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arXiv:1706.05528

Adiabatic Quantum Computing for Binary Clustering

Christian Bauckhage, Eduardo Barreto Brito, Kostadin Cvejoski, César Ojeda, Rafet Sifa, Stefan Wrobel

Published Jun 17, 2017• 4 citations
arXivHTMLPDF

Abstract

Quantum computing for machine learning attracts increasing attention and recent technological developments suggest that especially adiabatic quantum computing may soon be of practical interest. In this paper, we therefore consider this paradigm and discuss how to adopt it to the problem of binary clustering. Numerical simulations demonstrate the feasibility of our approach and illustrate how systems of qubits adiabatically evolve towards a solution.

DOI
10.48550/arxiv.1706.05528

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We study the problem of supervised binary classification from the perspective of deploying adiabatic quantum optimization in training. A vast body of prior academic work consisting of both theoretical and numerical studies has indicated that quantum technology promises to provide computational power that may be fundamentally superior to any classical computing methods. Given the abundance of NP-hard optimization problems that naturally arise in learning, it is clear that machine learning can immensely benefit from such an optimization tool. We describe a series of increasingly complex designs that result in computationally hard training problems of combinatorial nature. In return for accepting classical computational hardness, we retain theoretical properties such as maximal sparsity and robustness to label noise, which are otherwise sacrificed by convex methods for the sake of computational efficiency and sound theoretical footing. In order to be compatible with emerging quantum hardware technology, we formalize the training problem as quadratic unconstrained binary optimization. Our initial investigations focus on a simple training formulation with non-convex regularization that conforms to the architecture of existing quantum hardware and makes frugal use of a limited number of available physical qubits. Next, we extend this baseline formulation to a scalable algorithm, QBoost, which is able to train incrementally large-scale classifiers on data sets of practical interest. Further, we derive another algorithm, TotalQBoost, as a theoretically motivated totally corrective boosting algorithm with cardinality penalization that also makes use of quantum optimization. Both QBoost and TotalQBoost perform explicit cardinality regularization, which is the only known way of achieving maximal sparsity in the trained classifiers. We apply QBoost and TotalQBoost to three different real-world computer vision problems and make use of a quantum processor for solving the sequence of discrete optimization problems generated by one of them. Finally, we study a learning formulation with convex regularization and a non-convex loss function, q-loss, specifically designed for robust supervised learning in the presence of label noise as it occurs in practice. For compatibility with quantum hardware we derive the corresponding quadratic binary problem via variational approximation. For all proposed algorithms we compare results on a variety of popular synthetic and natural data sets against a rich selection of existing rival learning formulations.
Subtrajectory clustering is vital for real-world applications such as traffic bottleneck detection, public transportation optimization, and play pattern discovery in sports analytics. This problem is NP-hard and computationally intensive for largescale applications, and many existing classical implementations struggle with scalability and generalizability. While machine learning-based approaches allow for greater generalizability than existing rule-based methods, they still struggle with scalability. Quantum computing has shown promising performance improvements over classical computing for some machine learning tasks on regular point data. However, no research has been done on whether quantum computing can also offer improvements over classical computing for subtrajectory clustering. If that is the case, combining quantum computing with machine learning may enable solutions that are both scalable and generalizable. This paper discusses the drawbacks of current subtrajectory clustering approaches within the classical computing paradigm, the challenges associated with solving the problem using quantum computing, and a vision for the conversion of a state-of-the-art classical subtrajectory clustering algorithm to quantum.
Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Recent technological advancements suggest that the adiabatic quantum computing ansatz may soon see practical applications. In this work, we adopt this computation paradigm to develop a quantum computation based solver of the well-known multi-target data association (MTDA) problem, a complex nonlinear integer programming optimization task. The feasibility of the presented model is demonstrated by numerical simulation of the adiabatic evolution of a system of quantum bits towards the optimal solution encoded in the model Hamiltonian.