Improving the performance of сlustering with wavelet function by using inequality constraints

Abstract

Clustering methods based on gradient estimation are common in automated control and diagnostic systems, where reliable data processing is needed under noise and multimodality. Their use, however, is constrained by low robustness and high computational costs. Wavelet-based approaches are relevant because they enhance noise immunity and improve efficiency. The purpose of this work is to develop and study a clustering method that employs wavelet functions to introduce constraints and ensure stable performance under noisy conditions. The research included analysis of existing approaches, development of a wavelet-based method with inequality-type second-order constraints, creation of an algorithm for its implementation, and experimental evaluation. The proposed method relies on wavelet transforms with hyperbolic functions, which reduce the number of oracle calls, decrease computational stages, and accelerate convergence in classification and clustering problems. Experiments show that the method shortens the search time for the optimum by about one and a half to seven times at different signal-to-noise ratios, with a moderate increase in error of roughly five to fifteen percent for the De Jong test function. On synthetic datasets, the gain in computation time exceeded one point one compared with the baseline method. In a practical case of reliability assessment for resistors used in critical equipment, efficiency improved by nearly eight percent. Finally, the novelty lies in the clustering method with constraints-inequalities defined by wavelet processing. This can increase the computational speed in conditions of high noise levels, asymmetric objective functions, and small data samples.