Leveraging Sparsity for Efficient Submodular Data Summarization
This work addresses scalability issues in data summarization for applications like sensor placement and image retrieval, though it is incremental as it builds on existing sparsification techniques.
The paper tackles the computational inefficiency of submodular optimization for data summarization by showing that sparsification methods can achieve near-optimal results without strong assumptions, and validates this with rapid generation of interpretable summaries.
The facility location problem is widely used for summarizing large datasets and has additional applications in sensor placement, image retrieval, and clustering. One difficulty of this problem is that submodular optimization algorithms require the calculation of pairwise benefits for all items in the dataset. This is infeasible for large problems, so recent work proposed to only calculate nearest neighbor benefits. One limitation is that several strong assumptions were invoked to obtain provable approximation guarantees. In this paper we establish that these extra assumptions are not necessary---solving the sparsified problem will be almost optimal under the standard assumptions of the problem. We then analyze a different method of sparsification that is a better model for methods such as Locality Sensitive Hashing to accelerate the nearest neighbor computations and extend the use of the problem to a broader family of similarities. We validate our approach by demonstrating that it rapidly generates interpretable summaries.