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- Dustin G. Mixon, Soledad Villar, Rachel Ward
- ArXiv
- 2016

Education 2017 PhD in Mathematics, University of Texas at Austin, United States, Supervisor: Professor Rachel Ward. 2012 Master of Science in Mathematics, Universidad de la RepÃºblica, Montevideo,â€¦ (More)

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: k-means andâ€¦ (More)

- Takayuki Iguchi, Dustin G. Mixon, Jesse Peterson, Soledad Villar
- ArXiv
- 2015

Recently, [3] introduced an SDP relaxation of the k-means problem in R. In this work, we consider a random model for the data points in which k balls of unit radius are deterministically distributedâ€¦ (More)

- Takayuki Iguchi, Dustin G. Mixon, Jesse Peterson, Soledad Villar
- Math. Program.
- 2017

Recently, Bandeira [5] introduced a new type of algorithm (the so-called probably certifiably correct algorithm) that combines fast solvers with the optimality certificates provided by convexâ€¦ (More)

- Alex Nowak, Soledad Villar, Afonso S. Bandeira, Joan Bruna
- ArXiv
- 2017

2017 PhD in Mathematics, University of Texas at Austin, United States. Supervisor: Rachel Ward Dissertation: Relax, descend and certify: optimization techniques for typically tractable data problemsâ€¦ (More)

The Gromov-Hausdorff distance provides a metric on the set of isometry classes of compact metric spaces. Unfortunately, computing this metric directly is believed to be computationally intractable.â€¦ (More)

- Dustin G. Mixon, Soledad Villar, Rachel Ward
- 2016 IEEE Information Theory Workshop (ITW)
- 2016

We introduce a model-free, parameter-free relax-and-round algorithm for k-means clustering, based on a semidefinite programming relaxation (SDP) due to Peng and Wei [1]. The algorithm interprets theâ€¦ (More)

- Dustin G. Mixon, Soledad Villar
- ArXiv
- 2018

It has been experimentally established that deep neural networks can be used to produce good generative models for real world data. It has also been established that such generative models can beâ€¦ (More)

- Efe Onaran, Soledad Villar
- ArXiv
- 2017

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problemsâ€¦ (More)

- Timothy Carson, Dustin G. Mixon, Soledad Villar
- 2017 International Conference on Sampling Theoryâ€¦
- 2017

We introduce a manifold optimization relaxation for k-means clustering that generalizes spectral clustering. We show how to implement it as gradient descent in a compact manifold. We also presentâ€¦ (More)