One 、 The principle of spectral clustering

In order to avoid a single point into a class , Add some restrictions  

1.1 Laplace matrix  

Just look at the eigenvector until there are several independent partitions , How many connected domains are there （ Separate areas ） Just how many 0

• Laplace property  

1.2 Cutting area

Minimize the weight sum between the two regions , Take the minimum quantity as the constraint

Solve the eigenvector sorting , The first is connected domain information , The second is supplementary information , Use eigenvectors to form a matrix to K-MEANS clustering . 

The first figure is W matrix , The second is the split matrix

 1.3 Dimensionality reduction understanding

Spectral clustering k*k The matrix of is reduced to k*n

1.4 Mean Shift clustering

The core idea ： A pile of points , How to make a circle with a fixed radius contain as many points as possible . Put the center of the circle in a position coordinate , Calculate the average coordinates of all points included , The center of the circle moves to the average coordinate , Calculate the average coordinates of all points again , repeat , Until the central coordinates of the point are no longer changed . The result is not optimal .

• Clustering steps

You only need to set the radius of the circle , There is no need to set many classes , Automatically discover .（ Mountain climbing thoughts ）

Suppose the classification is ellipse  

 1.5 DBSCAN

The core idea ： water overflows golden hill , Based on point to point connection , As long as it can be connected, it is a kind of

Two 、 Model fitting

Applicable scenario

2.1 least square

Less noise

Least squares is particularly sensitive to noise

•   Enhanced version of least squares

Replace the loss function , It's not linear anymore

Nonlinear solution  （ Similar to neural network ）

2.2 Hough transform （Hough Transform）

The core idea ： The points in the original space are transformed into lines in the parameter space

The coordinate system becomes angular  

• Three parameters  

2.3 RANSAC 

Select two points each time to calculate parameters , Check out supporters , Until the supporters reach a certain threshold .

• N： Calculate how many iterations can calculate a satisfactory fitting

  commonly RANSAC Then we can use the least square to optimize