It has been a while since my last post on manifold learning, and I still have some things to speak about (unfortunately, it will be the end post of the dimensionality reduction series on my blog, as my current job is not about this anymore). After the multidimensional regression, it is possible to use it to project new samples on the modelized manifold, and to classify data.
I hope to present here some result in February, but I’ll expose what I’ve implemented so far :
- Laplacian Eigenmaps
- Hessian Eigenmaps
- Diffusion Maps (in fact a variation of Laplacian Eigenmaps)
- Curvilinear Component Analysis (the reduction part)
- NonLinear Mapping (Sammon)
- My own technique (reduction, regression and projection)
- PCA (usual reduction, but robust projection with an a priori term)
The results I will show here are mainly reduction comparison between the techniques, knowing that each technique has a specific field of application : LLE is not made to respect the geodesic distances, Isomap, NLM and my technique are.
As I approach the end of my PhD, I will propose my manifold learning code in a scikit (see this page) in a few weeks. For the moment, I don’t know which scikit will be used, but stay put…
The content of the scikit will be :
- Laplacian eigenmaps
- Diffusion maps