### Archive

Archive for June, 2009

## UF Logo

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/

Categories: iDea, Labs, Research Tags:

## Modeling Music by Mathematics

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

by Clifton Callender, Ian Quinn, Dmitri Tymoczko

Categories: Uncategorized

## Self-Organizing Maps (SOM)

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 Scholar pedia [link]
• There are some recommended books in the website
• SOM website [link] by Prof. Kohonen himself
• 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.

## Minimum Description Length (MDL)

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:

• There are 2 recommended books in the page:
• The Minimum Description Length Principle (Adaptive Computation and Machine Learning) [link]
• Information and Complexity in Statistical Modeling (Information Science and Statistics) [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.