Supervised Fuzzy Partitioning
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Centroid-based methods including k-means and fuzzy c-means (FCM) are known as effective and easy-to-implement approaches to clustering purposes in many areas of application. However, these algorithms cannot be directly applied to supervised tasks. We propose a generative model extending centroid-based clustering approaches to be applicable to classification and regression problems. Given an arbitrary loss function, our approach, termed supervised fuzzy partitioning (SFP), incorporates labels information into its objective function through a surrogate term penalizing the risk. We also fuzzify the partition and assign weights to features alongside entropy-based regularization terms, enabling the method to capture more complex data structure, to identify significant features, and to yield better performance facing high-dimensional data. An iterative algorithm based on block coordinate descent (BCD) scheme was formulated to efficiently find a local optimizer. The results show that the SFP performance in classification and supervised dimensionality reduction on synthetic and real-world datasets is competitive with state-of-the-art algorithms such as random forest and SVM. Our method has a major advantage over such methods in that it not only leads to a flexible model but also uses the loss function in training phase without compromising computational efficiency.
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