Ajinkya Borle

Nicholas R. Allgood, Ajinkya Borle, Charles K. Nicholas

Prototype-based clustering algorithms such as k-means are sensitive to the selection of initial cluster centroids, with poor initialization leading to slower convergence and suboptimal solutions trapped in local minima. We present Adaptive Quantum Optimized Centroid Initialization (AQOCI), a method that formulates the centroid initialization problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solves it using quantum annealing or quantum-inspired solvers. AQOCI extends a prior method (QOCI) by introducing an iterative refinement mechanism inspired by the Gauss-Seidel and Jacobi methods, enabling the recovery of real-valued centroid coordinates from binary solver outputs through adaptive scaling and offset adjustments. We evaluate AQOCI using three solver backends: TABU search, simulated annealing, and D-Wave's HybridBQM on synthetic Gaussian data with controlled sweeps over cluster separation, cluster count, dimensionality, and sample size, as well as on the MOTIF malware classification dataset, comparing against standard k-means with random initialization and k-means++ initialization. On the MOTIF dataset, AQOCI produces clusterings that are competitive with and, at smaller sample sizes, superior to k-means++, with V-measure improvements of up to 26\%. On synthetic data with heavily overlapping clusters, AQOCI--SimAnn outperforms k-means++ in V-measure. On well-separated synthetic data, k-means++ is clearly superior, and AQOCI exhibits a consistent performance plateau attributable to the binary encoding resolution. The dimensionality sweep demonstrates scalability to at least $d = 10$ without degradation.

Ajinkya Borle, Charles Nicholas, Uchenna Chukwu et al.

Non-negative matrix factorization (NMF) is a matrix decomposition problem with applications in unsupervised learning. The general form of this problem (along with many of its variants) is NP-hard in nature. In our work, we explore how this problem could be solved with an energy-based optimization method suitable for certain machines with non-von Neumann architectures. We used the Dirac-3, a device based on the entropy computing paradigm and made by Quantum Computing Inc., to evaluate our approach. Our formulations consist of (i) a quadratic unconstrained binary optimization model (QUBO, suitable for Ising machines) and a quartic formulation that allows for real-valued and integer variables (suitable for machines like the Dirac-3). Although current devices cannot solve large NMF problems, the results of our preliminary experiments are promising enough to warrant further research. For non-negative real matrices, we observed that a fusion approach of first using Dirac-3 and then feeding its results as the initial factor matrices to Scikit-learn's NMF procedure outperforms Scikit-learn's NMF procedure on its own, with default parameters in terms of the error in the reconstructed matrices. For our experiments on non-negative integer matrices, we compared the Dirac-3 device to Google's CP-SAT solver (inside the Or-Tools package) and found that for serial processing, Dirac-3 outperforms CP-SAT in a majority of the cases. We believe that future work in this area might be able to identify domains and variants of the problem where entropy computing (and other non-von Neumann architectures) could offer a clear advantage.

Radhakrishnan Balu, Ajinkya Borle

We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a directed acyclic graph (DAG) and the associated joint probability distribution of the nodes consistent with a given dataset. This is a combinatorial problem of structural learning of the underlying graph, starting from a single node and building one arc at a time, that fits a given ensemble using maximum likelihood estimators (MLE). It is cast as an optimization problem that consists of a scoring step performed on a classical computer, penalties for acyclicity and number of parents allowed constraints, and a search step implemented using a quantum annealer. We have assumed uniform priors in deriving the Bayesian network that can be relaxed by formulating the problem as an estimation Dirichlet parameters. We demonstrate the utility of the framework by applying to the problem of elucidating the gene regulatory network for the MAPK/Raf pathway in human T-cells using proteomics data where the concentration of proteins, nodes of the BN, are interpreted as probabilities.