# Analysis of Gut Microbiome Structure Based on GMPR+Spectrum
###### Abstract  
The gut microbiome is related to many major human diseases, and it is of great significance to study the structure of the gut microbiome under different conditions. Multivariate statistics or pattern recognition methods were often used to identify different structural patterns in gut microbiome data. However, these methods have some limitations. Minimal hepatic encephalopathy (MHE) datasets were taken as an example. Due to the physical lack or insufficient sampling of the gut microbiome in the sequencing process, the microbiome data contains many zeros. Therefore, the geometric mean of pairwise ratios (GMPR) was used to normalize gut microbiome data, then Spectrum was used to analyze the structure of the gut microbiome, and lastly, the structure of core microflora was compared with Network analysis. GMPR calculates the Intraclass correlation coefficient (ICC), whose reproducibility was significantly better than other normalization methods. In addition, running-time, Normalized Mutual Information (NMI), Davies-Boulding Index (DBI), and Calinski-Harabasz index (CH) of GMPR+Spectrum were far superior to other clustering algorithms such as M3C, iClusterPlus. GMPR+Spectrum can not only perform better but also effectively identify the structural differences of intestinal microbiota in different patients and excavate the unique critical bacteria such as _Akkermansia_, and _Lactobacillus_ in MHE patients, which may provide a new reference for the study of the gut microbiome in disease. spectrum; normalization; gut microbiome; minimal hepatic encephalopathy; hepatic encephalopathy +
Footnote †: journal: Medical  
distribution [11]. Normalization is crucial as it aims to correct or reduce bias caused by the sequencing depth and is an essential pre-processing step before any downstream statistical analysis of high-throughput sequencing experiments [12; 13]. Several normalization methods are commonly used for sequencing data, especially for RNA-Seq data [12; 13]. Other popular methods for normalization of microbiome data, besides the size-factor-based methods, such as the geometric mean of pairwise ratios (GMPR), Trimmed mean of M values (TMM), and Relative Log Expression (RLE), are all methods of sparsification. The above methods have disadvantages and advantages in specific applications. Sparsity, for example, leads to discarding most reads and may not be optimal from an information point of view. However, it is still widely used for microbiome data analysis, especially for \(\alpha\) and \(\beta\) diversity analysis. In addition, it suffers from a significant power loss due to the discarding of a large number of reading operations [14]. Instead, size factors can be included as offsets in a count-based parametric model to address the problem of uneven sequencing depth [15]. In comparison, GMPR consistently showed the best level of variability in reducing OTUs at different prevalence levels and increased reproducibility among replicates normalized to the abundance of taxonomic units [16]. In addition, GMPR normalization has been studied for distance-based (weighted) statistical methods such as ranking, clustering, and PERMANOVA based on GMPR-normalized abundance data [17; 18]. Clustering analysis plays an essential role in data mining and has many applications in image processing, data analysis, market research, pattern recognition and other fields [19; 20; 21]. In recent years, spectral clustering has become one of the widely used clustering algorithms [22]. Compared with traditional clustering methods, it is more adaptable to data distribution, especially for data sets with different densities, random complex shapes, and unstable sizes, and the computational effort in clustering is much smaller and less complicated to implement. It is also much less computationally intensive, not very complex to implement, and has higher performance. In contrast, Spectrum [23] used in this paper enhances the similarity between points sharing nearest neighbors using a self-adjusting density-aware kernel.