In unsupervised learning, clustering algorithm is of interest. A common clustering algorithm is spectral embedding, where we use eigen vectors of the graph laplacian of similarity matrix to embed points. This can be analogous to the normal modes of vibration system. In this module, we will construct a 1D system with pairwise strength . We will simulate the first few normal modes of the system for different value of . By varying the value of spring stiffness, we will show that the particles connected by strong values tend to vibrate together. Then, we will introduce the clustering problem with given similarity matrix between data points and as . Thus, we just need to let the data points connected by strong similarity to "vibrate" together. We will use the coordinates for the vibration to embed the system. If we want to embed into higher dimensions, we will include more eigen vectors. The coding is not heavy in the module but the math tends to be difficult.
In unsupervised learning, clustering algorithm is of interest. A common clustering algorithm is spectral embedding, where we use eigen vectors of the graph laplacian of similarity matrix to embed points. This can be analogous to the normal modes of vibration system. In this module, we will construct a 1D system with pairwise strength . We will simulate the first few normal modes of the system for different value of . By varying the value of spring stiffness, we will show that the particles connected by strong values tend to vibrate together. Then, we will introduce the clustering problem with given similarity matrix between data points and as . Thus, we just need to let the data points connected by strong similarity to "vibrate" together. We will use the coordinates for the vibration to embed the system. If we want to embed into higher dimensions, we will include more eigen vectors. The coding is not heavy in the module but the math tends to be difficult.