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I work for a business-to-business company that has a large database of existing clients (small businesses) with various columns of data (e.g., industry, credit-worthiness, financial data, etc) describing each client. There are several marketing data vendors I know of that maintain small-business databases with columns of data similar to what my company has.

Question: Using the data my company already has, how I can I identify which customers in the vendors' databases have the highest potential of becoming a customer if marketed to? Should I build a predictive model? Should I do some sort of clustering?

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The problem is that you only have positive instances (businesses who have become a customer) but no negative instances (businesses who haven't become a customer). This prevents use of supervised learning. You could try unsupervised learning -- e.g., a one-class classifier -- but I don't expect it to be particularly effective.

If you had data on businesses who you tried approaching, but ultimately did not become a customer of yours, then you could try applying supervised learning.

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I think that your problem would be well suited for Decision Tree Classification. The presentation that I linked to should give you a good overview to learn about decision tree models.

This Python tutorial will teach you how to build your own decision tree model from scratch. With this knowledge, and through searching many more decision tree examples online, I'm sure you'll find yourself in a good spot!

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