Before revision: The k-means for lines is a set of k centers (points)  that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
After revision: The k-means for lines is a set of k centers (points) that minimizes the sum of squared distances over every line in L and its nearest center . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .