Convex Non-negative Matrix Factorization Through Quantum Annealing

In this paper we provide the quantum version of the Convex Non-negative Matrix Factorization algorithm (Convex-NMF) by using the D-wave quantum annealer. More precisely, we use D-wave 2000Q to find the low rank approximation of a fixed real-valued matrix X by the product of two non-negative matrices...

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Published in:2021 IEEE 23rd Int Conf on High Performance Computing & Communications; 7th Int Conf on Data Science & Systems; 19th Int Conf on Smart City; 7th Int Conf on Dependability in Sensor, Cloud & Big Data Systems & Application (HPCC/DSS/SmartCity/DependSys) pp. 1253 - 1258
Main Authors: ZAIOU, Ahmed, MATEI, Basarab, BENNANI, Younes, HIBTI, Mohamed
Format: Conference Proceeding
Language:English
Published: IEEE 01.12.2021
Subjects:
Annealing
Computers
Convex-NMF
D-wave 2000Q
Machine learning algorithms
Quantum annealing
Quantum machine learning
Qubit
QUBO problem
Smart cities
Transforms
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Summary:In this paper we provide the quantum version of the Convex Non-negative Matrix Factorization algorithm (Convex-NMF) by using the D-wave quantum annealer. More precisely, we use D-wave 2000Q to find the low rank approximation of a fixed real-valued matrix X by the product of two non-negative matrices factors W and G such that the Frobenius norm of the difference X - XWG is minimized. In order to solve this optimization problem we proceed in two steps. In the first step we transform the global real optimization problem depending on W, G into two quadratic unconstrained binary optimization problems (QUBO) depending on W and G respectively. In the second step we use an alternative strategy between the two QUBO problems corresponding to W and G to find the global solution. The running of these two QUBO problems on D-wave 2000Q need to use an embedding to the chimera graph of D-wave 2000Q, this embedding is limited by the number of qubits of D-wave 2000Q. We perform a study on the maximum number of real data to be used by our approach on \mathbf{D} -wave 2000Q. The proposed study is based on the number of qubits used to represent each real variable. We also tested our approach on D-Wave 2000Q with several randomly generated data sets to prove that our approach is faster than the classical approach and also to prove that it gets the best results.
DOI:10.1109/HPCC-DSS-SmartCity-DependSys53884.2021.00191