#### Filter Results:

- Full text PDF available (7)

#### Publication Year

2015

2017

- This year (4)
- Last 5 years (9)
- Last 10 years (9)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn 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: <i>k</i>-means and <i>k</i>-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and (b) they are generic tools… (More)

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

We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei [PW07]. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this output to a hard clustering. We provide a generic method for proving performance guarantees for this algorithm, and… (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 convex relaxations. In this paper, we devise such an algorithm for the problem of k-means clustering. First, we prove that Peng and Wei’s semidefinite relaxation of k-means… (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 distributed throughout R, and then in each ball, n points are drawn according to a common rotationally invariant probability distribution. For any fixed ball configuration… (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. Motivated by applications in shape matching and point-cloud comparison, we study a semidefinite programming relaxation of the Gromov-Hausdorff metric. This… (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 the SDP output as a denoised version of the original data and then rounds this output to a hard clustering. We analyze the performance of this algorithm in the… (More)

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

Many inverse problems are formulated as optimization problems over certain appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems, not only in the worst case, but in an average-complexity sense under this same input distribution. In this note, we are interested… (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 problems (like the study of protein-protein interactions) and it is very closely related to the quadratic assignment problem which has graph isomorphism, traveling salesman… (More)

- Timothy Carson, Dustin G. Mixon, Soledad Villar
- 2017 International Conference on Sampling Theory…
- 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 present numerical simulations of the algorithm using Manopt [5]. An extended version of this article, with further theory and numerical simulations will be available as… (More)

- ‹
- 1
- ›