We address the problem of finding representative points of datasets by learning from multiple datasets and their ground-truth summaries. We develop a supervised subset selection framework, based on the facility location utility function, which learns to map datasets to their ground-truth representatives. To do so, we propose to learn representations of data so that the input of transformed data to the facility location recovers their ground-truth representatives. Given the NP-hardness of the utility function, we consider its convex relaxation based on sparse representation and investigate conditions under which the solution of the convex optimization recovers ground-truth representatives of each dataset. We design a loss function whose minimization over the parameters of the data representation network leads to satisfying the theoretical conditions, hence guaranteeing recovering ground-truth summaries. Given the non-convexity of the loss function, we develop an efficient learning scheme that alternates between representation learning by minimizing our proposed loss given the current assignments of points to ground-truth representatives and updating assignments given the current data representation. By experiments on the problem of learning key-steps (subactivities) of instructional videos, we show that our proposed framework improves the state-of-the-art supervised subset selection algorithms.

This paper proposes a sparse convex relation of the facility location utility function for subset selection, for the problem of recovering ground-truth representatives for datasets. This relaxation is used to develop a supervised learning approach for this problem, which involves a learning algorithm that alternatively updates three loss functions (Eq. The supervised facility learning approach described in this paper appears to be novel, and is described clearly. The experimental results are reasonably convincing overall. One weakness is that only one dataset is used, the Breakfast dataset.

The paper presents a supervised facility location based approach to subset selection, i.e., choosing a set of representative points from a new dataset. The paper considers a sparse convex relaxation of the problem and characterizes conditions for getting integral solutions. An alternating algorithm utilizing the integral solutions is presented for learning the subset mapping. Extensive experimental results are presented to illustrate the effectiveness of the proposed approach. The reviewers agree that the paper makes a novel contribution to an important problem and the paper is well written.

We address the problem of finding representative points of datasets by learning from multiple datasets and their ground-truth summaries. We develop a supervised subset selection framework, based on the facility location utility function, which learns to map datasets to their ground-truth representatives. To do so, we propose to learn representations of data so that the input of transformed data to the facility location recovers their ground-truth representatives. Given the NP-hardness of the utility function, we consider its convex relaxation based on sparse representation and investigate conditions under which the solution of the convex optimization recovers ground-truth representatives of each dataset. We design a loss function whose minimization over the parameters of the data representation network leads to satisfying the theoretical conditions, hence guaranteeing recovering ground-truth summaries.

We address the problem of finding representative points of datasets by learning from multiple datasets and their ground-truth summaries. We develop a supervised subset selection framework, based on the facility location utility function, which learns to map datasets to their ground-truth representatives. To do so, we propose to learn representations of data so that the input of transformed data to the facility location recovers their ground-truth representatives. Given the NP-hardness of the utility function, we consider its convex relaxation based on sparse representation and investigate conditions under which the solution of the convex optimization recovers ground-truth representatives of each dataset. We design a loss function whose minimization over the parameters of the data representation network leads to satisfying the theoretical conditions, hence guaranteeing recovering ground-truth summaries.