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The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from scalability issues. As an alternative, we introduce hierarchical optimal transport as a meta-distance between documents, where documents are modeled as distributions over topics, which themselves are modeled as distributions over words. We then solve an optimal transport problem on the smaller topic space to compute a similarity score. We give conditions on the topics under which this construction defines a distance, and we relate it to the word mover's distance. We evaluate our technique for k-NN classification and show better interpretability and scalability with comparable performance to current methods at a fraction of the cost.
Author Information
Mikhail Yurochkin (IBM Research, MIT-IBM Watson AI Lab)
Sebastian Claici (MIT)
Ed Chien (Massachusetts Institute of Technology)
Farzaneh Mirzazadeh (MIT IBM Watson AI Lab)
Justin M Solomon (MIT)
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2019 Poster: Statistical Model Aggregation via Parameter Matching »
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2017 Poster: Parallel Streaming Wasserstein Barycenters »
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2017 Tutorial: A Primer on Optimal Transport »
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2015 Poster: Embedding Inference for Structured Multilabel Prediction »
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