Are there any verification methods how good cluster I got?
All of verification methods are 'empirical'.

You can compare the different methods of clusterization and choose the best one.
The correlation comparison methods:
a) If correlation approximately 1. You need to calculate a row's average and median. Next step you compare this two value and drop bads row.
b) If corr are different in whole matrix. Calculate averages for all rows and compare the value and the mean average; choose god one like this 'value > mean(avg)'
I have a task about clusterization in python. When I did this clusterization I need to check the result with business logic.
I dont see the pattern in solved clusters. Next, I decided to do post analysis with correlation. I take one cluster and calculate a correlation pairwise. In calculation I used whole feature unlike a clusterization when I used only 3.
I got a high level of correlation from 0.99 to 1 in whole cluster. For me it means that algorithm watched the logic in cluster.
But, i did this clusterization to solved a problem with banks data (i wont to see the client's pattern like (issued amount > 50.000,age < 22, salary < 80.000 - this client, for instance bad)). And I cant see the business logic, for me it's random data.
With this description I have a question. How can i check the logic in the clusters except a simple self-checking ?
I think there are 2 reasons. First, my clusterization is bad and I need to write a new one. Second, the data is bad and I need to check data and do a post analysis
I did a BIRCH cluster with StandardScaler.