ML | spectral clustering

Tag: I/O for CTI Re C

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 ction 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.

The idea is to equate clustering with graph, and then clustering becomes the question of how to divide.

Algorithm

Different spectral clustering algorithms use different algorithms to calculate Laplacian matrix.

1. Calculate the similarity Matrix S (similar even edge );
2. Calculate the Laplacian matrix L (a concept in graph theory );
3. Calculate l feature vectors (note that here is the smallest k feature vectors) to form a conversion matrix;
4. Dimensionality Reduction;
5. Clustering; (k-means)

The simplest algorithm

Given a simple graph G with n vertices, its Laplacian Matrix $ L: = (\ ell _ {I, j}) _ {n \ times n} $ is defined:

$ 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.

I plan to sort out the basic algorithms for machine learning because it is a must-have knowledge when a graduate student is looking for a job. However, you cannot remember so many formulas and principles, so you can only remember some key ideas. If you want to learn more details, I believe you can find more on the Internet.