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Register a new userA Novel Clustering Algorithm Based on Quantum Random Walk
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Qiang Li
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one dimensional QRW. Then, the probability distributions on the positions induced by QRW in these algorithms are investigated, which also indicates the possibility of obtaining better results. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms are of fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.
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We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the preset rules in the modified model. Further, this data point may be also viewed as a local control subsystem, in which the controller adjusts its transition probability vector in terms of the feedbacks of all data points, and then its transition direction is identified by an event-generating function. Finally, the positions of all data points are updated. As they move in space, data points collect gradually and some separating parts emerge among them automatically. As a consequence, data points that belong to the same class are located at a same position, whereas those that belong to different classes are away from one another. Moreover, the experimental results have demonstrated that data points in the test datasets are clustered reasonably and efficiently, and the comparison with other algorithms also provides an indication of the effectiveness of the proposed algorithms.
Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each players expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.
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