Adapting k-means for graph clustering

Abstract

We propose two new algorithms for clustering graphs and networks. The first, called K‑algorithm, is derived directly from the k-means algorithm. It applies similar iterative local optimization but without the need to calculate the means. It inherits the properties of k-means clustering in terms of both good local optimization capability and the tendency to get stuck at a local optimum. The second algorithm, called the M-algorithm, gradually improves on the results of the K-algorithm to find new and potentially better local optima. It repeatedly merges and splits random clusters and tunes the results with the K-algorithm. Both algorithms are general in the sense that they can be used with different cost functions. We consider the conductance cost function and also introduce two new cost functions, called inverse internal weight and mean internal weight. According to our experiments, the M-algorithm outperforms eight other state-of-the-art methods. We also perform a case study by analyzing clustering results of a disease co-occurrence network, which demonstrate the usefulness of the algorithms in an important real-life application.

Clustering Diagnoses From 58 Million Patient Visits in Finland Between 2015 and 2018

“…There are several possibilities for measuring the strength of the relationship between 2 diseases ( Table 2 ). These include φ correlation (Pearson correlation) [ 14 , 34 ], co-occurrence correlation [ 49 ], Jaccard coefficient [ 50 ], Yule Q [ 21 , 22 ], Salton cosine index [ 17 ], and multiple variants of RR [ 18 , 19 , 26 ]. For a good review, refer to the study by Srinivasan et al [ 49 ].…”

“…Three cost functions were evaluated in the study by Sieranoja and Fränti [ 26 ] with controlled data— conductance , mean internal weight , and IIW . The last function produced the most accurate clustering result with balanced cluster sizes and was therefore chosen in this study as well.…”

“…This approach scales better as the network is remarkably smaller than the original data (205 nodes vs 58 million patients). K-means itself may require multiple runs [ 25 ] to create accurate clustering; however, we avoided this by using a more robust derivation called the M-algorithm [ 26 ].…”

“…We use a k-means–based algorithm called M-algorithm, which has been shown to provide highly accurate clustering with controlled validation data sets and scaling up to large-scale data [ 26 ].…”

“…We use inverse internal weight (IIW) in the network as a cost function as it has been shown to provide more balanced cluster sizes than other alternatives [ 26 ].…”