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I would like to ask readers, if you want to group the data in the following figure, you will divide it into clusters? How to divide? The problem of An*lysis, as the name suggests, is to perform grouping actions in Data. The typical problem is roughly the same as the above picture. There are “two groups” in the figure. In addition to the separate methods, there is another extremely difficult problem in Clustering An*lysis, which is to divide into several groups in DATA. For example, the above picture should have two groups, and in the following figures, it should be divided into four groups, one number is a cluster. In addition to the difference in the number of groups, it is obvious that we can feel that the method used to divide the numbers is absolutely very different from the method used to divide the first picture. The two groups of the first picture (Cluster) are simply sorted out. There are two important issues to be considered in the CLUSTERING AN*LYSIS problem: How many groups? is the problem of model selection, and then writes that the model method has There are many, depending on whether the organic rate model is behind, can be divided into model-based or algorithm-based; in addition, you can also follow the most common and simplest and most powerful algorithms in linear or an*lysis. The algorithm is divided into two parts: (1) Finding the point closest to the center of the group (the action of grouping) (2) Taking the center of the first part of the group as the center of the new group. (Animation as follows) Most of these methods have a matching probability model behind them, and when solving, most of them use the Maximal Likelihood Principle to solve the most probable parameters. EM Algorithm is often used as a tool for solving. This method is basically corresponding to k-means. However, the EM Algorithm solution is used here, but the idea of ​​Gaussian's EM Gaussian is roughly as follows. First, at each point, Imagine a random number with a number and then solve for max P (point Position, point number, model parameters). The last such method is the method used when the cluster does not present a circularly symmetric state such as Gaussian. Kernel Trick In the example below, k-mean is used on the left and spectral clustering is used on the right. It can be clearly seen that there is a big difference.