Detecting critical regions in multidimensional data sets. (English) Zbl 1211.57019
Summary: We propose a new approach, based on the Conley index theory, for the detection and classification of critical regions in multidimensional data sets. The use of homology groups makes this method consistent and successful in all dimensions and allows us to generalize visual classification techniques based solely on the notion of connectedness which may fail in higher dimensions.
MSC:
| 57R45 | Singularities of differentiable mappings in differential topology |
| 37B30 | Index theory for dynamical systems, Morse-Conley indices |
Keywords:
scalar fields; critical regions; data exploration; homology; conley index theory; Morse theorySoftware:
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