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To qualitative researchers, social media offers a novel opportunity to harvest a massive and diverse range of content without the need for intrusive or intensive data collection procedures. However, performing a qualitative analysis across a massive social media data set is cumbersome and impractical. Instead, researchers often extract a subset of content to analyze, but a framework to facilitate this process is currently lacking. We present a four-phased framework for improving this extraction process, which blends the capacities of data science techniques to compress large data sets into smaller spaces, with the capabilities of qualitative analysis to address research questions. We demonstrate this framework by investigating the topics of Australian Twitter commentary on climate change, using quantitative (non-negative matrix inter-joint factorization; topic alignment) and qualitative (thematic analysis) techniques. Our approach is useful for researchers seeking to perform qualitative analyses of social media, or researchers wanting to supplement their quantitative work with a qualitative analysis of broader social context and meaning.