[Basis of Academic Research] Cluster Analysis and learning

Author: gnuhpc
Source: http://www.cnblogs.com/gnuhpc/

1. What is cluster analysis?

Clustering Analysis, also known as group analysis, is a statistical analysis method used to study Classification Issues (samples or indicators. Clustering Analysis originated from taxonomy. In ancient categorization, people mainly rely on experience and professional knowledge for classification, and seldom use mathematical tools for Quantitative Classification. With the development of Human Science and Technology, the requirements for classification are getting higher and higher, and sometimes it is difficult to accurately classify based on experience and professional knowledge. As a result, people gradually reference mathematical tools to classification, then, the multivariate analysis technology was introduced into the numerical classification to form a clustering analysis.
Clustering definition: a collection of data objects in the same class. Data Objects are similar, and objects in different classes are not similar.
Clustering Analysis definition: a data set is divided into several clusters. clustering is a type of unsupervised classification with no predefined classes.
Typical applications: as an independent tool, pivot data distribution can be used as preprocessing steps for other algorithms.

Clustering Analysis is rich in content, including systematic clustering, ordered sample clustering, dynamic clustering, fuzzy clustering, graph theory clustering, and clustering prediction.

Clustering Analysis has the following calculation methods: partitioning Methods: hierarchicalmethods: density-based method ): grid-based methods: Model-based methods ).
Clustering Algorithm type (hierarchical clustering and non-hierarchical clustering)
Bottom-up and top-down (cohesion and split)
K-means (hard clustering, computing the center of each class)
2. What is a K-means clustering algorithm?

Input: the number of clusters is K, and the database that contains N data objects.
Output: k clusters that meet the minimum variance standard.

Process:
(1) Select K objects from n data objects as the initial cluster center;
(2) cycle (3) to (4) until each clustering does not change
(3) calculate the distance between each object and the central object based on the average value of each clustering object (central object), and re-divide the corresponding objects based on the minimum distance;
(4) recalculate the mean value (central object) of each (changed) Cluster)

The K-means algorithm accepts K input, and then divides n data objects into k clusters to meet the cluster requirements: the object similarity in the same cluster is high; the similarity between objects in different clusters is small. Clustering similarity is calculated by using the mean value of objects in each cluster to obtain a "central object" (gravity center.

K-means
The algorithm is described as follows: First, K objects are randomly selected from n data objects as the initial cluster center, then, based on their similarity (distance) with these Clustering Centers, they are allocated to the most similar (represented by the clustering Center) Clustering respectively; then calculate the clustering center of each new cluster (the mean of all objects in the cluster). repeat this process until the standard measure function starts to converge. The mean variance is generally used as the standard measure function.
K clusters have the following characteristics: each cluster itself is as compact as possible, and each cluster is separated as much as possible.

 

Author: gnuhpc
Source: http://www.cnblogs.com/gnuhpc/