A Category Theoretic Approach to Modeling and Analysis Using Music as a Case Study
Sarala Padi, Spencer J. Breiner, Eswaran Subrahmanian, Ram D. Sriram
The goal of this paper is to provide a category theoretic ontology for the creation of a collaborative platform where it allows group of people to share or use the knowledge in a domain. We use Indian music as a case study to demonstrate the power of Category Theory (CAT) for shared knowledge representation. Traditionally,the use of individual methods from machine learning which are independent from one another,has been the norm in the current analysis of musical patterns. These are typically applied at different levels of granularity, such as raga recognition, singer identification, and album detection. While there has been some effort toward creating an ontology for Carnatic music usingthe ontology language OWL, these approaches have failed to cover the entire ontological space of Carnatic music for modeling. In this paper we use OLOG, a knowledge representation model based on category theory, to create a complete ontology for Carnatic music. Using this ontology, we create a framework which allows us to integrate multiple analytical methods such as HMM, machine learning algorithms and other data mining techniques (clustering, bagging) and to apply theseto a variety of different musical features. The underlying ontological basis of this framework allows us to integrate results from different analytical methods to better analyze the results of different music processing tasks. Furthermore, the framework facilitates the storage of musical performances based on the proposed ontology, making these available for additional analysis and integration. The framework is also extensible, allowing future work in the area of raga recognition to build on our results, thereby facilitating collaborative research. The framework is also intended to be an exemplar for creating a collaborative framework for reproducibility of computational analysis and simulation.