FSTruct: An Fst-based tool for measuring ancestry variation in inference of population structure

In model-based inference of population structure from individual-level genetic data, individuals are assigned membership coefficients in a series of statistical clusters generated by clustering algorithms. Distinct patterns of variability in membership coefficients can be produced for different groups of individuals, for example, representing different predefined populations, sampling sites, or time periods. Such variability can be difficult to capture in a single numerical value; membership coefficient vectors are multivariate and potentially incommensurable across groups, as the number of clusters over which individuals are distributed can vary among groups of interest. Further, two groups might share few clusters in common, so that membership coefficient vectors are concentrated on different clusters. We introduce a method for measuring the variability of membership coefficients of individuals in a predefined group, making use of an analogy between variability across individuals in membership coefficient vectors and variation across populations in allele frequency vectors. We show that in a model in which membership coefficient vectors in a population follow a Dirichlet distribution, the measure increases linearly with a parameter describing the variance of a specified component of the membership vector. We apply the approach, which makes use of a normalized Fst statistic, to data on inferred population structure in three example scenarios. We also introduce a bootstrap test for equivalence of two or more groups in their level of membership coefficient variability. Our methods are implemented in the R package FSTruct.

A novel dynamical community detection algorithm based on weighting scheme

Network dynamics plays an important role in analyzing the correlation between the function properties and the topological structure. In this paper, we propose a novel dynamical iteration (DI) algorithm, which incorporates the iterative process of membership vector with weighting scheme, i.e. weighting W and tightness T. These new elements can be used to adjust the link strength and the node compactness for improving the speed and accuracy of community structure detection. To estimate the optimal stop time of iteration, we utilize a new stability measure which is defined as the Markov random walk auto-covariance. We do not need to specify the number of communities in advance. It naturally supports the overlapping communities by associating each node with a membership vector describing the node's involvement in each community. Theoretical analysis and experiments show that the algorithm can uncover communities effectively and efficiently.

A Fast Overlapping Community Detection Algorithm with Self-Correcting Ability

Due to the defects of all kinds of modularity, this paper defines a weighted modularity based on the density and cohesion as the new evaluation measurement. Since the proportion of the overlapping nodes in network is very low, the number of the nodes’ repeat visits can be reduced by signing the vertices with the overlapping attributes. In this paper, we propose three test conditions for overlapping nodes and present a fast overlapping community detection algorithm with self-correcting ability, which is decomposed into two processes. Under the control of overlapping properties, the complexity of the algorithm tends to be approximate linear. And we also give a new understanding on membership vector. Moreover, we improve the bridgeness function which evaluates the extent of overlapping nodes. Finally, we conduct the experiments on three networks with well known community structures and the results verify the feasibility and effectiveness of our algorithm.

CLUSTERING QUALITY MEASURES BASED ON COMPARING THE PROXIMITY MATRICES FOR THE MEMBERSHIP VECTORS AND THE OBJECTS

There are several commonly accepted clustering quality measures (clustering quality as opposed to cluster quality) such as the rand index, the adjusted rand index and the jacquard index. Each of these however is based on comparing the partition produced by the clustering process to a correct partition. They can therefore only be used to determine the quality of a clustering process when the correct partition is known. This paper therefore proposes another clustering quality measure that does not require the comparison to a correct partition. The proposed metric is based on the assumption that the proximities between the membership vectors should correlate positively with the proximities between the objects which may be the proximities between their feature vectors. The values of the components of the membership vector, corresponding to a pattern, are the membership degrees of the pattern in the various clusters. The membership vector is just another object data vector or type of feature vector with the feature values for an object being the membership values of the object in the various clusters. Based on this premise, this paper describes some new cluster quality metrics derived from standard correlation measures and other proposed correlation metrics. Simulations on data with a wide range of clusterability or separability show that the approach of comparing the proximity matrix based on the membership matrix to the object proximity matrix is quite effective.