High-Impact Clustering Feature Selection via Unsupervised Learning and Multinomial Logistic Regression

Abstract

This study proposes a novel clustering algorithm, termed UL-MLR, for identifying high-impact clustering (HIC) features in high-dimensional data. The proposed method integrates classical unsupervised learning (UL) with a new feature selection procedure, ggCGA, within a multinomial logistic regression (MLR) framework. The ggCGA procedure is specifically designed for high-dimensional MLR, and its selection consistency is established under mild conditions. The UL-MLR proceeds iteratively by alternating between two steps: an MLR step, which identifies HIC features via ggCGA using pseudo-labels generated by the UL step, and a UL step, which updates the pseudo-labels using the selected features. Through this recursive refinement, both feature selection and cluster assignments are progressively improved. Simulation studies and real-data applications demonstrate that UL-MLR effectively identifies HIC features and achieves reliable clustering performance in high-dimensional settings. 

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