Hierarchical Manifold Clustering on Diffusion Maps for Connectomics (MIT 18.S096 final project)

18.S096: Graphs, Diffusion Maps, and Semi-supervised Learning

These are lecture notes not in final form and will be continuously edited and/or corrected (as I am sure it contains many typos). Please let me know if you find any typo/mistake. Also, I am posting short descriptions of these notes (together with the open problems) on my Blog, see [Ban15]. Graphs will be one of the main objects of study through these lectures, it is time to introduce them. Grap...

18.S096: Spectral Clustering and Cheeger’s Inequality

Manifold Learning and Dimensionality Reduction with Diffusion Maps

This report gives an introduction to diffusion maps, some of their underlying theory, as well as their applications in spectral clustering. First, the shortcomings of linear methods such as PCA are shown to motivate the use of graph-based methods. We then explain Locally Linear Embedding [9], Isomap [11] and Laplacian eigenmaps [1], before we give details on diffusion maps and anisotropic diffu...

Unsupervised Shape Clustering using Diffusion Maps

The quotient space of all smooth and connected curves represented by a fixed number of boundary points is a finite-dimensional Riemannian manifold, also known as a shape manifold. This makes the preservation of locality a critically important issue when reducing the dimensionality of shapes on the manifold. We present a completely unsupervised clustering algorithm employing diffusion maps for l...

Hierarchical Clustering Via Localized Diffusion Folders

We present a short introduction to an hierarchical clustering method of high-dimensional data via localized