k-means, k-medoids, k-median and k-center 的区别

k-means, k-medoids, k-median and k-center, 先不要晕. 这4个都是聚类算法, 个中区别慢慢讲来.

1. k-means, 这位是最有名的了. 因为简单有效, 通常是聚类的第一选择.
   N data items —- > k clusters
   in each cluster, there is an averaged center (mean) called centroids.
   Object: minimize the sum of squared distance from each item to its nearest averaged center.
   EM algorithm is the most common and simple way to realize it.

2. k-medoids,
   N data items —- > k clusters
   in each cluster, there is a medoid, which is a real data item from the data set (not averaged !!!).
   Object: minimize the sum of squared distance from each item to its nearest medoids.
   Main realization : PAM, CLARA, CLARANS, EM algorithm (like k-means)
   PAM: global optimal, but very slow
   CLARA: use PAM on samples, efficient, not global optimal
   CLARANS: random search, better than CLARA
   EM: very fast, but not global optimal

3. k-median,
   N data items —- > k clusters
   in each cluster, there is a median (median !! not mean or medoids !!).
   Object: minimize the sum of distance from each item to its nearest median (sum of distance !! not sum of squared distance !!).

4. k-center,
   N data items —- > k clusters
   in each cluster, there is a cluster center.
   Object: minimize the maximum distance from each item to its nearest cluster centers (maximum distance !! not sum of distance !!)

5. According to (Bradley NIPS1997),
   k-median is to assign n points in m-dimensional real value space to k clusters so that the sum of distances of each point to the nearest center is minimized. The center is a vector in m-dimensional real value space, but not the one of n points. A center of one cluster is iteratively computed as the median vector of all points in this cluster.
   k-median algorithm uses the same strategy as k-means to update the centers, but it uses the 1-norm distance.
   In contrast the k-means algorithm uses squares of 2-norm distances to generate cluster centers.
   According to (Arya STOC2001), k-median problem is to minimize the average distance from data points to their closest cluster centers. k-center problem is to minimize the maximum distance from data points to their closest cluster centers, which is the min-max analogue of the k-median problem.
   In a general metric space, the k-median problem is known to be NP-hard. Its approximation has been widely studied in (Arya STOC2001, Guha JCSS2002).

转自：http://blog.sina.com.cn/s/blog_68db53590100nttp.html