Dimensionality reduction of clustered data sets

We present a novel probabilistic latent variable model to perform linear dimensionality reduction on data sets which contain clusters. We prove that the maximum likelihood solution of the model is an unsupervised generalisation of linear discriminant analysis. This provides a completely new approach to one of the most established and widely used classification algorithms. The performance of the model is then demonstrated on a number of real and artificial data sets

A comparative survey of integrated learning systems

This paper presents the duction framework for unifying the three basic forms of inference - deduction, abduction, and induction - by specifying the possible relationships and influences among them in the context of integrated learning. Special assumptive forms of inference are defined that extend the use of these inference methods, and the properties of these forms are explored. A comparison to a related inference-based learning frame work is made. Finally several existing integrated learning programs are examined in the perspective of the duction framework

Existence, Regularity, and Properties of Generalized Apparent Horizons

We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.Comment: 16 pages, thoroughly revised, no major changes, to appear in Comm. Math. Phy

Approximating Clustering of Fingerprint Vectors with Missing Values

The problem of clustering fingerprint vectors is an interesting problem in Computational Biology that has been proposed in (Figureroa et al. 2004). In this paper we show some improvements in closing the gaps between the known lower bounds and upper bounds on the approximability of some variants of the biological problem. Namely we are able to prove that the problem is APX-hard even when each fingerprint contains only two unknown position. Moreover we have studied some variants of the orginal problem, and we give two 2-approximation algorithm for the IECMV and OECMV problems when the number of unknown entries for each vector is at most a constant.Comment: 13 pages, 4 figure

The conjecturing process: perspectives in theory and implications in practice

[Abstract]: In this paper we analyze different types and stages of the conjecturing process. A classification of conjectures is discussed. A variety of problems that could lead to conjectures are considered from the didactical point of view. Results from a number of research studies are used to identify and investigate a number of questions related to the theoretical background of conjecturing as well as practical implications in the learning process