Discussion on Clustering algorithm (K-means)

The purpose of the Clustering algorithm (K-means) is to divide n objects into K different clusters according to their respective attributes, so that the similarity degree of each object in the cluster is as high as possible, and the similarity between the clusters is as small as possible.

And how to evaluate the similarity , The criterion function used is the sum of squared errors (and therefore called K-means algorithm):

where e is the squared error of all objects in the dataset and P is the point in the space representing the given object, MI is the mean value of the cluster CI. In fact, E represents the sum of the distances of all objects to the center of their own cluster. For different clusters, the size of E is definitely not the same, so the minimum clustering of E is the optimal result under the squared error and the criterion.

There are several options for choosing a representative point:

(1) Experience. Based on the nature of the problem, the empirical method is used to determine the number of categories, from the data to find out from the intuitive point of view more appropriate representation.

(2) Randomly dividing all the data into K classes, calculating the centers of each class, and the points as the representative points of each class.

(3) "Density" selection method. This method of thinking is still quite ingenious. First, each sample is a spherical ring, with a positive number a as a radius circle, the sample count is circled in the "density" of the sample point of the globe. Find the "density" of the largest sample point as the first class of the representative point. Then start selecting the second type of Representative point, and you cannot directly select the "density" sub-large representation point, because the second largest representative point is likely to be near the first representative point. A positive number B can be specified, and the "density" sub-large representation point is selected outside of the first representative point as the representative point for the second class, and the remaining representative points are followed by this principle.

(4) Use K sample as the representative point.

(5) The method of generating the representative point of K cluster partition problem by using K-1 clustering problem is introduced. The idea is to think of all the data as a cluster, the representative point is the mean of all samples, and then determine the two clustering problem of the representative point is a cluster problem divided by the total mean and farthest from its representative point. The rest and so on.

Discussion on Clustering algorithm (K-means)