any other instance where Barzel and Barabási’s work was used meaningfully other than the three citations just mentioned.

When a citation is a citation

As mentioned, two papers have benchmarked global silencing (and also network deconvolution, from Feizi et al.). One was a paper by Nie et al. on Minimum Partial Correlation: An Accurate and Parameter-Free Measure of Functional Connectivity in fMRI. Table 1 from the paper shows the results of global silencing, network deconvolution and other methods on a series of simulations using the measure of c-sensitivity for accuracy:

Table 1 from Nie et al. showing performance of methods for “network cleanup”.

EPC is the “Elastic PC-algorithm” developed by the authors, which they argue is the best method. Interestingly, however, global silencing (GS) is equal to or worse than simply choosing the top entries from the partial correlation matrix (FP) in 19/28 cases- that’s 67% of the time! This is consistent with the results we published in Bray & Pachter 2013. In these simulations network deconvolution performs better than partial correlation, but still only 2/3 of the time. However in another benchmark of global silencing and network deconvolution published by Izadi et al. 2016 (A comparative analytical assay of gene regulatory networks inferred using microarray and RNA-seq datasets) network deconvolution underperformed global silencing. Also network deconvolution was examined in the paper Graph reconstruction Using covariance-based methods by Sulaimanov and Koeppl 2016 who show, with specific examples, that the scaling parameter we criticized in Bray & Pachter 2013 is indeed problematic:

The scaling parameter α is introduced in [Feizi et al. 2013] to improve network deconvolution. However, we show with simple examples that particular choices for α can lead to unwanted elimination of direct edges.

It’s therefore difficult to decide which is worse, network deconvolution or global silencing, however in either case it’s fair to consider the two papers that actually tested global silencing as legitimately citing the paper the method was described in.

The single paper I found that used global silencing to analyze a biological network for biological purposes is A Transcriptional and Metabolic Framework for Secondary Wall Formation in Arabidopsis by Li et al. in Plant Physiology, 2016. In fact the paper combined the results of network deconvolution and global silencing as follows:

First, for the given data set, we calculated the Pearson correlation coefficients matrix Sg×g. Given g1 regulators and g2 nonregulators, with g = g1+g2, the correlation matrix can be modified as

where O denotes the zero matrix, to include biological roles (TF and non-TF genes). We extracted the regulatory genes (TFs) from different databases, such as AGRIS (Palaniswamy et al., 2006), PlnTFDB (Pérez-Rodríguez et al., 2010), and DATF (Guo et al., 2005). We then applied the network deconvolution and global silencing methods to the modified correlation matrix S′. However, global silencing depends on finding the inverse of the correlation matrix that is rank deficient in the case p » n, where p is the number of genes and n is the number of features, as with the data analyzed here. Since finding an inverse for a rank-deficient matrix is an ill-posed problem, we resolved it by adding a noise term that renders the matrix positive definite. We then selected the best result, with respect to a match with experimentally verified regulatory interactions, from 10 runs of the procedure as a final outcome. The resulting distribution of weighted matrices for the regulatory interactions obtained by each method was decomposed into the mixture of two Gaussian distributions, and the value at which the two distributions intersect was taken as a cutoff for filtering the resulting interaction weight matrices. The latter was conducted to avoid arbitrary selection of a threshold value and prompted by the bimodality of the regulatory interaction weight matrices resulting from these methods. Finally, the gene regulatory network is attained by taking the shared regulatory interactions between the resulting filtered regulatory interactions obtained by the two approaches. The edges were rescored based on the geometric mean of the scores obtained by the two approaches.

In light of the benchmarks of global silencing and network deconvolution, and in the absence of analysis of the ad hoc method combining their results, it is difficult to believe that this methodology resulted in a meaningful network. However its citation of the relevant papers is certainly legitimate. Still, the results of the paper, which constitute a crude analysis of the resulting networks, are a far cry from revealing the “precise wiring diagram of the system”. The authors acknowledge this writing

From the cluster-based networks, it is clear that a wide variety of ontology terms are associated with each network, and it is difficult to directly associate a distinct process with a certain transcript profile.

The factor of use correction

The analysis of the Barzel and Barabási citations suggests that, because a citation is not always a citation (thanks to Nicolas Bray for suggesting the title for the post), to reflect the ultimate impact of a paper the quantity $c^{\infty}$ needs to be adjusted. I propose adjustment by the factor

$f^u = \frac{C-d_b}{C},$

where C is the total number of citations of a paper and $d_b$ is the number of drive by citations. The fraction $\frac{d_b}{C}$ is essentially a factor of use correction. It should be possible (and interesting) to develop text analytics algorithms for estimating $d_b$ so as to be able to correct $c^{\infty}$ to  $f^u \cdot c^{\infty}$, and similarly adjusting citations counts, h-indices, impact factors of journals and related metrics. Explicit computation and publication of the factor of use correction for papers would also incentivize authors to reduce or eliminate gratuitous drive by citation practices.

For now I decided to compute the factor of use correction for the Barzel-Barabási paper by generously estimating that $d_b=92$. This yielded $f^u = \frac{3}{95} = 0.0315$. Barabási has an h-index of 117, but applying this factor of use correction to all of his published papers I obtained the result that Barabasi’s factor of use corrected h-index is 30.