Reconstruction and Recognition of Spatial Patterns from Sparse Data in the Problem of Biological Invasion

In the modern world of big data there are still a plenty of ecological applications where data available for analysis are extremely sparse because of financial, labour, and other reasons. Accurate reconstruction of spatial patterns from sparse data remains a challenging problem where the results of reconstruction may heavily depend on the sampling protocol. One example is a problem of biological invasion where distinguishing between a patchy spatial density pattern and a continuous front spatial density pattern is crucial for monitoring and control of the invasive species. From the pattern recognition viewpoint, a continuous front density distribution can be classified as a single object, while a `no front' patchy invasion presents a collection of separate objects in a spatial domain. Sensitivity of such classification to the definition of a monitoring protocol remains an open question and will be discussed in the talk. Two basic properties of the monitoring protocol (i.e. the cutoff density value and the number of sampling locations) will be investigated and it will be shown how their variation affects reconstruction of spatial density patterns and recognition of the invasion type.