In the context of a segmentation solution, a Markov chain can be used to model the progression of time and how the segmentation changes over time. The different states in the Markov chain represent the other segmentation solutions at other points in time. The probabilities of transitioning from one state to another represent the likelihood of the segmentation changing from one key to another.

Lila Oudjoudi Time progression in a segmentation solution based on Markov chains refers to the movement of the system from one state to another through time. In other words, it refers to the time-dependent development of the system's state as dictated by the transition probabilities between the various states.

The Markov chain model presumes that the likelihood of transitioning from the current state to any other state in the system is determined only by the present state and not by any prior states. The Markov property allows the model to reflect the temporal evolution of the system using a transition matrix that defines the probability of changing from one state to another.

The system transitions from one state to another over time depending on the transition probabilities provided by the transition matrix. When fresh observations become available, the transition matrix may be updated over time, allowing the segmentation solution to adapt to changes in the system and increase its accuracy over time.

Overall, temporal progression is a critical component of Markov chain-based segmentation systems because it controls how the system progresses over time and responds to changes in the underlying data.