1,721,063 research outputs found
Why Topology for Machine Learning and Knowledge Extraction?
No full textData has shape, and shape is the domain of geometry and in particular of its “free” part, called topology. The aim of this paper is twofold. First, it provides a brief overview of applications of topology to machine learning and knowledge extraction, as well as the motivations thereof. Furthermore, this paper is aimed at promoting cross-talk between the theoretical and applied domains of topology and machine learning research. Such interactions can be beneficial for both the generation of novel theoretical tools and finding cutting-edge practical applications
Range size functions
No full textA 2-parameter family of size functions is introduced, which allows the recognition of planar finite sets up to congruence. Some experiments on digital images are shown
Range size functions
No full textA 2-parameter family of size functions is introduced, which allows the recognition of planar finite sets up to congruence. Some experiments on digital images are shown
The ACAT Project
No full textThis is a presentation of the ACAT Project of the European Science Foundation, gathering 13 national teams, active in Applied and Computational Algebraic Topology
VC-dimension on manifolds: A first approach
No full textVC-dimension is an index of the capacity of a learning machine. It
has been computed in several cases, but always in a Euclidean context.
This paper extends the notion to classifiers acting in the more general environment of a manifold. General properties are proved, and some examples of simple classifiers on elementary manifolds are given. A large part of the research is directed towards a still open problem on product manifolds
Persistent Topology for Natural Data Analysis — A Survey
No full textNatural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, liver and skin lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown
Special section on computational topology in image context
No full textMetodi innovativi per la visione artificiale e la comprensione delle immagin
Symmetric functions for fast image retrieval with persistent homology
Full text linkPersistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certain filtering function. Comparing the persistence diagram of a query with those of a database allows automatic classification or retrieval, but unfortunately, the standard method for comparing persistence diagrams, the bottleneck distance, has a high computational cost. A possible algebraic solution to this problem is to switch to comparisons between the complex polynomials whose roots are the cornerpoints of the persistence diagrams. This strategy allows to reduce the computational cost in a significant way, thereby making persistent homology based applications suitable for large‐scale databases. The definition of new distances in the polynomial framework poses some interesting problems, both of theoretical and practical nature. In this paper, these questions have been addressed by considering possible transformations of the half‐plane where the persistence diagrams lie onto the complex plane, and by considering a certain re‐normalisation the symmetric functions associated with the polynomial roots of the resulting transformed polynomial. The encouraging numerical results, obtained in a dermatology application test, suggest that the proposed method may even improve the achievements obtained by the standard methods using persistence diagrams and the bottleneck distance
Leukocyte classification by size functions
No full textLeukocytes are divided into classes. Their automatic classification is accomplished by means of size functions, based on two measuring functions defined expressly for taking into account the specific morphological features of the cell classes. A successful experimentation on 45 cells is reported. The original contribution resides in the use of this new geometrical-topological technique, size theory, so confirming its suitableness for recognition of natural objects
- …
