# How to convert cluster information across observations to a meaningful structure?

I have a dataset in which each row corresponds to a a sentence in a financial report. We have a column date containing the publication time of such report. Given a date, I do a clustering whose the number of cluster is $$10$$.

As such, we have such information as

day $$1$$: $$(\mu_1, p_1) \quad (\mu_2, p_2) \quad \cdots (\mu_{10}, p_{10})$$

day $$2$$: $$(\mu_1, p_1) \quad (\mu_2, p_2) \quad \cdots (\mu_{10}, p_{10})$$

$$\cdots$$

day $$n$$: $$(\mu_1, p_1) \quad (\mu_2, p_2) \quad \cdots (\mu_{10}, p_{10})$$

Here:

• $$\mu$$ is the center of the cluster.

• $$p$$ is its weight (usually computed as the proportion of rows that belongs to that cluster).

Given a day, the index of the cluster is just to differentiate them. The cluster $$1$$ in day $$1$$ has nothing to do with cluster $$1$$ in day $$2$$. It's possible that cluster $$1$$ in day $$1$$ is closer to cluster $$2$$ in day $$2$$ than to cluster $$1$$ in day $$2$$. Hence it's naive to put all clusters $$1$$ in a column, all clusters $$2$$ in a column, and so on. Unfortunately, the machine learning model requires a structured input.

I would like to ask for a method (or reference to a method) that takes into account this information permutation. In another word, I'm looking for a meaningful representation of clustering information across days.

Thank you so much!