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And GARSON, A. (1978): Mathematical typology: A Grade of Membership technique for obtaining disease deﬁnition. Computers and Biomedical Research, 11, 277–298. Predicting Protein Secondary Structure with Markov Models Paul Fischer, Simon Larsen, and Claus Thomsen Informatics and Mathematical Modelling Technical University of Denmark DK-2800 Kongens Lyngby Abstract. The primary structure of a protein is the sequence of its amino acids. The secondary structure describes structural properties of the molecule such as which parts of it form sheets, helices or coils.
We employ the mean of this Dirichlet as an estimate of the “weight” of the document on each aspect. 0255. This estimated Dirichlet, which is the generative distribution of membership scores, is “bathtub shaped” on the simplex; as a result, articles will tend to have relatively high membership scores in only a few aspects. To summarize the aspect distributions for each topic, we provide a graphical representation of these values for K = 8 and K = 10 in Figure 1 and Figure 2, respectively. Examining the rows of Figure 1, we see that, with the exception of Evolution and Immunology, the subtopics in Biological Sciences are concentrated on more than one internal category.
2004) and Griﬃths and Styvers (2004) have used mixed membership models to analyse related data bases involving abstracts, text, and references of articles drawn from the Proceedings of the National Academy of Sciences U S A (PNAS). Their mutual goal was to understand the organization of scientiﬁc publications in PNAS and we explore the similarities and diﬀerences between their approaches and results later in Section 4. What these examples have in common is the mixed membership structure. In the following sections, we ﬁrst introduce our general framework for mixed membership models and then we illustrate its application in two of the examples, using the PNAS and NLTCS data sets.