If you want to put UF identities (e.g. logo, template, color, font, etc.) on your presentation slides, businesscard, website, etc., you can find everything in the “UF Identity” – http://identity.ufl.edu/ and more specifically “signature system” – http://identity.ufl.edu/signatureSystem/
I intend to collect some interesting article discussing about the relationship between music and mathematics. There are a lot of things we can do with music via mathematics. Here are some great examples
Music theory: Geometrical music theory [link]
by Rachel Wells Hall
Generalized Voice-Leading Spaces [link]
by Clifton Callender, Ian Quinn, Dmitri Tymoczko
SOM is a method to reduce dimensionality of data/feature which is useful for data visualization, and learning on manifold. Here are some references.
- SOM on Wikipedia [link]
- SOM on Scholar pedia [link]
- There are some recommended books in the website
- SOM website [link] by Prof. Kohonen himself
- SOM MATLAB toolbox [link]
- SOM book [link] by Prof. Kohonen
- Neural Networks – A Systematic Introduction [e-book] by Raul Rojas also contains a chapter on Kohonen map.
I heard from Dr. Jose Principe (after we were back from WSOM2009 in St. Augustine) that even though SOM works well in practice, there have been nobody completely understand how SOM work yet. This might be a motivation for you to figure out!
It might be helpful if we build a bridge between SOM and other popular dimensionality reduction method like LLE, ISOMAP, MDS or even PCA. There might be something there that helps you understand SOM better.
The basic idea of MDL is about the minimum length of code or symbol used to represent an entity. There are so many applications that MDL is applicable to. For example, model selection, data/signal compression, structure learning, curve fitting, etc. Good references for a beginner are:
- MDL in Wiki [link]
- MDL on Scholarpedia [link]
- MDL on the web [link]
- You can find good tutorials there. I would recommend the tutorial “P.Grünwald, A tutorial introduction to the minimum description length principle. In: Advances in Minimum Description Length: Theory and Applications (edited by P. Grünwald, I.J. Myung, M. Pitt), MIT Press, 2005 (80 pages).”
- MDL tutorial by Prof. Rissanen “An Introduction to the MDL Principle” [pdf]
MDL has a strong connection with Kolmogorov Complexity. In terms of model selectin there might be some other topics that you may find interesting to make connection with MDL, for example, BIC, AIC and NML.
There are so many possible ways to learn the causality in a particular dataset. However, I think SOM is also an alternative…I will investigate this!
Also in autoregressive community, Granger causality plays quite an important role in time-series causal structure learning. There might be some connections between this Granger causality and other standard structure learnign algorithm in BN community.
One big problem for structure learning is the complexity of the data. Most of the time we would like to have the simplest model that works well for the dataset according to Occam’s razor. So we would like to have a function that penalizes the complexity. This problem is also referred as “model selection” problem. There are a lot of model selection criteria that I would like to investigate in order to use with Bayesian network structure learning. Here are some possible criteria:
AIC, BIC, CIC, MDL, NML, factorized NML