A SIMULATED ANNEALING ALGORITHM FOR THE CLUSTERING PROBLEM

In this paper we discuss the solution of the clustering problem usually solved by the K-means algorithm. The problem is known to have local minimum solutions which are usually what the K-means algorithm obtains. The simulated annealing approach for solving optimization problems is described and is proposed for solving the clustering problem. The parameters of the algorithm are discussed in detail and it is shown that the algorithm converges to a global solution of the clustering problem. We also find optimal parameters values for a specific class of data sets and give recommendations on the choice of parameters for general data sets. Finally, advantages and disadvantages of the approach are presented

A SIMULATED ANNEALING ALGORITHM FOR THE CLUSTERING PROBLEM

In this paper we discuss the solution of the clustering problem usually solved by the K-means algorithm. The problem is known to have local minimum solutions which are usually what the K-means algorithm obtains. The simulated annealing approach for solving optimization problems is described and is proposed for solving the clustering problem. The parameters of the algorithm are discussed in detail and it is shown that the algorithm converges to a global solution of the clustering problem. We also find optimal parameters values for a specific class of data sets and give recommendations on the choice of parameters for general data sets. Finally, advantages and disadvantages of the approach are presented

Redistricting using Heuristic-Based Polygonal Clustering

Redistricting is the process of dividing a geographic area into districts or zones. This process has been considered in the past as a problem that is computationally too complex for an automated system to be developed that can produce unbiased plans. In this paper we present a novel method for redistricting a geographic area using a heuristic-based approach for polygonal spatial clustering. While clustering geospatial polygons several complex issues need to be addressed – such as: removing order dependency, clustering all polygons assuming no outliers, and strategically utilizing domain knowledge to guide the clustering process. In order to address these special needs, we have developed the Constrained Polygonal Spatial Clustering (CPSC) algorithm that holistically integrates domain knowledge in the form of cluster-level and instance-level constraints and uses heuristic functions to grow clusters. In order to illustrate the usefulness of our algorithm we have applied it to the problem of formation of unbiased congressional districts. Furthermore, we compare and contrast our algorithm with two other approaches proposed in the literature for redistricting, namely – graph partitioning and simulated annealing

Track clustering with a quantum annealer for primary vertex reconstruction at hadron colliders

Clustering of charged particle tracks along the beam axis is the first step in reconstructing the positions of hadronic interactions, also known as primary vertices, at hadron collider experiments. We use a 2036 qubit D-Wave quantum annealer to perform track clustering in a limited capacity on artificial events where the positions of primary vertices and tracks resemble those measured by the Compact Muon Solenoid experiment at the Large Hadron Collider. The algorithm, which is not a classical-quantum hybrid but relies entirely on quantum annealing, is tested on a variety of event topologies from 2 primary vertices and 10 tracks up to 5 primary vertices and 15 tracks. It is benchmarked against simulated annealing executed on a commercial CPU constrained to the same processor time per anneal as time in the physical annealer, and performance is found to be comparable for small numbers of vertices with an intriguing advantage noted for 2 vertices and 16 tracks