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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!

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