Quantum computing is a promising paradigm that can provide viable solutions to high-complexity problems. The
k-medoids algorithm is a powerful clustering method ubiquitously used in data mining, image processing, pattern recognition, etc. The core of
k-medoids algorithm is to perform cluster assignment and center update, which are time-consuming for large data sets. A\"{\i}meur et al. proposed a quantum
k-medoids algorithm [A\"{\i}meur, Brassard, and Gambs, Mach. Learn. 90, 261 (2013)] by quantizing the center update. Nevertheless, it has a query complexity
O(N3/2) for one iteration, which is computationally expensive for a large
N where
N is the number of points. In this paper, we propose a complete quantum algorithm for
k-medoids algorithm. Specifically, in cluster assignment, we devise a quantum subroutine to calculate the Manhattan distance between any two points and then assign all points to the closest center in parallel, which is faster than what is achievable classically. In center update, for a cluster, we use parallel amplitude estimation to calculate the average distance of each point to all the others. It makes our algorithm polynomially faster than the algorithm of A\"{\i}meur et al., whose sum of distances of each point to all the others is computed by adding the distances one by one. Our quantum
k-medoids algorithm, with time complexity $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{O}({N}^{1/2})$, achieves a polynomial speedup in
N compared to the existing one.
Acquired Immunodeficiency Syndrome (AIDS) caused by the Human Immunodeficiency Virus (HIV) is one of the deadliest infectious diseases in the world. Understanding its spread and epidemiological characteristics is crucial for developing and preventing more effective treatments. This study uses the K-Medoids method with a quantum computing approach to predict AIDS based on clinical and demographic data. K-Medoids is chosen to group large amounts of data using a clustering technique that determines the center point (medoid) of each cluster, minimizing the overall distance between data in a cluster. The Manhattan distance is used because it is easier to process data. The quantum computing approach is used to overcome the limitations of classical computing when processing large-scale medical data. This study shows that the application of quantum algorithms to the K-Medoids method allows for faster and more accurate predictions in the diagnosis of AIDS. The tests carried out showed that the prediction accuracy of classical and quantum methods was comparable, namely 85%. The results support the great potential of quantum computing to improve the efficiency of medical predictions. The research involves converting data into quantum format, processing it with the K-Medoids algorithm, and evaluating its performance based on metrics such as intercluster distance and computation time. The research will also identify patterns and risk factor for the spread of AIDS that can be used to develop more effective health interventions. The conclusion of the research is that integrating the K-Medoids techniques can only increase the speed of data processing but also provide competitive accuracy compared to traditional techniques. This research opens up new possibilities in medical data analysis, especially when managing large and complex data sets. The bottom line is that these findings can help make better medical decisions and strategically support AIDS prevention and treatment efforts.
The low accuracy of anemia diagnosis with the classical K-Medoids method shows the need for alternative, more effective techniques in processing medical record data. This research aims to analyze the effectiveness of the quantum computing approach as a solution to develop an anemia diagnostic method by integrating the K-Medoids algorithm and Manhattan distance calculation. This research is an experimental study with a comparative design. The research subjects comprised anemia patient medical record data covering 5 attributes and 1 target, with 20 samples taken from the Kaggle.com platform. Data collection was conducted using data mining techniques, while the instrument used was computational modeling software. The data was analyzed using the accuracy comparison method between the classical and quantum computing-based K-Medoids methods. The analysis results show that the quantum computing-based K-Medoids method can achieve 80% accuracy, which is equivalent to the classical K-Medoids method, but with higher data processing efficiency. This research confirms that integrating quantum computing in the K-Medoids method can be an alternative in diagnosing anemia, offering the potential for broader application to more complex medical record data. The implication of this research is the creation of opportunities for innovation in quantum computing-based medical decision support systems that are more efficient.