#Paper reading# x-means:extending K-means with efficient estimation of the number of Clusters_paper

Title: X-means:extending K-means with efficient estimation of the number of clusters
Paper Address: http://cs.uef.fi/~zhao/Courses/Clustering2012/Xmeans.pdf

General contents of the thesis:
Aiming at some disadvantages of K-means, this paper proposes a K-means--x-means clustering algorithm, which can be faster than K-means.

1, K-means has three major disadvantages: ① calculation cost, ②k need artificial designation, ③ easy to lead to local minimization. Therefore, this paper presents a x-means algorithm to solve the problem of ①② and improve the ③ problem.

2. X-means used three improvements: ① used Kd-tree to accelerate each iteration of the original K-means, ② the user to specify the range of K, according to the BIC score Select the optimal K;③ each iteration of the cycle is only 2-means (2-means is not sensitive to local optimal solution). [1]

3, the detailed process of X-means:
The ① starts from a cluster center point;
② to all the current cluster centers, find two relatively distant points of each class as the initial center point, and then run a K-means (k=2) on the current class;
③ calculates the Score (Bic Score) before splitting and splitting the BIC, so as to decide whether to retain the state before the split or after the split;
④ back to ② for iteration, ending if two results (number of center points) are the same.

4, after the experiment, the X-means speed is the enumeration K K-means algorithm 2 to 8 times times, can effectively shorten the computation time.

5, think: Through this article can be seen, there are many times, X-means compared to the violent enumeration of K-means in the K, the result is a little unsatisfactory, but also the efficiency of the algorithm is higher. But if the direct two points to traverse K-means K, that may also be better than the results of X-means, efficiency is high. Therefore, I think when clustering, if the number of classes is relatively small, then the direct enumeration K-value run K-means; If the class number is larger, the binary K value runs K-means, or X-means can try.

6, Expansion: k-means++ algorithm: Because the results of K-means and the initial clustering of the central position has a great relationship, so the k-means++ algorithm is: the initial cluster center between the distance to as far as possible. [2]
Detailed steps are as follows:
① randomly selects a point from the set of input data points as the first cluster center;
② for each point x in the dataset, compute its distance d (x) from the nearest cluster center (meaning the selected cluster center);
③ Select a new data point as the new cluster Center, the principle is: D (x) larger point, the probability of being selected as the center of the cluster is large, the roulette algorithm can be used to select;
④ repeated ② and ③ until K cluster centers were selected;
⑤ uses the K Initial cluster center to run the standard K-means algorithm.

Resources:
1, http://www.cnblogs.com/porco/p/xmeans_intro.html
2, http://www.cnblogs.com/shelocks/archive/2012/12/20/2826787.html

All of the above are personal insights, because my level is limited, if found to have errors and omissions, please point out, thank you.