2,999 research outputs found
Geometrical complexity of data approximators
There are many methods developed to approximate a cloud of vectors embedded
in high-dimensional space by simpler objects: starting from principal points
and linear manifolds to self-organizing maps, neural gas, elastic maps, various
types of principal curves and principal trees, and so on. For each type of
approximators the measure of the approximator complexity was developed too.
These measures are necessary to find the balance between accuracy and
complexity and to define the optimal approximations of a given type. We propose
a measure of complexity (geometrical complexity) which is applicable to
approximators of several types and which allows comparing data approximations
of different types.Comment: 10 pages, 3 figures, minor correction and extensio
Modeling Graph Languages with Grammars Extracted via Tree Decompositions
Work on probabilistic models of natural language tends to focus on strings and trees, but there is increasing interest in more general graph-shaped structures since they seem to be better suited for representing natural language semantics, ontologies, or other varieties of knowledge structures. However, while there are relatively simple approaches to defining generative models over strings and trees, it has proven more challenging for more general graphs. This paper describes a natural generalization of the n-gram to graphs, making use of Hyperedge Replacement Grammars to define generative models of graph languages.9 page(s
Content-based Video Retrieval by Integrating Spatio-Temporal and Stochastic Recognition of Events
As amounts of publicly available video data grow the need to query this data efficiently becomes significant. Consequently content-based retrieval of video data turns out to be a challenging and important problem. We address the specific aspect of inferring semantics automatically from raw video data. In particular, we introduce a new video data model that supports the integrated use of two different approaches for mapping low-level features to high-level concepts. Firstly, the model is extended with a rule-based approach that supports spatio-temporal formalization of high-level concepts, and then with a stochastic approach. Furthermore, results on real tennis video data are presented, demonstrating the validity of both approaches, as well us advantages of their integrated us
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
We present several applications of non-linear data modeling, using principal
manifolds and principal graphs constructed using the metaphor of elasticity
(elastic principal graph approach). These approaches are generalizations of the
Kohonen's self-organizing maps, a class of artificial neural networks. On
several examples we show advantages of using non-linear objects for data
approximation in comparison to the linear ones. We propose four numerical
criteria for comparing linear and non-linear mappings of datasets into the
spaces of lower dimension. The examples are taken from comparative political
science, from analysis of high-throughput data in molecular biology, from
analysis of dynamical systems.Comment: 12 pages, 9 figure
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