None of them work very well. You could say: A system based on deep neural networks whose purpose (or the purpose of which ) is to classify text messages into categories. A system based on deep neural networks whose purpose (or the purpose of which ) is to categorize text messages.
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Henox :A system based on deep neural networks whose purpose is to categorize text messages.and this not? :A system based on deep neural networks which purpose is to categorize text messages.Because 'which' does not contain withing itself the genitive/possessive/of idea.