Feature Weighting-Based Deep Fuzzy C-Means for Clustering Incomplete Time Series

Time-series clustering is a crucial unsupervised technique for analyzing data, commonly used in various fields, including medicine and stock analysis. However, in real-world scenarios, time-series data inevitably contain missing values, consequently reducing the efficiency of traditional clustering methods. In incomplete time series, existing clustering methods typically adopt a two-stage strategy, i.e., initially imputing missing values followed by clustering. However, this approach of separating imputation from clustering may lead to inconsistencies in the optimization objectives and increase the complexity of parameter tuning, potentially resulting in unsatisfactory clustering results. This article proposes an end-to-end deep fuzzy clustering (EEDFC) model for incomplete time series, which jointly optimizes imputation and clustering within a unified framework by integrating multiple losses. In the imputation part, an attention mechanism is integrated to tackle challenges associated with dependencies in extended sequences. In addition, an adversarial strategy is introduced to enhance the encoder's imputation and feature representation learning capability, thus reducing the error propagation from imputation to clustering. In the clustering part, EEDFC combines a feature weighting-based fuzzy clustering, which considers intracluster compactness and intercluster separateness. Furthermore, exponential distance is adopted, and feature and cluster weighting are also integrated into the Kullback–Leibler divergence loss to improve clustering performance. We conduct extensive experiments comparing our proposed model with eleven other methods across ten benchmark datasets. The experimental results demonstrate that our proposed model performs better than eleven comparative methods.