# Correlation Measures in Metagenomic Data: The Blessing of Dimensionality
## 4 Discussion  
The network analysis framework is a robust tool for enhancing our comprehension of metagenomic studies, enabling us to unravel the intricate dynamics of microbial ecosystems. Although network reconstruction from second-order statistics such as correlation offers a straightforward methodology, the compositional nature of metagenomic data presents  
Figure 4: Impact of Sparsity on Correlation Coefficients in CLR-Transformed Data: (**A**) Heatmap depicting the mean absolute error (MAE) of correlation coefficients across different values of sparsity and correlation strength. (**B,C**) Effect of CLR transformation on negatively correlated OTU pairs from the HMP2 dataset, before (**B**) and after (**C**) transformation. (**D,E**) Same for positively correlated OTU pairs, before (**D**) and after (**E**) CLR transformation. Colored dots indicate zero patterns (black: both non-zero; red: both zero; green/blue: one zero). Linear regression lines are shown to emphasize the direction and strength of the observed association. unique analytical challenges that require specialized techniques. Our study conducts a detailed investigation into the potential biases that affect the accuracy of correlation measures, considering factors such as dimensionality, diversity, and sparsity of datasets, characteristics commonly associated with metagenomics data of any type. Our analysis is focused on the effect of the centered log-ratio (CLR) transformation when applied to compositional data. We initially used synthetic datasets to isolate and systematically study the influence of key parameters such as dimensionality (D), within-sample diversity (Pielou's index), and sparsity (zero counts). These controlled experiments allowed us to disentangle their individual and combined effects on correlation distortions. We then confirmed the main findings on real-world data from Human Microbiome Project 2 (HMP2), showing that the same patterns of spurious correlation behavior observed in synthetic settings persist in practical scenarios. Specifically, we found that the spurious correlations introduced by the CLR transformation decrease as a function of sample dimensionality. This contrasts with the L1 transformation, where spurious correlations are mainly influenced by the diversity within the dataset and do not decrease with sample dimensionality. Given the high dimensionality that characterizes metagenomic datasets--in the order of hundreds or more OTUs or taxa--the spurious correlations associated with CLR thus become negligible, in general, when the commonly adopted assumption of a sparse correlation network is maintained. The CLR transformation is also adequate to remove the effect of diversity for sufficiently high-dimensionality data (in the order of hundreds) without additional adjustments, at difference with L1 transformation for which high diversity remains an issue. To validate the role of the CLR transformation in compositional data analysis, we conducted a comparative study using various algorithms specifically designed to estimate associations in metagenomic datasets. Our findings indicate a striking convergence of SparCC and Rho with Pearson correlation on CLR-transformed data, particularly in high-dimensional settings. This agreement supports the idea that CLR, despite its simplicity, is sufficient to recover robust correlation patterns when dimensionality is high, with more complex corrections (such as those implemented in SparCC) becoming relevant only in low-dimensional contexts. This convergence suggests that the log-ratio transformation is the critical normalizing step across all methods, effectively neutralizing the compositional bias inherent to the data. However, we must also acknowledge the substantial impact of dataset sparsity (i.e., the presence of many species with zero counts in many samples) on correlation measures: the large number of zero counts associated with low-abundance taxa can significantly distort correlations, more severely affecting negative correlations.