Gaussian model for closed curves
This work addresses a domain-specific problem in data clustering and pattern detection, particularly for applications requiring closed curve templates, but it appears incremental as it builds on existing Gaussian-based methods.
The paper tackles the problem of modeling clusters as closed curves (e.g., circles, ellipses) in data, which is challenging for Gaussian Mixture Models (GMM) due to their poor adaptation to curved and nonlinear data. It proposes a new probability distribution for closed curves, constructs a mixture of such distributions, and demonstrates effective training for one-dimensional closed curves.
Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of clusters to the complicated shapes defined by the family of functions. But still, it is challenging to model clusters as closed curves (e.g., circles, ellipses, etc.). In this work, we propose a density representation of the closed curve, which can be used to detect the complicated templates in the data. For this purpose, we define a new probability distribution to model closed curves. Then we construct a mixture of such distributions and show that it can be effectively trained in the case of the one-dimensional closed curves.