Markov Random Walk Representations with Continuous Distributions
This work addresses the need for incorporating continuous data densities and prior knowledge in clustering and classification tasks, representing an incremental extension of existing discrete methods.
The authors tackled the problem of extending random walk representations from discrete to continuous data distributions by using a diffusion equation with a density-dependent coefficient, relating it to a path integral and deriving a probability measure.
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the data density. We relate this diffusion equation to a path integral and derive the corresponding path probability measure. The framework is useful for incorporating continuous data densities and prior knowledge.