ML | spectral clustering

What's xxx

In multivariate statistics and the clustering of data, spectral clustering techniques make use of the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions. The similarity matrix is provided as an input and consists of a quantitative assessment of the relative similarity of each pair of points in the dataset.

它的思想就是将聚类和图划分等同起来，然后聚类就成了要怎么划分的问题了。

Algorithm

不同的谱聚类算法就是计算Laplacian matrix的算法不一样。

1. 计算相似矩阵S；(相似就连边）；
2. 计算Laplacian矩阵L（是图论里的概念）；
3. 计算L的特征向量（注意这里是最小的k个特征向量）；组成转换矩阵；
4. 降维；
5. 聚类；（k-means）

The simplest algorithm

Given a simple graph G with n vertices, its Laplacian matrix $L:=(ell_{i,j})_{n imes n}$ is defined as:

$L = D - A.$
That is, it is the difference of the degree matrix D and the adjacency matrix A of the graph. In the case of directed graphs, either the indegree or outdegree might be used, depending on the application.

打算整理关于《机器学习》的基础算法，是因为现在研究生找工作的时候机器学习基本是个必考点了，懂一点总是好的。但是那么多公式、原理估计自己也记不住，所以还是只记一些关键的思路。如果想了解更多的细节，我相信网上可以找到更多。