Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196

Global variation in anastomosis and end colostomy formation following left-sided colorectal resection

Background End colostomy rates following colorectal resection vary across institutions in high-income settings, being influenced by patient, disease, surgeon and system factors. This study aimed to assess global variation in end colostomy rates after left-sided colorectal resection. Methods This study comprised an analysis of GlobalSurg-1 and -2 international, prospective, observational cohort studies (2014, 2016), including consecutive adult patients undergoing elective or emergency left-sided colorectal resection within discrete 2-week windows. Countries were grouped into high-, middle- and low-income tertiles according to the United Nations Human Development Index (HDI). Factors associated with colostomy formation versus primary anastomosis were explored using a multilevel, multivariable logistic regression model. Results In total, 1635 patients from 242 hospitals in 57 countries undergoing left-sided colorectal resection were included: 113 (6·9 per cent) from low-HDI, 254 (15·5 per cent) from middle-HDI and 1268 (77·6 per cent) from high-HDI countries. There was a higher proportion of patients with perforated disease (57·5, 40·9 and 35·4 per cent; P < 0·001) and subsequent use of end colostomy (52·2, 24·8 and 18·9 per cent; P < 0·001) in low- compared with middle- and high-HDI settings. The association with colostomy use in low-HDI settings persisted (odds ratio (OR) 3·20, 95 per cent c.i. 1·35 to 7·57; P = 0·008) after risk adjustment for malignant disease (OR 2·34, 1·65 to 3·32; P < 0·001), emergency surgery (OR 4·08, 2·73 to 6·10; P < 0·001), time to operation at least 48 h (OR 1·99, 1·28 to 3·09; P = 0·002) and disease perforation (OR 4·00, 2·81 to 5·69; P < 0·001). Conclusion Global differences existed in the proportion of patients receiving end stomas after left-sided colorectal resection based on income, which went beyond case mix alone