Asymmetric page split generalized index search trees for formal concept analysis

Formal Concept Analysis is an unsupervised machine learning technique that has successfully been applied to document organisation by considering documents as objects and keywords as attributes. The basic algorithms of Formal Concept Analysis then allow an intelligent information retrieval system to cluster documents according to keyword views. This paper investigates the scalability of this idea. In particular we present the results of applying spatial data structures to large datasets in formal concept analysis. Our experiments are motivated by the application of the Formal Concept Analysis idea of a virtual filesystem [11,17,15]. In particular the libferris [1] Semantic File System. This paper presents customizations to an RD-Tree Generalized Index Search Tree based index structure to better support the application of Formal Concept Analysis to large data sources.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.