Algorithmic Composition : Directed Acyclic Graphs

As I collect object-oriented classes to compose my applied research, I am taking a moment to think about the process of algorithmic composition with

• mathematical models
• knowledge based systems
• grammars
• evolutionary methods
• learning systems

Of course, using stochastic processes such as Markov Chains for composition is obvious as well as fractals from L-Systems. Personally, I like the idea of developing grammars for a particular content domain and mixing all approaches with evolutionary methods like genetic algorithms and learning systems like neural networks. Therefore, I am moving toward stochastic context-free grammars(SCFG) involved with speech recognition systems demonstrated in Hierarchical Hidden Markov Models (HMM). Knudsen and Hein (1999) provide a context for RNA prediction with SCFG at http://bioinformatics.oxfordjournals.org/cgi/reprint/15/6/446 . Shokhirev has C++ code and a discussion on HMM at http://www.shokhirev.com/nikolai/abc/alg/hmm/hmm.html .

Of course, all this talk brings us to Directed Acyclic Graphs (DAG). A good, general powerpoint on DAG is at http://www.google.com/search?hl=en&q=Direct+Acyclic+graphs . The Code Project has a discussion on using DAG on SQL databases which is instructive for the construction of ontologies at http://www.codeproject.com/KB/database/Modeling_DAGs_on_SQL_DBs.aspx . Microsoft has a good article on setting up adjacency matrices with DAGS in graph classes and examples for common graph algorithms. The spatial domain can be included with HMM as in the example by http://www.stats.bris.ac.uk/~peter/papers/asatm-01209r1.pdf for Disease Mapping.

An excellent article for estimating High Dimensional DAGs is at http://jmlr.csail.mit.edu/papers/volume8/kalisch07a/kalisch07a.pdf. The authors use the R statistical language in their simulations. Back in 2005, I was looking at using DAG for stream networks and estimating the analyte concentration through sampling as part of a Bayesian MCMC framework for a West Virginia watershed. Thus, a grammar if you will that would serve me well for the algorithmic composition of paintings that extended the work of the Russian painter, Wassily Kandinsky. who stated that

"Of all the arts, abstract painting is the most difficult. It demands that you know how to draw well, that you have a heightened sensitivity for composition and for colors, and that you be a true poet. This last is essential."

More later.